For many years, the interest at WIAS concerning the modeling of semiconductor devices was focused to classical models like the drift-diffusion model, its analysis and numerical implementation. The model was augmented by including optical fields (laser and photo-voltaic modeling), device temperature (energy models) and other effects.

However, in the last 20 years the typical length scale of semiconductor devices has moved from microns to a few nanometers. This has the consequences that quantum effects become more and more important. Hence for the WIAS this yields the natural task to follow this development in modeling. In particular this means, to move from classical modeling to a quantum mechanical description of semiconductor devices. Since the existing classical models are very successful and since a pure quantum description is in fact impossible one follows the strategy at WIAS, to find models which combine the advantages of classical modeling with the accuracy of quantum description.

Multiscale modeling

Following this hybrid strategy one uses a classical drift-diffusion model in regions, where quantum effects can be neglected, and a quantum description in regions, where quantum effects (for instance tunneling and resonances) are important for the understanding of the physical processes going on. Both descriptions have to be combine in a suitable manner. For the quantum description this leads to the problem to handle open quantum systems which is closely related to the problem of transparent boundary conditions. Typical examples of such semiconductor devices are nanowires (nanowire-transistors, resonant-tunneling diodes etc.), embedded quantum dots, lasers and optoelectronic devices (LEDs, VCSELs, solar cells etc.).

From the mathematical point of view one has to verify the correctness of hybrid models and their solvability. The concept was implemented in 1D for a simple drift-diffusion model without generation and recombination. In view of nanowire devices efforts have been made to carry over the concept from 1D to 2D and 3D. The basic tool for the quantum description is an open Schrödinger-Poisson system. One has to point out that closed Schrödinger-Poisson systems were intensively studied at WIAS in the past. Lasers and optoelectronic devices require to include optical fields into the hybrid modeling which leads to new mathematical challenges.

For optoelectronic devices with optically active nanostructures (quantum wells and dots) multi-species approaches turned out to provide a suitable descriptions of the device behavior. Here, the free charge carriers are described by the classical drift-diffusion model, while the carriers in confined states obey quantum-kinetic models. Currently, at WIAS we pursue the approach to couple the drift-diffusion model to quantum master equations of Lindblad type to describe the embedded open quantum systems. Such hybrid systems allow to model complex devices such as quantum dot lasers or single photon emitters. On the mathematical level the formulation of the governing equations in the form of gradient-flow equations is investigated.

Publications

  Monographs

  • P. Exner, W. König, H. Neidhardt, eds., Mathematical Results in Quantum Mechanics. Proceedings of the QMath12 Conference, World Scientific Publishing, Singapore, 2015, xii+383 pages, (Collection Published).

  • A. Zisowsky, A. Arnold, M. Ehrhardt, Th. Koprucki, Chapter 7: Transient Simulation of k$cdot$p-Schrödinger Systems Using Discrete Transparent Boundary Conditions, in: Multi-Band Effective Mass Approximations -- Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 247--272, (Chapter Published).

  • D. Klindworth, M. Ehrhardt, Th. Koprucki, Chapter 8: Discrete Transparent Boundary Conditions for Multi-band Effective Mass Approximations, in: Multi-Band Effective Mass Approximations -- Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 273--318, (Chapter Published).

  • M. Ehrhardt, Th. Koprucki, eds., Multi-Band Effective Mass Approximations --- Advanced Mathematical Models and Numerical Techniques, 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, xvi+318 pages, (Monograph Published).

  • A. Mielke, Chapter 21: Dissipative Quantum Mechanics Using GENERIC, in: Recent Trends in Dynamical Systems -- Proceedings of a Conference in Honor of Jürgen Scheurle, A. Johann, H.-P. Kruse, F. Rupp, S. Schmitz, eds., 35 of Springer Proceedings in Mathematics & Statistics, Springer, Basel et al., 2013, pp. 555--585, (Chapter Published).
    Abstract
    Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for Non-Equilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradient-flow contribution, which satisfy a particular non-interaction condition. One of our models couples a quantum system to a finite number of heat baths each of which is described by a time-dependent temperature. The dissipation mechanism is modeled via the canonical correlation operator, which is the inverse of the Kubo-Mori metric for density matrices and which is strongly linked to the von Neumann entropy for quantum systems. Thus, one recovers the dissipative double-bracket operators of the Lindblad equations but encounters a correction term for the consistent coupling to the dissipative dynamics. For the finite-dimensional and isothermal case we provide a general existence result and discuss sufficient conditions that guarantee that all solutions converge to the unique thermal equilibrium state. Finally, we compare of our gradient flow formulation for quantum systems with the Wasserstein gradient flow formulation for the Fokker-Planck equation and the entropy gradient flow formulation for reversible Markov chains.

  Articles in Refereed Journals

  • P. Exner, A.S. Kostenko, M.M. Malamud, H. Neidhardt, Infinite quantum graphs, Rossiiskaya Akademiya Nauk. Doklady Akademii Nauk, 472 (2017), pp. 253--258.

  • A. Boitsev, H. Neidhardt, I.Y. Popov, Dirac operator coupled to bosons, Nanosystems: Physics, Chemistry, Mathematics, 7 (2016), pp. 332--339.

  • H. Neidhardt, L. Wilhelm, V. Zagrebnov, A new model for quantum dot light emitting-absorbing devices: Proofs and supplements, Nanosystems: Physics, Chemistry, Mathematics, 6 (2015), pp. 6--45.

  • C. Kreisbeck, L. Mascarenhas, Asymptotic spectral analysis in semiconductor nanowire heterostructures, Applicable Analysis. An International Journal, (published online on June 2, 2014), DOI 10.1080/00036811.2014.919052 .

