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Volumn 84, Issue 5, 2005, Pages 580-614

Semiclassical analysis of the Schrödinger equation with a partially confining potential

Author keywords

Semiclassical limit; Subband transport; Two dimensional electron gas; Wigner measures

Indexed keywords


EID: 17144395862     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2004.10.004     Document Type: Article
Times cited : (11)

References (35)
  • 1
    • 85032069152 scopus 로고
    • Electronic properties of two-dimensional systems
    • T. Ando B. Fowler F. Stern Electronic properties of two-dimensional systems Rev. Mod. Phys. 54 1982 437-672
    • (1982) Rev. Mod. Phys. , vol.54 , pp. 437-672
    • Ando, T.1    Fowler, B.2    Stern, F.3
  • 3
    • 0003154771 scopus 로고    scopus 로고
    • Semiclassical limits in a crystal with a Coulombian self-consistent potential: Effective mass theorem
    • P. Béchouche Semiclassical limits in a crystal with a Coulombian self-consistent potential: Effective mass theorem Asymptot. Anal. 19 1999 95-116
    • (1999) Asymptot. Anal. , vol.19 , pp. 95-116
    • Béchouche, P.1
  • 4
    • 0040792475 scopus 로고    scopus 로고
    • Semiclassical limit of a Schrödinger equation for a stratified material
    • P. Béchouche F. Poupaud Semiclassical limit of a Schrödinger equation for a stratified material Monatsh. Math. 129 2000 281-301
    • (2000) Monatsh. Math. , vol.129 , pp. 281-301
    • Béchouche, P.1    Poupaud, F.2
  • 5
    • 0032188065 scopus 로고    scopus 로고
    • (Semi)-nonrelativistic limits of the Dirac equation with external time-dependent electromagnetic field
    • P. Béchouche N. Mauser F. Poupaud (Semi)-nonrelativistic limits of the Dirac equation with external time-dependent electromagnetic field Comm. Math. Phys. 197 2 1998 405-425
    • (1998) Comm. Math. Phys. , vol.197 , Issue.2 , pp. 405-425
    • Béchouche, P.1    Mauser, N.2    Poupaud, F.3
  • 6
    • 0035593772 scopus 로고    scopus 로고
    • Semiclassical limit for the Schrödinger-Poisson equation in a crystal
    • P. Béchouche N. Mauser F. Poupaud Semiclassical limit for the Schrödinger-Poisson equation in a crystal Comm. Pure Appl. Math. 54 2001 851-890
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 851-890
    • Béchouche, P.1    Mauser, N.2    Poupaud, F.3
  • 9
    • 0034338421 scopus 로고    scopus 로고
    • Fokker-Planck equations as scaling limits of reversible quantum systems
    • F. Castella L. Erdös F. Frommlet P.A. Markowich Fokker-Planck equations as scaling limits of reversible quantum systems J. Stat. Phys. 100 3-4 2000 543-601
    • (2000) J. Stat. Phys. , vol.100 , Issue.3-4 , pp. 543-601
    • Castella, F.1    Erdös, L.2    Frommlet, F.3    Markowich, P.A.4
  • 11
    • 0033451117 scopus 로고    scopus 로고
    • The Boltzmann equation for a one-dimensional quantum Lorentz gas
    • R. Esposito M. Pulvirenti A. Teta The Boltzmann equation for a one-dimensional quantum Lorentz gas Comm. Math. Phys. 204 3 1999 619-649
    • (1999) Comm. Math. Phys. , vol.204 , Issue.3 , pp. 619-649
    • Esposito, R.1    Pulvirenti, M.2    Teta, A.3
  • 12
    • 0034418177 scopus 로고    scopus 로고
    • Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
    • L. Erdös H.T. Yau Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation Comm. Pure Appl. Math. 53 6 2000 667-735
    • (2000) Comm. Pure Appl. Math. , vol.53 , Issue.6 , pp. 667-735
    • Erdös, L.1    Yau, H.T.2
  • 15
    • 0003072370 scopus 로고
    • Mesures semi-classiques et ondes de Bloch
    • P. Gérard Mesures semi-classiques et ondes de Bloch Sem. École Polytechnique XVI 1991 1-19
    • (1991) Sem. École Polytechnique , vol.16 , pp. 1-19
    • Gérard, P.1
  • 17
    • 0035540307 scopus 로고    scopus 로고
    • A time-dependent Born-Oppenheimer approximation with exponentially small error estimates
