Over the years we published many papers on using the Wigner function for quantum transport in electronics -- see below. If you are using our WEMC simulation software, we would appreciate if you could cite (aside from this web page) the following two papers, which discuss the fundamental computational aspects of the simulator in 1D as well as the critical parallelization approach for 2D problems:

J. Weinbub, P. Ellinghaus, M. Nedjalkov: "Domain Decomposition Strategies for the Two-Dimensional Wigner Monte Carlo Method"; Journal of Computational Electronics, 14 (2015), 922 - 929 doi: 10.1007/s10825-015-0730-0.

P. Ellinghaus, J. Weinbub, M. Nedjalkov, S. Selberherr, I. Dimov: "Distributed-Memory Parallelization of the Wigner Monte Carlo Method using Spatial Domain Decomposition"; Journal of Computational Electronics, 14 (2015), 151 - 162 doi: 10.1007/s10825-014-0635-3.

1. M. Nedjalkov, J. Weinbub, D.K. Ferry: "Introduction to the Special Issue on Wigner Functions"; Journal of Computational Electronics, 14 (2015), 857 - 858 doi:10.1007/s10825-015-0745-6.

1. J. Weinbub, M. Ballicchia, M. Nedjalkov: "Electron Interference in a Double-Dopant Potential Structure"; Physica Status Solidi - Rapid Research Letters, 12, (2018), 1800111-1 - 1800111-4 doi:10.1002/pssr.201800111.
2. M. Nedjalkov, P. Ellinghaus, J. Weinbub, T. Sadi, A. Asenov, I. Dimov, S. Selberherr: "Stochastic Analysis of Surface Roughness Models in Quantum Wires"; Computer Physics Communications, 228, (2018), 30 - 37 doi:10.1016/j.cpc.2018.03.010.
3. P. Ellinghaus, J. Weinbub, M. Nedjalkov, S. Selberherr: "Analysis of Lense-Governed Wigner Signed Particle Quantum Dynamics"; Physica Status Solidi - Rapid Research Letters, 11, (2017), 1700102-1 - 1700102-5 doi:10.1002/pssr.201700102.
4. I. Dimov, M. Nedjalkov, J. M. Sellier, S. Selberherr: "Boundary Conditions and the Wigner Equation Solution"; Journal of Computational Electronics, 14 (2015), 859 - 863 doi:10.1007/s10825-015-0720-2.
5. P. Ellinghaus, J. Weinbub, M. Nedjalkov, S. Selberherr, I. Dimov: "Distributed-Memory Parallelization of the Wigner Monte Carlo Method using Spatial Domain Decomposition"; Journal of Computational Electronics, 14 (2015), 151 - 162 doi: 10.1007/s10825-014-0635-3.
6. M. Nedjalkov, J. Weinbub, P. Ellinghaus, S. Selberherr: "The Wigner Equation in the Presence of Electromagnetic Potentials"; Journal of Computational Electronics, 14 (2015), 888 - 893 doi:10.1007/s10825-015-0732-y.
7. J. M. Sellier, M. Nedjalkov, I. Dimov:
   "An Introduction to Applied Quantum Mechanics in the Wigner Monte Carlo Formalism";
   Physics Reports, 577 (2015), 1 - 34 doi:10.1016/j.physrep.2015.03.001.
8. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr:
   "A Comparison of Approaches for the Solution of the Wigner Equation";
   Mathematics and Computers in Simulation, 107, (2015), 108 - 119 doi:10.1016/j.matcom.2014.06.001.
9. J. Weinbub, P. Ellinghaus, M. Nedjalkov: "Domain Decomposition Strategies for the Two-Dimensional Wigner Monte Carlo Method"; Journal of Computational Electronics, 14 (2015), 922 - 929 doi: 10.1007/s10825-015-0730-0.
10. J. M. Sellier, S. Amoroso, M. Nedjalkov, S. Selberherr, A. Asenov, I. Dimov:
    "Electron Dynamics in Nanoscale Transistors by Means of Wigner and Boltzmann Approaches";
    Physica A: Statistical Mechanics and its Applications, 398, (2014), 194 - 198 doi:10.1016/j.physa.2013.12.045.
11. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "A Benchmark Study of the Wigner Monte Carlo Method"; Monte Carlo Methods and Applications, 20 (2014), 43 - 51 doi:10.1515/mcma-2013-0018.
12. M. Nedjalkov, P. Schwaha, S. Selberherr, J. M. Sellier, D. Vasileska: "Wigner Quasi-Particle Attributes - An Asymptotic Perspective"; Applied Physics Letters, 102 (2013), 163113-1 - 163113-4 doi:10.1063/1.4802931.
13. P. Schwaha, D. Querlioz, P. Dollfus, J. Saint-Martin, M. Nedjalkov, S. Selberherr: "Decoherence Effects in the Wigner Function Formalism"; Journal of Computational Electronics, 12 (2013), 388 - 396 doi:10.1007/s10825-013-0480-9.
14. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "Decoherence and Time Reversibility: The Role of Randomness at Interfaces"; Journal of Applied Physics, 114 (2013), 174902-1 - 174902-7 doi:10.1063/1.4828736.
15. M. Nedjalkov, S. Selberherr, D.K. Ferry, D. Vasileska, P. Dollfus, D. Querlioz, I. Dimov, P. Schwaha: "Physical Scales in the Wigner-Boltzmann Equation"; Annals of Physics, 328 (2012), 220 - 237 doi:10.1016/j.aop.2012.10.001.
16. M. Nedjalkov, H. Kosina, P. Schwaha: "Device Modeling in the Wigner Picture"; Journal of Computational Electronics, 9 (2010), 218 - 223 doi:10.1007/s10825-010-0316-9.