  • P. Exner, H. Neidhardt, M. Tatar, V. Zagrebnov, Non-equilibrium current via geometric scatterers, Journal of Physics. A. Mathematical and General, 47 (2014), pp. 395301/1--395301/16.

  • H. Neidhardt, L. Wilhelm, V.A. Zagrebnov, A new model of quantum dot light emitting-absorbing devices, Journal of Mathematical Physics, Analysis, Geometry (MAG), 10 (2014), pp. 1--37.
    Abstract
    Motivated by the Jaynes-Cummings (JC) model, we consider here a quantum dot coupled simultaneously to a reservoir of photons and to two electric leads (free-fermion reservoirs). This Jaynes-Cummings-Leads (JCL) model makes possible that the fermion current through the dot creates a photon flux, which describes a light-emitting device. The same model is also describe a transformation of the photon flux into current of fermions, i.e. a quantum dot light-absorbing device. The key tool to obtain these results is an abstract Landauer-Büttiker formula.

  • P.N. Racec, S. Schade, H.-Chr. Kaiser, Eigensolutions of the Wigner--Eisenbud problem for a cylindrical nanowire within finite volume method, Journal of Computational Physics, 252 (2013), pp. 52--64.
    Abstract
    We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostructure features such as double-barriers or quantum dots. The three dimensional Schrödinger operator is reduced to a family of two dimensional Schrödinger operators distinguished by a centrifugal potential. Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. The 1/r singularity is eliminated by approximating r at the vertexes of the Voronoi boxes. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy. This anisotropic discretization yields best accuracy also in the presence of a mildly varying scattering potential, shown exemplarily for a nanowire resonant tunneling diode. For potentials with 1/r singularity one retrieves the theoretically established first order convergence, while the second order convergence is recovered only on uniform grids with an anisotropy correction.

  • J. Giannoulis, A. Mielke, Ch. Sparber, High-frequency averaging in semi-classical Hartree-type equations, Asymptotic Analysis, 70 (2010), pp. 87--100.
    Abstract
    We investigate the asymptotic behavior of solutions to semi-classical Schröodinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a high-frequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras.

  • R. Racec, U. Wulf, P.N. Racec, Fano regime of transport through open quantum dots, Phys. Rev. B., 82 (2010), pp. 085313/1--085313/16.
    Abstract
    We analyze a quantum dot strongly coupled to the conducting leads via quantum point contacts - Fano regime of transport - and report a variety of resonant states which demonstrate the dominance of the interacting resonances in the scattering process in a low confining potential. There are resonant states similar to the eigenstates of the isolated dot, whose widths increase with increasing the coupling strength to the environment, and hybrid resonant states. The last ones are approximatively obtained as a linear combination of eigenstates with the same parity in the lateral direction, and the corresponding resonances show the phenomena of resonance trapping or level repulsion. The existence of the hybrid modes suggests that the open quantum dot behaves in the Fano regime like an artificial molecule.

  • K. Hoke, H.-Chr. Kaiser, J. Rehberg, Analyticity for some operator functions from statistical quantum mechanics, Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics, 10 (2009), pp. 749--771.
    Abstract
    For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain factorizes over the space of essentially bounded functions.

  • P.N. Racec, R. Racec, H. Neidhardt, Evanescent channels and scattering in cylindrical nanowire heterostructures, Phys. Rev. B., 79 (2009), pp. 155305/1--155305/14.
    Abstract
    We investigate the scattering phenomena produced by a general finite range non-separable potential in a multi-channel two-probe cylindrical nanowire heterostructure. The multi-channel current scattering matrix is efficiently computed using the R-matrix formalism extended for cylindrical coordinates. Considering the contribution of the evanescent channels to the scattering matrix, we are able to put in evidence the specific dips in the tunneling coefficient in the case of an attractive potential. The cylindrical symmetry cancels the ”selection rules” known for Cartesian coordinates. If the attractive potential is superposed over a non-uniform potential along the nanowire, then resonant transmission peaks appear. We can characterize them quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances (dips and peaks). Our formalism is applied to a variety of model systems like a quantum dot, a core/shell quantum ring or a double barrier, embedded into the nano-cylinder.

  • H.D. Cornean, H. Neidhardt, V.A. Zagrebnov, The effect of time-dependent coupling on non-equilibrium steady states, Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics, 10 (2009), pp. 61--93.
    Abstract
    Consider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the Landau-Lifschitz and Landauer-Büttiker formulas.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Monotonicity properties of the quantum mechanical particle density: An elementary proof, Monatshefte fur Mathematik, 158 (2009), pp. 179--185.
    Abstract
    An elementary proof of the anti-monotonicity of the quantum mechanical particle density with respect to the potential in the Hamiltonian is given for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included.

  • H. Neidhardt, V.A. Zagrebnov, Linear non-autonomous Cauchy problems and evolution semigroups, Advances in Differential Equations, 14 (2009), pp. 289--340.
    Abstract
    The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomous evolution Cauchy problem of hyperbolic type in separable Banach spaces. The problem is solved using the so-called evolution semigroup approach which reduces the existence problem for propagators to a perturbation problem of semigroup generators. The results are specified to abstract linear non-autonomous evolution equations in Hilbert spaces where the assumption is made that the domains of the quadratic forms associated with the generators are independent of time. Finally, these results are applied to time-dependent Schrödinger operators with moving point interactions in 1D.

  • J.A. Griepentrog, W. Höppner, H.-Chr. Kaiser, J. Rehberg, A bi-Lipschitz continuous, volume preserving map from the unit ball onto a cube, Note di Matematica, 28 (2008), pp. 185--201.
    Abstract
    We construct two bi-Lipschitz, volume preserving maps from Euclidean space onto itself which map the unit ball onto a cylinder and onto a cube, respectively. Moreover, we characterize invariant sets of these mappings.