    • G.A. Hagedorn A. Joye A time-dependent Born-Oppenheimer approximation with exponentially small error estimates Comm. Math. Phys. 223 3 2001 583-626
    • (2001) Comm. Math. Phys. , vol.223 , Issue.3 , pp. 583-626
    • Hagedorn, G.A.1    Joye, A.2
  • 21
    • 0000269855 scopus 로고
    • The classical limit of a self-consistent quantum-Vlasov equation in 3-D
    • P. Markowich N. Mauser The classical limit of a self-consistent quantum-Vlasov equation in 3-D Math. Models Methods Appl. Sci. 3 1993 109-124
    • (1993) Math. Models Methods Appl. Sci. , vol.3 , pp. 109-124
    • Markowich, P.1    Mauser, N.2
  • 22
    • 36449006348 scopus 로고
    • A Wigner function approach to semiclassical limits: Electrons in a periodic potential
    • P. Markowich N. Mauser F. Poupaud A Wigner function approach to semiclassical limits: Electrons in a periodic potential J. Math. Phys. 35 1994 1066-1094
    • (1994) J. Math. Phys. , vol.35 , pp. 1066-1094
    • Markowich, P.1    Mauser, N.2    Poupaud, F.3
  • 23
    • 85129697344 scopus 로고    scopus 로고
    • The Maxwell equation in a periodic medium: Homogenization of the energy density
    • P. Markowich F. Poupaud The Maxwell equation in a periodic medium: homogenization of the energy density Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 23 2 1996 301-324
    • (1996) Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 , vol.23 , Issue.2 , pp. 301-324
    • Markowich, P.1    Poupaud, F.2
  • 24
    • 0011569744 scopus 로고    scopus 로고
    • The pseudo-differential approach to finite differences revisited
    • P. Markowich F. Poupaud The pseudo-differential approach to finite differences revisited Calcolo 36 3 1999 161-186
    • (1999) Calcolo , vol.36 , Issue.3 , pp. 161-186
    • Markowich, P.1    Poupaud, F.2
  • 25
    • 0007014905 scopus 로고    scopus 로고
    • On the time-dependent Born-Oppenheimer approximation with smooth potential
    • Preprint Archive mp_arc 01-37
    • A. Martinez, V. Sordoni, On the time-dependent Born-Oppenheimer approximation with smooth potential, Math. Phys. Preprint Archive mp_arc 01-37, 2001
    • (2001) Math. Phys.
    • Martinez, A.1    Sordoni, V.2
  • 26
    • 0034148496 scopus 로고    scopus 로고
    • Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary
    • L. Miller Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary J. Math. Pures Appl. (9) 79 3 2000 227-269
    • (2000) J. Math. Pures Appl. (9) , vol.79 , Issue.3 , pp. 227-269
    • Miller, L.1
  • 27
    • 0001485147 scopus 로고    scopus 로고
    • A semi-classical picture of quantum scattering
    • F. Nier A semi-classical picture of quantum scattering Ann. Sci. École Norm. Sup. 29 1996 149-183
    • (1996) Ann. Sci. École Norm. Sup. , vol.29 , pp. 149-183
    • Nier, F.1
  • 29
    • 0040062089 scopus 로고    scopus 로고
    • Semiclassical limits in a crystal with external potentials and effective mass theorems
    • F. Poupaud C. Ringhofer Semiclassical limits in a crystal with external potentials and effective mass theorems Comm. Partial Differential Equations 21 1996 1897-1918
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 1897-1918
    • Poupaud, F.1    Ringhofer, C.2
  • 32
    • 0035539929 scopus 로고    scopus 로고
    • Adiabatic decoupling and time-dependent Born-Oppenheimer theory
    • H. Spohn S. Teufel Adiabatic decoupling and time-dependent Born-Oppenheimer theory Comm. Math. Phys. 224 1 2001 113-132
    • (2001) Comm. Math. Phys. , vol.224 , Issue.1 , pp. 113-132
    • Spohn, H.1    Teufel, S.2
  • 35
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • E. Wigner On the quantum correction for thermodynamic equilibrium Phys. Rev. 40 1932 749-759
    • (1932) Phys. Rev. , vol.40 , pp. 749-759
    • Wigner, E.1


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