1. J. Cervenka, P. Ellinghaus, M. Nedjalkov:
   "Deterministic Solution of the Discrete Wigner Equation";
   Numerical Methods and Applications (2015), 149 - 156 doi:10.1007/978-3-319-15585-2_17.
2. J. Cervenka, P. Ellinghaus, M. Nedjalkov, E. Langer:
   "Optimization of the Deterministic Solution of the Discrete Wigner Equation";
     Lecture Notes in Computer Science, 9374 (2015), 269 - 276 doi:10.1007/978-3-319-26520-9_29.
3. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Optimized Particle Regeneration Scheme for the Wigner Monte Carlo Method";
     Lecture Notes in Computer Science, 8962 (2015), 27 - 33 doi:10.1007/978-3-319-15585-2_3.
4. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "The Influence of Electrostatic Lenses on Wave Packet Dynamics";
     Lecture Notes in Computer Science", 9374 (2015), 277 - 284 doi:10.1007/978-3-319-26520-9_30.
5. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Efficient Calculation of the Two-Dimensional Wigner Potential";
     The 17th International Workshop on Computational Electronics (IWCE), (2014), 1 - 3 doi:10.1109/IWCE.2014.6865812.
6. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Implications of the Coherence Length on the Discrete Wigner Potential";
     The 17th International Workshop on Computational Electronics (IWCE), (2014), 1 - 3 doi:10.1109/IWCE.2014.6865852.
7. P. Schwaha, M. Nedjalkov, S. Selberherr, J. M. Sellier, I. Dimov, R. Georgieva: "Stochastic Alternative to Newton's Acceleration"; Lecture Notes in Computer Science, 8353 (2014),  178 - 18 doi:10.1007/978-3-662-43880-0_19.
8. J.M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "The Role of Annihilation in a Wigner Monte Carlo Approach"; Lecture Notes in Computer Science, 8353 (2014), 186 - 193 doi:10.1007/978-3-662-43880-0_20.
9. S. Ahmed, M. Nedjalkov, D. Vasileska: "Comparative Study of Various Self-Consistent Event Biasing Schemes for Monte Carlo Simulations of Nanoscale MOSFETs"; Theory and  Applications of Monte Carlo Simulations, (2013), 109 - 133 doi:10.5772/53113.
10. P. Schwaha, M. Nedjalkov, S. Selberherr, I. Dimov: "Phonon-Induced Decoherence in Electron Evolution"; Lecture Notes in Computer Science, 7116 (2012), 472 - 479 doi:10.1007/978-3-642-29843-1_53.
11. P. Schwaha, M. Nedjalkov, S. Selberherr, I. Dimov: "Monte Carlo Investigations of Electron Decoherence due to Phonons"; Monte Carlo Methods and Applications, (2012), 203 - 211 doi:10.1515/9783110293586.203.
12. M. Nedjalkov, S. Selberherr, I. Dimov: "Stochastic Algorithm for Solving the Wigner-Boltzmann Correction Equation"; Lecture Notes in Computer Science, 6046 (2011), 95 - 102 doi:10.1007/978-3-642-18466-6_10.
13. M. Nedjalkov, D. Querlioz, P. Dollfus, H. Kosina: "Wigner Function Approach"; Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling, (2011), 289-358 doi:10.1007/978-1-4419-8840-9_5 (invited).