  • J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering matrices and Weyl functions, Proceedings of the London Mathematical Society. Third Series, 97 (2008), pp. 568--598.
    Abstract
    For a scattering system consisting of two selfadjoint extensions of a symmetric operator A with finite deficiency indices, the scattering matrix and the spectral shift function are calculated in terms of the Weyl function associated with the boundary triplet for A* and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar- and matrix-valued potentials, to Dirac operators and to Schroedinger operators with point interactions.

  • J. Behrndt, H. Neidhardt, R. Racec, P.N. Racec, U. Wulf, On Eisenbud's and Wigner's R-matrix: A general approach, Journal of Differential Equations, 244 (2008), pp. 2545--2577.
    Abstract
    The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's R-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite deficiency indices. In the framework of boundary triplets and associated Weyl functions an abstract generalization of the R-matrix method is developed and the results are applied to Schrödinger operators on the real axis.

  • H. Cornean, K. Hoke, H. Neidhardt, P.N. Racec, J. Rehberg, A Kohn--Sham system at zero temperature, Journal of Physics. A. Mathematical and General, 41 (2008), pp. 385304/1--385304/21.
    Abstract
    An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain $W^1,2$-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.

  • J. Giannoulis, A. Mielke, Ch. Sparber, Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential, Journal of Differential Equations, 245 (2008), pp. 939--963.
    Abstract
    We consider a cubic nonlinear Schrödinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses.

  • R. Haller-Dintelmann, H.-Chr. Kaiser, J. Rehberg, Elliptic model problems including mixed boundary conditions and material heterogeneities, Journal de Mathématiques Pures et Appliquées, 89 (2008), pp. 25--48.

  • J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering theory for open quantum systems with finite rank coupling, Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics, 10 (2007), pp. 313--358.
    Abstract
    Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $[A_D,sH]$, but since $widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $[A(mu)]$ of maximal dissipative operators depending on energy $mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schrödinger-Poisson systems.

  • J. Even, F. Doré, C. Cornet, L. Pedesseau, A. Schliwa, D. Bimberg, Semianalytical evaluation of linear and nonlinear piezoelectric potentials for quantum nanostructures with axial symmetry, Applied Physics Letters, 91 (2007), pp. 122112/1--122112/3.

  • A. Marent, M. Geller, A. Schliwa, D. Feise, K. Pötschke, D. Bimberg, N. Akcay, N. Öncan, 10$^6$ years extrapolated hole storage time in GaSb/AlAs quantum dots, Applied Physics Letters, 91 (2007), pp. 242109/1--242109/3.

  • V. Mlinar, A. Schliwa, D. Bimberg, F.M. Peeters, Theoretical study of electronic and optical properties of inverted GaAs/AlGaAs quantum dots with smoothed interfaces in an external magnetic field, Phys. Rev. B., 75 (2007), pp. 205308/1--205308/9.

  • M. Winkelnkemper, R. Seguin, S. Rodt, A. Schliwa, L. Reimann, A. Strittmatter, A. Hoffmann, D. Bimberg, Polarized emission lines from A- and B-type excitonic complexes in single InGaN/GaN quantum dots, Journal of Applied Physics, 101 (2007), pp. 113708/1--113708/4.

  • U. Wulf, P.N. Racec, E.R. Racec, Admittance of planar two-terminal quantum systems, Phys. Rev. B., 75 (2007), pp. 075320/1--075320/9.

  • J. Elschner, H.-Chr. Kaiser, J. Rehberg, G. Schmidt, $W^1,q$ regularity results for elliptic transmission problems on heterogeneous polyhedra, Mathematical Models & Methods in Applied Sciences, 17 (2007), pp. 593--615.

  • H. Neidhardt, J. Rehberg, Scattering matrix, phase shift, spectral shift and trace formula for one-dimensional Schrödinger-type operators, Integral Equations and Operator Theory, 58 (2007), pp. 407--431.
    Abstract
    The paper is devoted to Schroedinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the Lax-Phillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed, in particular, trace formula and Birman-Krein formula are verified directly. The results are used for dissipative Schroedinger-Poisson systems.

  • P.N. Racec, U. Wulf, Small-signal circuit elements of MIS-type nanostructures, Solid State Phenomena, 121--123 (2007), pp. 549--552.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Classical solutions of quasilinear parabolic systems on two dimensional domains, NoDEA. Nonlinear Differential Equations and Applications, 13 (2006), pp. 287-310.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Convexity of trace functionals and Schrödinger operators, Journal of Functional Analysis, 234 (2006), pp. 45--69.

  • M. Baro, N. Ben Abdallah, P. Degond, A. El Ayyadi, A 1D coupled Schrödinger drift-diffusion model including collisions, Journal of Computational Physics, 203 (2005), pp. 129-153.

  • M. Baro, H. Neidhardt, J. Rehberg, Current coupling of drift-diffusion models and dissipative Schrödinger--Poisson systems: Dissipative hybrid models, SIAM Journal on Mathematical Analysis, 37 (2005), pp. 941--981.

  • TH. Koprucki, M. Baro, U. Bandelow, Th. Tien, F. Weik, J.W. Tomm, M. Grau, M.-Ch. Amann, Electronic structure and optoelectronic properties of strained InAsSb/GaSb multiple quantum wells, Applied Physics Letters, 87 (2005), pp. 181911/1--181911/3.

  • H. Neidhardt, J. Rehberg, Uniqueness for dissipative Schrödinger--Poisson systems, Journal of Mathematical Physics, 46 (2005), pp. 113513/1--113513/28.

