Adiabatic approximation of the Schrödinger-Poisson system with a partial confinement: The stationary case

Journal of Mathematical Physics

Volumn 45, Issue 5, 2004, Pages 2029-2050

  Pinaud, Olivier ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2542585356     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1688432     Document Type: Article

References (38)

1. Adams, R. A., Sobolev Spaces (Academic, New York, 2003).
2. Ando, T., Fowler, A. B., and Stern, F., "Electronic properties of two-dimensional systems," Rev. Mod. Phys. 54, 437-672 (1982).
3. Bastard, G., Wave mechanics applied to semiconductor hetererostructures, Les éditions de physique, 1996.
4. Bechouche, P., and Poupaud, F., "Semiclassical limits of Schrödinger equations in stratified media," Monatsh. Math. 129, 281-301 (2000).
5. Ben Abdallah, N., "A hybrid kinetic-quantum model for stationary electron transport," J. Stat. Phys. 90, 627-662 (1998).
6. Ben Abdallah, N., "On a multidimensional Schrödinger-Poisson scattering model for semiconductors," J. Math. Phys. 41, 4241-4261 (2000).
7. Ben Abdallah, N., Degond, P., and Markowich, P. A., "On a one-dimensional Schrödinger-Poisson scattering model," Z. Angew. Math. Phys. 48, 135-155 (1997).
8. Ben Abdallah, N., Degond, P., and Gamba, I., "Coupling one-dimensional time-dependent classical and quantum transport models," J. Math. Phys. 43, 1-24 (2002).
9. Ben Abdallah, N., and Méhats, F., "Semi-classical limit of the Schrödinger equation with a partially confining potential," J. Math. Pures Appl. (to be published).
10. Ben Abdallah, N., and Méhats, F., "On a Vlasov- Schrödinger-Poisson model," Comm. Partial Differ. Eq. 29, 173-206 (2004).
11. Ben Abdallah, N., Méhats, F., and Pinaud, O., "Adiabatic approximation of the Schrödinger-Poisson system with a partial confinement," submitted.
12. Ben Abdallah, N., and Pinaud, O., "A mathematical model for the transient evolution of a resonant tunneling diode," C. R. Acad. Sci., Ser. I: Math. 334, 283-288 (2002).
13. Brézis, H., Analyze fonctionnelle (Masson, 1993).
14. 2 solutions to the Schrödinger- Poisson system: existence, uniqueness, time behavior and smoothing effects," Math. Methods Appl. Sci. 7, 1051-1083 (1997).
15. Chevoir, F., and Vinter, B., "Scattering-assisted tunneling in double-barriers diode: scattering rates and valley current," Phys. Rev. B 47, 7260-7274 (1993).
16. da Costa, R. C. T., "Quantum mechanics for a constraint particule," Phys. Rev. A 23, 1982-1987 (1981).
17. Davies, J. H., The Physics of Low Dimensional Semiconductors (Cambridge University Press, Cambridge, 1998).
18. Degond, P., and El Ayyadi, A., "A coupled Schrödinger drift-diffusion model for quantum semiconductor device simulations," J. Comput. Phys. 181, 222-259 (2002).
19. Ensslin, K., Wixforth, A., Sundaram, M., Hopkins, P. F., English, J. H., and Gossard, A. C., "Single-particle subband spectroscopy in a parabolic quantum well via transport experiments," Phys. Rev. B 47, 1366-1378 (1993).
20. 1-xAs-GaAs quantum wells," Phys. Rev. B 37, 10 150-10 153 (1988).
21. Ensslin, K., Pistisch, C., Wixforth, A., Sundaram, M., Hopkins, P. F., and Gossard, A. C., "Direct observation of resonant subband-Landau-level coupling in a transport experiment," Phys. Rev. B 45, 11 407-11 410 (1992).
22. Frensley, W. R., "Boundary conditions for open quantum systems driven far equilibrium," Rev. Mod. Phys. 62, 745-791 (1990).
23. Froese, R., and Herbst, I., "Realizing holonomic constraints in classical and quantum mechanics," Commun. Math. Phys. 220, 489-535 (2001).
24. Hagedorn, G. A. and Joye, A., "A time-dependent Born-Oppenheimer approximation with exponentially small error estimates," Commun. Math. Phys. 223, 583-626 (2001).
25. -1," J. Appl. Phys. 61, 1219-1221 (1987).
26. Lent, C., and Kirkner, D., "The quantum transmitting boundary method," J. Appl. Phys. 67, 6353-6359 (1990).
27. Markowich, P. A., Mauser, N. J., and Poupaud, F., "A Wigner function approach to (semi)classical limits: electrons in a periodic potential," J. Math. Phys. 35, 1066-1094 (1994).
28. Mitchell, K. A., "Geometric phase, curvature and extrapotentials in constrained quantum systems," quant-phys/0001059 (2000).
29. Mounaix, P., Vanbésien, O., and Lippens, D., "Effects of cathode space layer on the current-voltage characteristics of resonant tunneling diodes," Appl. Phys. Lett. 57, 1571-1519 (1990).
30. Pfeiffer, L., West, K. W., Stormer, H. L., and Baldwin, K. W., "Electron mobilities exceeding 107 cm2/V s in modulation-doped GaAs," Appl. Phys. Lett. 55, 1888-1890 (1989).
31. Pinaud, O., "Transient simulations of a resonant tunneling diode," J. Appl. Phys. 92, 1987-1994 (2002).
32. Polizzi, E. and Ben Abdallah, N., Modeling of Quantum Ballistic Transport in Electron Waveguide Devices, Proceeding Mathematics in Industry ECMI (Springer, New York, 2001).
33. Polizzi, E., and Ben Abdallah, N., "Self-consistent three dimensional models for quantum ballistic transport in open systems," Phys. Rev. B 66, 245301 (2002).
34. Reed, M., and Simon, B., Methods of Modern Mathematical Physics (Academic, New York, 1980), Vol. IV.
35. Spohn, H., and Teufel, S., "Adiabatic decoupling and time-dependent Born-Oppenheimer theory," Commun. Math. Phys. 224, 113-132 (2001).
36. Stormer, H. L., Gossard, A. C., and Wiegmann, W., "Observation of intersubband scattering in a 2-dimensional electron system," Solid State Commun. 41, 707-709 (1982).
37. Teufel, S., Adiabatic Perturbation Theory in Quantum Dynamics, Lecture Notes in Mathematics 1821 (Springer-Verlag, Berlin, 2003).
38. Weisbuch, C., and Vinter, B., Quantum Semiconductor Structures (Academic, New York, 1991).