1. M. Nedjalkov, J. Weinbub, S. Selberherr:
   "The Description of Carrier Transport for Quantum Systems";
    in Book of Abstracts of the Energy Materials Nanotechnology Meeting on Quantum, (2016), 41 - 42 (invited).
2. P. Ellinghaus, J. Weinbub, M. Nedjalkov, S. Selberherr:
   "ViennaWD - Applications";
   in Booklet of the 1st International Wigner Workshop (IW2), (2015), 9.
3. J. Weinbub, P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Comparison of Slab and Block Decomposition Strategies for the Two-Dimensional Wigner Monte Carlo Method";
   in Abstracts International Symposium on Advanced Nanodevices and Nanotechnology (ISANN 2015), (2015).
4. J. Weinbub, P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "ViennaWD - Status and Outlook";
   in Booklet of the 1^st International Wigner Workshop (IW2), (2015), 8.
5. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Improved Drive-Current into Nanoscaled Channels using Electrostatic Lenses";
   in Proceedings of the 20^th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), (2015), 24 - 27 doi:10.1109/SISPAD.2015.7292249.
6. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Improved Particle Annihilation for Wigner Monte Carlo Simulations on a High-Resolution Mesh";
   in Book of Abstracts 18^th International Workshop on Computational Electronics (IWCE), (2015), 93 - 94.
7. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "Memory-efficient Particle Annihilation Algorithm for Wigner Monte Carlo Simulations";
   in Proceedings of the 2015 International Workshop on Computational Electronics (IWCE), (2015), 4 page(s) doi:10.1109/IWCE.2015.7301955.
8. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
   "The Influence of Electrostatic Lenses on Wave Packet Dynamics";
   in Abstracts International Conference on Large-Scale Scientific Computations (LSSC), (2015), 39 - 40.
9. M. Nedjalkov, P. Ellinghaus, S. Selberherr:
   "The Aharanov-Bohm Effect from a Phase Space Perspective";
   in "Abstracts International Conference on Large-Scale Scientific Computations (LSSC), (2015), 59 - 60.
10. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
    "The Wigner Monte Carlo Method for Accurate Semiconductor Device Simulation";
    in Proceedings of the 19th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), (2014), 113 - 116 doi:10.1109/SISPAD.2014.6931576.
11. J. Cervenka, P. Ellinghaus, M. Nedjalkov:
    "Deterministic Solution of the Discrete Wigner Equation";
    in Eighth International Conference on Numerical Methods and Applications, (2014), 36.
12. P. Ellinghaus, M. Nedjalkov, S. Selberherr:
    "Optimized Particle Regeneration Scheme for the Wigner Monte Carlo Method";
    in Eighth International Conference on Numerical Methods and Applications, (2014), 19.
13. I. Dimov, M. Nedjalkov, J. M. Sellier, S. Selberherr:
    "Neumann Series Analysis of the Wigner Equation Solution";
    in Abstracts of The 18th European Conference on Mathematics for Industry, (2014), 459 (invited).
14. P. Ellinghaus, M. Nedjalkov, S. Selberherr: "Efficient Calculation of the Two-Dimensional Wigner Potential"; in Proceedings of the 17th International Workshop on Computational Electronics (IWCE), (2014), 1-3 doi:10.1109/IWCE.2014.6865812.
15. P. Ellinghaus, M. Nedjalkov, S. Selberherr: "Implications of the Coherence Length on the Discrete Wigner Potential"; in Proceedings of the 17th International Workshop on Computational Electronics (IWCE), (2014), 1-3 doi:10.1109/IWCE.2014.6865852.
16. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr:
    "The Multi-Dimensional Transient Challenge: The Wigner Particle Approach";
    in Book of Abstracts of the 17th International Workshop on Computational Electronics (IWCE), (2014), 119 - 120 (invited).
17. S. Amoroso, L. Gerrer, A. Asenov, J. M. Sellier, I. Dimov, M. Nedjalkov, S. Selberherr: "Quantum Insights in Gate Oxide Charge-Trapping Dynamics in Nanoscale MOSFETs"; in Proceedings of the 18th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), (2013), 25 - 28 doi:10.1109/SISPAD.2013.6650565.
18. J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "Two-Dimensional Transient Wigner Particle Model"; in Proceedings of the 18th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), (2013), 404 - 407 doi:10.1109/SISPAD.2013.6650660.
19. P. Schwaha, J. M. Sellier, M. Nedjalkov, I. Dimov, S. Selberherr: "The Ultimate Equivalence Between Coherent Quantum and Classical Regimes"; in Proceedings of the 16th International Workshop on Computational Electronics (IWCE), (2013), 152 - 153, ISBN 978-3-901578-26-7.
20. M. Nedjalkov, P. Schwaha, S. Selberherr, D.K. Ferry, D. Vasileska, P. Dollfus, D. Querlioz: "Role of the Physical Scales on the Transport Regime"; in Proceedings of the 15th International Workshop on Computational Electronics (IWCE), (2012), 1 - 3 doi:10.1109/IWCE.2012.6242848.
21. P. Schwaha, M. Nedjalkov, S. Selberherr, I. Dimov: "Particle-Grid Techniques for Semiclassical and Quantum Transport Simulations"; in Proceedings of the 15th International Workshop on Computational Electronics (IWCE), (2012), 1 - 3 doi:10.1109/IWCE.2012.6242860.
22. M. Nedjalkov, P. Schwaha, S. Selberherr, D.K. Ferry: "Phonon Decoherence in Wigner-Boltzmann Transport"; in Proceedings of the International Winterschool on New Developments in Solid State Physics, (2012), 61 - 62.