  • M. Baro, H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, A quantum transmitting Schrödinger-Poisson system, Reviews in Mathematical Physics. A Journal for Both Review and Original Research Papers in the Field of Mathematical Physics, 16 (2004), pp. 281--330.

  • M. Baro, H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Dissipative Schrödinger--Poisson systems, Journal of Mathematical Physics, 45 (2004), pp. 21--43.

  • M. Baro, H. Neidhardt, Dissipative Schrödinger-type operator as a model for generation and recombination, Journal of Mathematical Physics, 44 (2003), pp. 2373--2401.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Macroscopic current induced boundary conditions for Schrödinger-type operators, Integral Equations and Operator Theory, 45 (2003), pp. 39--63.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, On 1-dimensional dissipative Schrödinger-type operators, their dilations and eigenfunction expansions, Mathematische Nachrichten, 252 (2003), pp. 51--69.

  • H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Density and current of a dissipative Schrödinger operator, Journal of Mathematical Physics, 43 (2002), pp. 5325--5350.

  • P. Exner, H. Neidhardt, V.A. Zagrebnov, Potential approximation to $delta'$: An inverse Klauder phenomenon with norm-resolvent convergence, Communications in Mathematical Physics, 224 (2001), pp. 593--612.

  • U. Bandelow, H.-Chr. Kaiser, Th. Koprucki, J. Rehberg, Spectral properties of $k cdot p$ Schrödinger operators in one space dimension, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 379--409.

  • V.M. Adamyan, H. Neidhardt, On the absolutely continuous subspace for non-selfadjoint operators, , 210 (2000), pp. 5--42.

  • H.-Chr. Kaiser, J. Rehberg, About a stationary Schrödinger-Poisson system with Kohn-Sham potential in a bounded two- or three-dimensional domain, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 41 (2000), pp. 33--72.

  Contributions to Collected Editions

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Multi-scale modelling and simulation of single-photon sources on a device level, in: Euro-TMCS II -- Theory, Modelling & Computational Methods for Semiconductors, 7th -- 9th December 2016, Tyndall National Institute, University College Cork, Ireland, E. O'Reilly, S. Schulz, S. Tomic, eds., Tyndall National Institute, 2016, pp. 65.

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Modeling and numerical simulation of electrically pumped single-photon emitters, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. Yuh-Renn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 151--152.

  • D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, Th. Schröder, G. Capellini, Th. Koprucki, On device concepts for CMOS-compatible edge-emitters based on strained germanium, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. Yuh-Renn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 129--130.

  • G. Capellini, M. Virgilio, Y. Yamamoto, L. Zimmermann, B. Tillack, D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, Th. Koprucki, Th. Schroeder, Modeling of an edge-emitting strained-Ge laser, in: Advanced Solid State Lasers, OSA Technical Digest (online) (Optical Society of America, 2015), 2015, pp. ATu2A.19/1--ATu2A.19/3.
    Abstract
    By using fully-coupled 2D optoelectronic simulations with embedded microscopic gain calculations, we study the optoelectronic performance of a monolithically integrated edge-emitting laser based on strained germanium microstrips fabricated using CMOS standard processes.

  • A. Mielke, On thermodynamical couplings of quantum mechanics and macroscopic systems, in: Mathematical Results in Quantum Mechanics. Proceedings of the QMath12 Conference, P. Exner, W. König, H. Neidhardt, eds., World Scientific Publishing, Singapore, 2015, pp. 331--348.
    Abstract
    Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the Liouville equation for the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradient-flow contribution, which satisfy a particular non-interaction condition:
    formel
    We give three applications of the theory. First, we consider a finite-dimensional quantum system that is coupled to a finite number of simple heat baths, each of which is described by a scalar temperature variable. Second, we model quantum system given by a one-dimensional Schrödinger operator connected to a one-dimensional heat equation on the left and on the right. Finally, we consider thermo-opto-electronics, where the Maxwell-Bloch system of optics is coupled to the energy-drift-diffusion system for semiconductor electronics.

  • A. Glitzky, A. Mielke, L. Recke, M. Wolfrum, S. Yanchuk, D2 -- Mathematics for optoelectronic devices, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 243--256.

  • P.N. Racec, R. Racec, H. Neidhardt, R-matrix formalism for electron scattering in two dimensions with applications to nanostructures with quantum dots, in: Trends in Nanophysics, A. Aldea, V. Bârsan, eds., Engineering Materials, Springer, Berlin/Heidelberg, 2010, pp. 149--174.
    Abstract
    We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the dimensionality of the scattering problem new processes as the scattering between conducting channels and the scattering from conducting to evanescent channels are allowed. For certain values of the energy, called resonance energy, the transmission through the scattering region changes dramatically in comparison with an one-dimensional problem. If the potential has an attractive character even the evanescent channels can be seen as dips of the total transmission. The multi-channel current scattering matrix is determined using its representation in terms of the R-matrix. The resonant transmission peaks are characterized quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances. Our formalism is applied to a quantum dot in a two dimensional electron gas and a conical quantum dot embedded inside a nanowire.

  • J. Behrndt, M.M. Malamud, H. Neidhardt, Finite rank perturbations, scattering matrices and inverse problems, in: Operator Theory in Krein Spaces and Spectral Analysis, J. Behrndt, K.-H. Förster, C. Trunk, H. Winkler, eds., 198 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2009, pp. 61--85.
    Abstract
    In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. The representation results are extended to dissipative scattering systems and an explicit solution of an inverse scattering problem for the Lax-Phillips scattering matrix is presented.

  • J. Behrndt, M. Malamud, H. Neidhardt, Trace formula for dissipative and coupled scattering systems, in: Spectral Theory in Inner Product Spaces and Applications, J. Behrndt, K.-H. Förster, H. Langer, C. Trunk, eds., 188 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2008, pp. 57--93.
    Abstract
    For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.

