@article{AIHPC_2008__25_5_937_0, author = {Bonnaillie-No\"el, V. and Nier, F. and Patel, Y.}, title = {Far from equilibrium steady states of 1D-Schr\"odinger-Poisson systems with quantum wells I}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {25}, year = {2008}, pages = {937-968}, doi = {10.1016/j.anihpc.2007.05.007}, mrnumber = {2457818}, zbl = {1149.82349}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_5_937_0} }
Bonnaillie-Noël, V.; Nier, F.; 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, Tome 25 (2008) pp. 937-968. doi : 10.1016/j.anihpc.2007.05.007. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_5_937_0/
[1] Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions, Commun Math. Phys. 22 (1971) 280-294. | MR 345552 | Zbl 0219.47005
, ,[2] A quantum transmitting Schrödinger-Poisson system, Rev. Math. Phys. 16 (3) (2004) 281-330. | MR 2063049 | Zbl 1134.82336
, , , ,[3] Dissipative Schrödinger-Poisson systems, J. Math. Phys. 45 (1) (2004) 21-43. | MR 2026356 | Zbl 1070.82019
, , , ,[4] On a one-dimensional Schrödinger-Poisson scattering model, Z. Angew. Math. Phys. 48 (1) (1997) 135-155. | MR 1439739 | Zbl 0885.34067
, , ,[5] Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures, J. Comp. Phys. 219 (2006) 644-670. | MR 2274952 | Zbl pre05080109
, , ,[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. | Zbl 1157.82046
[7] Generalized many-channel conductance formula with application to small rings, Phys. Rev. B 31 (1985) 6207-6215.
, , , ,[8] Scattering assisted tunneling in double barriers diode: scattering rates and valley current, Phys. Rev. B 47 (1993) 7260-7274.
, ,[9] Spectral Theory and Differential Operators, Cambridge Studies in Advanced Mathematics, vol. 42, Cambridge University Press, Cambridge, 1995. | MR 1349825 | Zbl 0893.47004
,[10] Quantum hydrodynamic models derived from the entropy principle, Contemp. Math. 371 (2005) 107-131. | MR 2143862 | Zbl 1080.35152
, , ,[11] Asymptotic Completeness of Classical and Quantum N-Particles Systems, Texts and Monographs in Physics, Springer-Verlag, 1997.
, ,[12] Spectral Asymptotics in the Semi-Classical Limit, London Mathematical Society Lecture Note Series, vol. 268, Cambridge University Press, 1999. | MR 1735654 | Zbl 0926.35002
, ,[13] Semiclassical asymptotics for the spectral function of long-range Schrödinger operators, J. Funct. Anal. 84 (1) (1989) 226-254. | MR 999499 | Zbl 0692.35069
, ,[14] Semi-Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, vol. 1336, Springer-Verlag, 1988. | MR 960278 | Zbl 0647.35002
,[15] Résonances en limite semi-classique, Mém. Soc. Math. France 24-25 (1986). | Numdam | Zbl 0631.35075
, ,[16] Multiple wells in the semi-classical limit I, Comm. Partial Differential Equations 9 (4) (1984) 337-408. | MR 740094 | Zbl 0546.35053
, ,[17] Puits Multiples en limite semi-classique II. Interaction moléculaire. Symétries. Perturbation, Ann. Inst. H. Poincaré Phys. Théor. 42 (2) (1985) 127-212. | Numdam | MR 798695 | Zbl 0595.35031
, ,[18] Analyse semiclassique pour l'équation de Harper, Mém. Soc. Math. France 34 (1988). | Numdam | Zbl 0714.34130
, ,[19] Introduction to Spectral Theory with Applications to Schrödinger Operators, Applied Mathematical Sciences, vol. 113, Springer-Verlag, New York, 1996. | MR 1361167 | Zbl 0855.47002
, ,[20] Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs, Commun. Math. Phys. 226 (1) (2002) 131-162. | MR 1889995 | Zbl 0990.82017
, ,[21] On Schrödinger equations with concentrated nonlinearities, Ann. Phys. 240 (1) (1995) 1-21. | MR 1329589 | Zbl 0820.34050
, , ,[22] Self-oscillations of domains in doped GaAs-Al-As superlatices, Phys. Rev. B 52 19 (1995) 13761-13764.
, , , , , , , , ,[23] Spatial variation of currents and fields due to localized scatterers in metallic conduction, IBM J. Res. Develop. 1 (1957) 223-231. | MR 90369
,[24] A variational formulation of Schrödinger-Poisson systems in dimension , Comm. Partial Differential Equations 18 (7-8) (1993) 1125-1147. | MR 1233187 | Zbl 0785.35086
,[25] Schrödinger-Poisson systems in dimension : the whole-space case, Proc. Roy. Soc. Edinburgh Sect. A 123 (6) (1993) 1179-1201. | MR 1263914 | Zbl 0807.35119
,[26] The dynamics of some quantum open systems with short-range nonlinearities, Nonlinearity 11 (4) (1998) 1127-1172. | MR 1632618 | Zbl 0909.34052
,[27] Nonlinear asymptotics for quantum out-of-equilibrium 1D systems: reduced models and algorithms, in: , (Eds.), Multiscale Methods in Quantum Mechanics: Theory and Experiment, Birkhäuser, 2004, pp. 99-111. | MR 2089718
, ,[28] M. Patel, Développement de modèles macroscopiques pour des systèmes quantiques non-linéaires hors-équilibre, Ph.D. Thesis, Université de Rennes 1, 2005.
[29] Transport properties in resonant tunneling heterostructures, J. Math. Phys. 37 (10) (1996) 4816-4844. | MR 1411610 | Zbl 0868.35112
, ,[30] Trace Ideals and Their Applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, 1979. | MR 541149 | Zbl 0423.47001
,[31] J. Sjöstrand, M. Zworski, Elementary linear algebra for advanced spectral problems, http://math.berkeley.edu/~zworsky/.
[32] Mathematical Scattering Theory, General Theory, Translation of Mathematical Monographs, vol. 105, Amer. Math. Soc., 1992. | MR 1180965 | Zbl 0761.47001
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