Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells I
V. Bonnaillie-Noël; F. Nier; Y. Patel
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 5, page 937-968
- ISSN: 0294-1449
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topBonnaillie-Noël, V., Nier, F., and Patel, Y.. "Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells I." Annales de l'I.H.P. Analyse non linéaire 25.5 (2008): 937-968. <http://eudml.org/doc/78820>.
@article{Bonnaillie2008,
author = {Bonnaillie-Noël, V., Nier, F., Patel, Y.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Schrödinger-Poisson system; asymptotic analysis; multiscale problems},
language = {eng},
number = {5},
pages = {937-968},
publisher = {Elsevier},
title = {Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells I},
url = {http://eudml.org/doc/78820},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Bonnaillie-Noël, V.
AU - Nier, F.
AU - Patel, Y.
TI - Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells I
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 5
SP - 937
EP - 968
LA - eng
KW - Schrödinger-Poisson system; asymptotic analysis; multiscale problems
UR - http://eudml.org/doc/78820
ER -
References
top- [1] Balslev E., Combes J.M., Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions, Commun Math. Phys.22 (1971) 280-294. Zbl0219.47005MR345552
- [2] Baro M., Kaiser H.-Chr., Neidhardt H., Rehberg J., A quantum transmitting Schrödinger–Poisson system, Rev. Math. Phys.16 (3) (2004) 281-330. Zbl1134.82336MR2063049
- [3] Baro M., Kaiser H.-Chr., Neidhardt H., Rehberg J., Dissipative Schrödinger–Poisson systems, J. Math. Phys.45 (1) (2004) 21-43. Zbl1070.82019MR2026356
- [4] Ben Abdallah N., Degond P., Markowich P.A., On a one-dimensional Schrödinger–Poisson scattering model, Z. Angew. Math. Phys.48 (1) (1997) 135-155. Zbl0885.34067MR1439739
- [5] Bonnaillie-Noël V., Nier F., Patel M., Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures, J. Comp. Phys.219 (2006) 644-670. Zbl1189.82129MR2274952
- [6] V. Bonnaillie-Noël, F. Nier, M. Patel, Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells II, Prépublications IRMAR, 2007. Zbl1157.82046
- [7] Büttiker M., Imry Y., Landauer R., Pinhas S., Generalized many-channel conductance formula with application to small rings, Phys. Rev. B31 (1985) 6207-6215.
- [8] Chevoir F., Vinter B., Scattering assisted tunneling in double barriers diode: scattering rates and valley current, Phys. Rev. B47 (1993) 7260-7274.
- [9] Davies E.B., Spectral Theory and Differential Operators, Cambridge Studies in Advanced Mathematics, vol. 42, Cambridge University Press, Cambridge, 1995. Zbl0893.47004MR1349825
- [10] Degond P., Mehats F., Ringhofer C., Quantum hydrodynamic models derived from the entropy principle, Contemp. Math.371 (2005) 107-131. Zbl1080.35152MR2143862
- [11] Derezinski J., Gérard C., Asymptotic Completeness of Classical and Quantum N-Particles Systems, Texts and Monographs in Physics, Springer-Verlag, 1997.
- [12] Dimassi M., Sjöstrand J., Spectral Asymptotics in the Semi-Classical Limit, London Mathematical Society Lecture Note Series, vol. 268, Cambridge University Press, 1999. Zbl0926.35002MR1735654
- [13] Gérard C., Martinez A., Semiclassical asymptotics for the spectral function of long-range Schrödinger operators, J. Funct. Anal.84 (1) (1989) 226-254. Zbl0692.35069MR999499
- [14] Helffer B., Semi-Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, vol. 1336, Springer-Verlag, 1988. Zbl0647.35002MR960278
- [15] Helffer B., Sjöstrand J., Résonances en limite semi-classique, Mém. Soc. Math. France24–25 (1986). Zbl0631.35075
- [16] Helffer B., Sjöstrand J., Multiple wells in the semi-classical limit I, Comm. Partial Differential Equations9 (4) (1984) 337-408. Zbl0546.35053MR740094
- [17] Helffer B., Sjöstrand J., Puits Multiples en limite semi-classique II. Interaction moléculaire. Symétries. Perturbation, Ann. Inst. H. Poincaré Phys. Théor.42 (2) (1985) 127-212. Zbl0595.35031MR798695
- [18] Helffer B., Sjöstrand J., Analyse semiclassique pour l'équation de Harper, Mém. Soc. Math. France34 (1988). Zbl0714.34130
- [19] Hislop P.D., Sigal I.M., Introduction to Spectral Theory with Applications to Schrödinger Operators, Applied Mathematical Sciences, vol. 113, Springer-Verlag, New York, 1996. Zbl0855.47002MR1361167
- [20] Jakšić V., Pillet C.-A., Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs, Commun. Math. Phys.226 (1) (2002) 131-162. Zbl0990.82017MR1889995
- [21] Jona-Lasinio G., Presilla C., Sjöstrand J., On Schrödinger equations with concentrated nonlinearities, Ann. Phys.240 (1) (1995) 1-21. Zbl0820.34050MR1329589
- [22] Kastrup J., Klann R., Grahn H., Ploog K., Bonilla L., Galàn J., Kindelan M., Moscoso M., Merlin R., Self-oscillations of domains in doped GaAs–Al–As superlatices, Phys. Rev. B52 19 (1995) 13761-13764.
- [23] Landauer R., Spatial variation of currents and fields due to localized scatterers in metallic conduction, IBM J. Res. Develop.1 (1957) 223-231. MR90369
- [24] Nier F., A variational formulation of Schrödinger–Poisson systems in dimension , Comm. Partial Differential Equations18 (7–8) (1993) 1125-1147. Zbl0785.35086MR1233187
- [25] Nier F., Schrödinger–Poisson systems in dimension : the whole-space case, Proc. Roy. Soc. Edinburgh Sect. A123 (6) (1993) 1179-1201. Zbl0807.35119MR1263914
- [26] Nier F., The dynamics of some quantum open systems with short-range nonlinearities, Nonlinearity11 (4) (1998) 1127-1172. Zbl0909.34052MR1632618
- [27] Nier F., Patel M., Nonlinear asymptotics for quantum out-of-equilibrium 1D systems: reduced models and algorithms, in: Blanchard, Dell'Antonio (Eds.), Multiscale Methods in Quantum Mechanics: Theory and Experiment, Birkhäuser, 2004, pp. 99-111. Zbl1322.82003MR2089718
- [28] M. Patel, Développement de modèles macroscopiques pour des systèmes quantiques non-linéaires hors-équilibre, Ph.D. Thesis, Université de Rennes 1, 2005.
- [29] Presilla C., Sjöstrand J., Transport properties in resonant tunneling heterostructures, J. Math. Phys.37 (10) (1996) 4816-4844. Zbl0868.35112MR1411610
- [30] Simon B., Trace Ideals and Their Applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, 1979. Zbl0423.47001MR541149
- [31] J. Sjöstrand, M. Zworski, Elementary linear algebra for advanced spectral problems, http://math.berkeley.edu/~zworsky/. Zbl1140.15009
- [32] Yafaev D., Mathematical Scattering Theory, General Theory, Translation of Mathematical Monographs, vol. 105, Amer. Math. Soc., 1992. Zbl0761.47001MR1180965
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