  • S. Ahmed, M. Usman, C. Heitzinger, R. Rahman, A. Schliwa, G. Klimeck, Symmetry breaking and fine structure splitting in zincblende quantum dots: Atomistic simulations of long-range strain and piezoelectric field, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 849--850.

  • J. Behrndt, H. Neidhardt, J. Rehberg, Block matrices, optical potentials, trace class perturbations and scattering, in: Operator Theory in Inner Product Spaces, K.-H. Förster, P. Jonas, H. Langer, C. Trunk, eds., 175 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2007, pp. 33--49.

  • C. Cornet, M. Hayne, A. Schliwa, F. Doré, C. Labbé, H. Folliot, J. Even, D. Bimberg, Theory and experiment of InAs/InP quantum dots: From calculations to laser emission, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 779--780.

  • F. Doré, C. Cornet, A. Schliwa, N. Bertru, O. Dehaese, I. Alghoraibi, H. Folliot, R. Piron, A. Le Corre, A theoretical and experimental study of $>2 mu$m luminescence of quantum dots on InP substrate, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 889--890.

  • U. Wulf, P.N. Racec, H. Richter, Quantentransport in Nanotransistoren, in: vol. 90 (2007) of Sitzungsberichte der Leibniz-Sozietät, traem fo verlag dr. wolfgang weist, Berlin, pp. 121--137.

  • J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering systems and characteristic functions, in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto, Japan, July 24--28, 2006, pp. 1940--1945.

  • H.-Chr. Kaiser, U. Bandelow, Th. Koprucki, J. Rehberg, Modelling and simulation of strained quantum wells in semiconductor lasers, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 377--390.

  • U. Bandelow, H. Gajewski, H.-Chr. Kaiser, Modeling combined effects of carrier injection, photon dynamics and heating in Strained Multi-Quantum-Well Laser, in: Physics and Simulation of Optoelectronic Devices VIII, R.H. Binder, P. Blood, M. Osinski, eds., 3944 of Proceedings of SPIE, SPIE, Bellingham, WA, 2000, pp. 301--310.

  • H.-Chr. Kaiser, J. Rehberg, About some mathematical questions concerning the embedding of Schrödinger-Poisson systems into the drift-diffusion model of semiconductor devices, in: EQUADIFF 99: International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels, eds., 2, World Scientific, Singapore [u. a.], 2000, pp. 1328--1333.

  Preprints, Reports, Technical Reports

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantum-classical modeling of quantum dot devices, Preprint no. 2412, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2412 .
    Abstract, PDF (5602 kByte)
    The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semi-classical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantum-classical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

  Talks, Poster

  • A. Mielke, Mathematical modeling of semiconductors: From quantum mechanics to devices, CIM-WIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6 - 8, 2017, Centro de Matemática, Lisboa, Portugal.

  • M. Mittnenzweig, Gradient flow structures for quantum master equations, Analysis-Seminar Augsburg-München, Universität Augsburg, Institut für Mathematik, June 8, 2017.

  • M. Kantner, Multi-scale modeling and numerical simulation of single-photon emitters, Matheon Workshop--9th Annual Meeting ``Photonic Devices", Zuse Institut, Berlin, March 3, 2016.

  • M. Kantner, Multi-scale modelling and simulation of single-photon sources on a device level, Euro--TMCS II Theory, Modelling & Computational Methods for Semiconductors, Tyndall National Institute and University College Cork, Cork, Ireland, December 9, 2016.

  • A. Mielke, On entropic gradient structures for classical and quantum Markov processes with detailed balance, Pure Analysis and PDEs Seminar, Imperial College London, Department of Mathematics, UK, May 11, 2016.

  • M. Kantner, Multi-scale modeling and simulation of electrically pumped single-photon sources, International Nano-Optoelectronics Workshop (iNOW 2015), Tokio, Japan, August 3 - 7, 2015.

  • A. Mielke, Geometric approaches at and for theoretical and applied mechanics, Phil Holmes Retirement Celebration, October 8 - 9, 2015, Princeton University, Mechanical and Aerospace Engineering, New York, USA, October 8, 2015.

  • P.N. Racec, Transport in semiconductor nanowires with constrictions: Cylindrical quantum point contact, 3èmes Journées Modélisation et Calcul, March 21 - 22, 2013, Université de Reims Champagne-Ardenne, Laboratoire de Mathématiques, France, March 21, 2013.

  • P.N. Racec, Wigner--Eisenbud problem within finite volume method: application to electronic transport in cylindrical nanowire heterostructures, QMATH12 -- Mathematical Results in Quantum Mechanics, September 10 - 13, 2013, Humboldt-Universität zu Berlin, Berlin, September 12, 2013.

  • A. Mielke, Coupling quantum mechanical systems with dissipative environments via GENERIC, Applied Analysis Seminar, University of Bath, Department of Mathematical Sciences, UK, May 23, 2013.

  • A. Mielke, Entropy-driven dissipative coupling of quantum mechanics to simple heat baths, QMATH12 -- Mathematical Results in Quantum Mechanics, September 10 - 13, 2013, Humboldt-Universität zu Berlin, Berlin, September 10, 2013.

  • A. Mielke, Mathematische und thermodynamische Modellierung von Halbleiterstrukturen, Block-Seminar des SFB 787 ``Nanophotonik'', May 6 - 8, 2013, Technische Universität Berlin, Graal-Müritz, May 8, 2013.

  • A. Mielke, On entropy-driven dissipative quantum mechanical systems, Analysis and Stochastics in Complex Physical Systems, March 20 - 22, 2013, Universität Leipzig, Mathematisches Institut, March 21, 2013.

  • A. Mielke, Thermodynamic modeling of the Maxwell--Bloch and the semiconductor equations via GENERIC, Modeling, Analysis and Simulation of Optical Modes in Photonic Devices (MASOMO 13), April 10 - 12, 2013, WIAS Berlin, April 10, 2013.

  • H. Neidhardt, Boundary triplets and tunnel junction formula with applications, Mathematical Challenge of Quantum Transport in Nanosystems, March 12 - 15, 2013, Saint Petersburg National Research University of Informational Technologies, Mechanics, and Optics, Russian Federation, March 14, 2013.

  • P.N. Racec, Quantum modeling for semiconductor nanowires with embedded subsystems, Interdisciplinary Workshop on Quantum Device -- through Mathematical Structure -- 2013, National Institute of Informatics/Okayama University, Tokyo, Japan, January 15, 2013.

  • A. Mielke, Dissipative quantum mechanics: Geometry meets thermodynamics, Symposium ``Recent Trends in Dynamical Systems'', dedicated to Jürgen Scheurle's 60th birthday, January 11 - 14, 2012, Technische Universität München, Zentrum Mathematik, January 11, 2012.

  • A. Mielke, On consistent couplings of quantum mechanical and dissipative systems, Jahrestagung der Deutschen Mathematiker-Vereinigung (DMV) 2012, Minisymposium ``Dynamical Systems'', September 17 - 20, 2012, Universität des Saarlandes, Fakultät für Mathematik und Informatik, Saarbrücken, September 19, 2012.

  • H. Neidhardt, An application of the Landauer--Büttiker formula to photon emitting and absorbing systems, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24 - 28, 2012, WIAS Berlin, September 28, 2012.

  • H. Neidhardt, Jaynes--Cummings model coupled to leads: A model for LEDs?, Quantum Circle Seminar, Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Doppler Institute for Mathematical Physics and Applied Mathematics, Prague, Czech Republic, March 13, 2012.

  • H. Neidhardt, Landauer--Büttiker formula applied to photon emitting and absorbing systems, Kolloquium ``Mathematische Physik'', December 13 - 14, 2012, Technische Universität Clausthal/Technische Universität Braunschweig, Clausthal-Zellerfeld, December 14, 2012.

  • P.N. Racec, H. Neidhardt, H.-Chr. Kaiser, R. Racec, Electronic quantum transport in semiconductor nanostructures, Fachtagung Leibniz-Nano (1. Nanotechnologie-Workshop der Leibniz-Gemeinschaft), Berlin, January 30 - 31, 2012.

  • P.N. Racec, Fano regime of transport through open quantum dots, Seminar ``Quanteneffekte in Festkörpern'', Leibniz Universität Hannover, Institut für Festkörperphysik, June 13, 2012.

  • P.N. Racec, Finite volume discretization and R-matrix formalism for cylindrical nanowire heterostructures, Seminar Laboratory 30 ``Nanoscale Condensed Matter Laboratory'', National Institute of Materials Physics, Bucharest, Romania, October 9, 2012.

  • P.N. Racec, Optimal finite volume discretization of Schrödinger equations for cylindrical symmetric nanowires, 76. Jahrestagung der DPG und DPG Frühjahrstagung 2012 of the Condensed Matter Section, Sektion ``Semiconductor Physics Division'', Sitzung ``Quanum Dots and Wires: Transport Properties I'', March 26 - 29, 2012, Technische Universität Berlin, March 28, 2012.

  • P.N. Racec, Quantum transport and the R-matrix formalism for cylindrical nanowire heterostructures, Technische Universität Graz, Institut für Theoretische Physik, Austria, September 13, 2012.

  • P.N. Racec, Quantum transport in cylindrical nanowires with constrictions, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Mini-Symposium ``Scattering problems for quantum, electromagnetic, and acoustic waveguides'', September 10 - 14, 2012, Universität Wien, Austria, September 10, 2012.

  • P.N. Racec, Quantum transport in semiconductor nano-heterostructures, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24 - 28, 2012, WIAS Berlin, September 28, 2012.

  • TH. Koprucki, Semi-classical modeling of quantum dot lasers with microscopic treatment of Coulomb scattering, Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems, February 4 - 5, 2011, WIAS, February 4, 2011.

  • A. Mielke, Geometry and thermodynamics for the coupling of quantum mechanics and dissipative systems, Workshop ``Applied Dynamics and Geometric Mechanics'', August 15 - 19, 2011, Mathematisches Forschungsinstitut Oberwolfach, August 16, 2011.

  • P.N. Racec, Efficient simulation of cylindrical nanowire heterostructures by means of the R-matrix formalism, 75. Jahrestagung der DPG und DPG Frühjahrstagung 2011, Sektion ``Semiconductor Physics Division'', Sitzung ``Quantum Wires: Transport'', March 15 - 17, 2011, Technische Universität Dresden, March 16, 2011.

  • L. Wilhelm, An abstract Landauer--Büttiker formula with application to a toy model of a quantum dot LED, Analysis Seminar, Aalborg University, Department of Mathematical Sciences, Denmark, June 16, 2011.

  • L. Wilhelm, An abstract approach to the Landauer--Büttiker formula with application to an LED toy model, Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems, February 4 - 5, 2011, WIAS, February 5, 2011.

  • H. Neidhardt, Comments on the Landauer--Büttiker formula and its applications, Quantum Transport Days, November 14 - 15, 2011, Université Aix-Marseille 2, Centre de Physique Théorique, France, November 14, 2011.

  • H. Neidhardt, Scattering for self-adjoint extensions, Analysis Seminar, Aalborg University, Department of Mathematical Sciences, Denmark, April 22, 2010.

  • H. Neidhardt, Scattering matrices and Weyl function, Research seminar of the Graduate School of Natural Science and Technology, Okayama University, Department of Mathematics, Japan, September 14, 2010.

  • P.N. Racec, Fano regime of transport through open quantum dots, International Workshop ``Advanced Functionality with Three-Dimensionally Controlled Quantum Structures'' within the Strategic Japanese-German Cooperative Program on ``Nanoelectronics'', August 30 - 31, 2010, Paul-Drude-Institut für Festkörperelektronik Berlin, Abteilung ``Semiconductor Spectroscopy'', Potsdam, August 31, 2010.

  • K. Hoke, Hartree solution of the Kohn--Sham system for semiconductor devices, Berlin-Leipzig Seminar on Numerics, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, March 18, 2009.

  • K. Hoke, Iterative solution of the Kohn--Sham system for semiconductor devices, International Conference ``Mathematics of Finite Elements and Applications 2009 (MAFELAP)'', Minisymposium ``Numerical Problems in Density Functional Theory'', June 9 - 12, 2009, The Brunel Institute of Computational Mathematics (BICOM), Uxbridge, UK, June 12, 2009.

  • TH. Koprucki, Spectral properties and band gap estimates for kp Hamiltonians for quantum wells, International Nano-Optoelectronics Workshop (iNOW 2009), Stockholm, Sweden, and Berlin, Germany, August 2 - 15, 2009.

  • P.N. Racec, Evanescent channels and scattering in cylindrical nanowire heterostructures, Spring Meeting of the Deutsche Physikalische Gesellschaft, Session of Semiconductor Physics Division on Quantum Wires: Optical and Transport Properties, Deutsche Physikalische Gesellschaft/Technische Universität Dresden, March 24, 2009.

  • P.N. Racec, Evanescent channels and scattering in cylindrical nanowire heterostructures, Physikalisches Kolloquium, Brandenburgische Technische Universität Cottbus, April 14, 2009.

  • P.N. Racec, Quantum transport in cylindrical nanowire heterostructures: The scattering problem, Paul-Drude-Institut für Festkörperelektronik, Abteilung Epitaxie, Berlin, May 13, 2009.

  • H.-Chr. Kaiser, Transient Kohn--Sham theory, Jubiläumssymposium ``Licht -- Materialien -- Modelle'' (100 Jahre Innovation aus Adlershof), Berlin-Adlershof, September 7 - 8, 2009.

  • H. Neidhardt, On carrier transport modeling in semiconductor devices at WIAS: A survey, Satellite Meeting of the International Congress of Mathematical Physics ``Mathematical Aspects of Quantum Transport and Applications in Nanophysics'', August 10 - 13, 2009, Aalborg University, Department of Mathematical Sciences, Denmark, August 10, 2009.

  • P.N. Racec, Scattering in cylindrical heterostructures, Workshop ``Trends in Nanoscience: Theory, Experiments, Technology'', August 23 - 30, 2009, Abdus Salam International Centre for Theoretical Physics, Trieste (ICTP), Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest (IFIN-HH), International Atomic Energy Agency, Vienna (IAEN), Sibiu, Romania, August 26, 2009.

  • P.N. Racec, Scattering states in cylindrical nanowire heterostructures, International Nano-Optoelectronic Workshop (iNOW 2009), Stockholm, Sweden, and Berlin, Germany, August 2 - 15, 2009.

  • P.N. Racec, Scattering theory in cylindrical nanowire heterostructures, Seminar of Nonequilibrium Many-Body Systems Group, Martin-Luther-Universität Halle-Wittenberg, Institut für Physik, December 7, 2009.

  • J. Rehberg, Functional analytic properties of the quantum mechanical particle density operator, International Workshop on Quantum Systems and Semiconductor Devices: Analysis, Simulations, Applications, April 20 - 24, 2009, Peking University, School of Mathematical Sciences, Beijing, China, April 21, 2009.

  • K. Hoke, Numerical treatment of the Kohn--Sham system for semiconductor devices, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, Dublin, Ireland, December 4 - 7, 2008.

  • K. Hoke, On the numerics of the 3D Kohn--Sham system, 4th Workshop on Mathematical Models for Transport in Macroscopic and Mesoscopic Systems, February 8 - 9, 2008, WIAS, February 9, 2008.

  • P.N. Racec, Electrical transport through quantum systems with non-separable scattering potential, University of Iceland, Science Institute, Reykjavik, June 20, 2008.

  • H.-Chr. Kaiser, A drift-diffusion model for semiconductors with internal interfaces, Annual Meeting of the Deutsche Mathematiker-Vereinigung 2008, Minisymposium ``Analysis of Reaction-Diffusion Systems with Internal Interfaces'', September 15 - 19, 2008, Friedrich-Alexander-Universität Erlangen-Nürnberg, September 15, 2008.

  • H.-Chr. Kaiser, A thermodynamic approach to transient Kohn--Sham theory, 100th Statistical Mechanics Conference, December 13 - 18, 2008, Rutgers, The State University of New Jersey, New Brunswick, USA, December 16, 2008.

  • H.-Chr. Kaiser, On drift-diffusion Kohn--Sham theory, 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2008), session ``Applied Analysis'', March 31 - April 4, 2008, University of Bremen, April 1, 2008.

  • H. Neidhardt, Kohn--Sham systems at zero temperature, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, December 4 - 7, 2008, Dublin Institute for Advanced Studies, School of Theoretical Physics, Ireland, December 5, 2008.

  • P.N. Racec, Quantum transport in cylindrical nanowire heterostructures, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, December 4 - 7, 2008, Dublin Institute for Advanced Studies, School of Theoretical Physics, Ireland, December 6, 2008.

  • K. Hoke, The Kohn--Sham system in case of zero temperature, Mini-Workshop on PDE's and Quantum Transport, March 12 - 16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 15, 2007.

  • H.-Chr. Kaiser, A drift-diffusion model of transient Kohn--Sham theory, First Joint International Meeting between the American Mathematical Society and the Polish Mathematical Society, Special Session ``Mathematics of Large Quantum Systems'', July 31 - August 3, 2007, University of Warsaw, Poland, August 3, 2007.

  • H. Neidhardt, On a quantum transmitting Schrödinger--Poisson system, Mini-Workshop on PDE's and Quantum Transport, March 12 - 16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 15, 2007.

  • J. Rehberg, On Schrödinger--Poisson systems, International Conference ``Nonlinear Partial Differential Equations'' (NPDE 2007), September 10 - 15, 2007, Institute of Applied Mathematics and Mechanics of NASU, Yalta, Ukraine, September 13, 2007.

  • J. Rehberg, Operator functions inherit monotonicity, Mini-Workshop on PDE's and Quantum Transport, March 12 - 16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 14, 2007.

  • J. Rehberg, Über Schrödinger-Poisson-Systeme, Chemnitzer Mathematisches Colloquium, Technische Universität Chemnitz, Fakultät für Mathematik, May 24, 2007.

  • J. Rehberg, The Schrödinger--Poisson system, Colloquium in Honor of Prof. Demuth, September 10 - 11, 2006, Universität Clausthal, September 10, 2006.

  • H. Neidhardt, A quantum transmitting Schrödinger--Poisson system, Workshop ``Quantum Transport and Exitations from Macro to Nanoscale: Theory and Applications'', November 10 - 13, 2005, Aalborg University, Denmark, November 11, 2005.

  • H. Neidhardt, Dissipative Schrödinger-Poisson systems and uniqueness, Workshop on ``Mathematical Models of Nanostructures: Spectral Problems and Scattering Properties'', April 25 - 27, 2005, Humboldt-Universität zu Berlin, April 26, 2005.

  • H. Neidhardt, Hybrid models for semiconductors, Physikalisches Kolloquium, Brandenburgische Technische Universität Cottbus, Lehrstuhl für Theoretische Physik, November 29, 2005.

  • H.-Chr. Kaiser, About quantum transmission on an up to three dimensional spatial domain, University of Texas at Dallas, USA, October 28, 2005.

  • H.-Chr. Kaiser, An open quantum system driven by an external flow, Workshop ``Nonlinear spectral problems in solid state physics'', April 4 - 8, 2005, Institut Henri Poincaré, Paris, France, April 7, 2005.

  • H.-Chr. Kaiser, Modeling and quasi-3D simulation of indium grains in (In,Ga)N/GaN quantum wells by means of density functional theory, Physikalisches Kolloquium, Brandenburgische Technische Universität, Lehrstuhl Theoretische Physik, Cottbus, February 15, 2005.

  • H.-Chr. Kaiser, On quantum transmission, Mathematical Physics Seminar, November 9 - 11, 2005, University of Texas at Austin, USA, November 9, 2005.

  • H.-Chr. Kaiser, Quasi-3D simulation of multi-excitons by means of density functional theory, Oberseminar ``Numerik/Wissenschaftliches Rechnen'', Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, January 11, 2005.

  • H.-Chr. Kaiser, Spectral resolution of a velocity field on the boundary of a Lipschitz domain, 2nd Joint Meeting of AMS, DMV, ÖMG, June 16 - 19, 2005, Johannes Gutenberg-Universität, Mainz, June 16, 2005.

  • J. Rehberg, Some analytical ideas concerning the quantum-drift-diffusion systems, Workshop ``Problèmes spectraux non-linéaires et modèles de champs moyens'', April 4 - 8, 2005, Institut Henri Poincaré, Paris, France, April 5, 2005.

  • J. Rehberg, Analysis of macroscopic and quantum mechanical semiconductor models, International Visitor Program ``Nonlinear Parabolic Problems'', August 8 - November 18, 2005, Finnish Mathematical Society (FMS), University of Helsinki, and Helsinki University of Technology, Finland, November 1, 2005.

  • H. Neidhardt, A model for resonant tunneling diodes, Seminar in Statistical Physics & Condensed Matter, July 2, 2004, Centre de Physique Théorique, Marseille, France, June 2, 2004.

  • H. Neidhardt, Hybrid models for semiconductors and dissipative Schrödinger-Poisson systems, Academy of Sciences of the Czech Republic, Nuclear Physics Institute, Prague, February 17, 2004.

  • J. Fuhrmann, H.-Chr. Kaiser, Th. Koprucki, G. Schmidt, Electronic states in semiconductor nanostructures and upscaling to semi-classical models, Evaluation Colloquium of the DFG Priority Program ``Analysis, Modeling and Simulation of Multiscale Problems'', Bad Honnef, May 20 - 21, 2004.

  • H. Gajewski, R. Hünlich, H.-Chr. Kaiser, M. Baro, Quantum mechanical and macroscopic models for optoelectronic devices, DFG Research Center sc Matheon, Technische Universität Berlin, July 19, 2004.

  • H.-Chr. Kaiser, Density functional theory for multi-excitons in quantum boxes, ``Molecular Simulation: Algorithmic and Mathematical Aspects'', Institut Henri Poincaré, Paris, France, December 1 - 3, 2004.

  • M. Baro, H. Gajewski, R. Hünlich, H.-Chr. Kaiser, Optoelektronische Bauelemente: mikroskopische & makroskopische Modelle, MathInside --- Überall ist Mathematik, event of the DFG Research Center ``Mathematics for Key Technologies'' on the occasion of the Open Day of Urania, Berlin, September 13, 2003 - December 3, 2004.