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Volumn 245, Issue 1, 2008, Pages 154-200

Time averaging for the strongly confined nonlinear Schrödinger equation, using almost-periodicity

Author keywords

Adiabatic approximation; Almost periodic functions; Error estimates; Nonlinear analysis; Sobolev scale associated with a self adjoint operator; Two dimensional electron gas

Indexed keywords


EID: 43049119578     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.02.002     Document Type: Article
Times cited : (45)

References (36)
  • 1
    • 0004157168 scopus 로고
    • Opérateurs pseudo-différentiels et théorème de Nash–Moser
    • S. Alinhac P. Gérard Opérateurs pseudo-différentiels et théorème de Nash–Moser Savoirs Actuels 1991 Interéditions/Éditions du CNRS Paris
    • (1991)
    • Alinhac, S.1    Gérard, P.2
  • 2
    • 0003978095 scopus 로고
    • Mathematical Methods of Classical Mechanics
    • V.I. Arnol'd Mathematical Methods of Classical Mechanics Grad. Texts in Math. vol. 60 1989 Springer-Verlag
    • (1989)
    • Arnol'd, V.I.1
  • 3
    • 85032069152 scopus 로고
    • Electronic properties of two-dimensional systems
    • T. Ando B. Fowler F. Stern Electronic properties of two-dimensional systems Rev. Modern Phys. 54 1982 437 672
    • (1982) Rev. Modern Phys. , vol.54 , pp. 437-672
    • Ando, T.1    Fowler, B.2    Stern, F.3
  • 4
    • 0003493885 scopus 로고    scopus 로고
    • Wave Mechanics Applied to Semiconductor Heterostructures
    • G. Bastard Wave Mechanics Applied to Semiconductor Heterostructures 1996 Les éditions de physique
    • (1996)
    • Bastard, G.1
  • 5
    • 18644371907 scopus 로고    scopus 로고
    • On the Gross–Pitaevski equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments
    • W. Bao P. Markowich C. Schmeiser R. Weishäupl On the Gross–Pitaevski equation with strongly anisotropic confinement: Formal asymptotics and numerical experiments M3AS 15 5 2005 767 782
    • (2005) M3AS , vol.15 , Issue.5 , pp. 767-782
    • Bao, W.1    Markowich, P.2    Schmeiser, C.3    Weishäupl, R.4
  • 6
    • 17144395862 scopus 로고    scopus 로고
    • Semiclassical analysis of the Schrödinger equation with a partially confining potential
    • N. Ben Abdallah F. Méhats Semiclassical analysis of the Schrödinger equation with a partially confining potential J. Math. Pures Appl. 84 2005 580 614
    • (2005) J. Math. Pures Appl. , vol.84 , pp. 580-614
    • Ben Abdallah, N.1    Méhats, F.2
  • 7
    • 33144477052 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation with strong anisotropic harmonic potential
    • N. Ben Abdallah F. Méhats C. Schmeiser R.M. Weishäupl The nonlinear Schrödinger equation with strong anisotropic harmonic potential SIAM J. Math. Anal. 37 1 2005 189 199
    • (2005) SIAM J. Math. Anal. , vol.37 , Issue.1 , pp. 189-199
    • Ben Abdallah, N.1    Méhats, F.2    Schmeiser, C.3    Weishäupl, R.M.4
  • 8
    • 18744400250 scopus 로고    scopus 로고
    • The adiabatic approximation of the Schrödinger Poisson system with a partial confinement
    • N. Ben Abdallah F. Méhats O. Pinaud The adiabatic approximation of the Schrödinger Poisson system with a partial confinement SIAM J. Math. Anal. 36 3 2005 986 1013
    • (2005) SIAM J. Math. Anal. , vol.36 , Issue.3 , pp. 986-1013
    • Ben Abdallah, N.1    Méhats, F.2    Pinaud, O.3
  • 11
    • 0003126597 scopus 로고
    • Espaces fonctionnels associés au calcul de Weyl–Hörmander
    • J.-M. Bony J.-Y. Chemin Espaces fonctionnels associés au calcul de Weyl–Hörmander Bull. Soc. Math. France 122 1 1994 77 118
    • (1994) Bull. Soc. Math. France , vol.122 , Issue.1 , pp. 77-118
    • Bony, J.-M.1    Chemin, J.-Y.2
  • 12
    • 33751059243 scopus 로고    scopus 로고
    • Diffusion dynamics of classical systems driven by an oscillatory force
    • F. Castella P. Degond T. Goudon Diffusion dynamics of classical systems driven by an oscillatory force J. Stat. Phys. 124 2–4 2006 913 950
    • (2006) J. Stat. Phys. , vol.124 , Issue.2–4 , pp. 913-950
    • Castella, F.1    Degond, P.2    Goudon, T.3
  • 13
    • 34250629714 scopus 로고    scopus 로고
    • Large time dynamics of a classical system subject to a fast varying force
    • F. Castella P. Degond T. Goudon Large time dynamics of a classical system subject to a fast varying force Comm. Math. Phys. 276 1 2007 23 49
    • (2007) Comm. Math. Phys. , vol.276 , Issue.1 , pp. 23-49
    • Castella, F.1    Degond, P.2    Goudon, T.3
  • 14
    • 10844227674 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations
    • T. Cazenave Semilinear Schrödinger equations Courant Lect. Notes Math. vol. 10 2003 Amer. Math. Soc. Providence, RI
    • (2003)
    • Cazenave, T.1
  • 15
    • 0003395273 scopus 로고    scopus 로고
    • Spectral Asymptotics in the Semiclassical Limit
    • M. Dimassi J. Sjöstrand Spectral Asymptotics in the Semiclassical Limit London Math. Soc. Lecture Note Ser. vol. 268 1999 Cambridge Univ. Press
    • (1999)
    • Dimassi, M.1    Sjöstrand, J.2
  • 16
    • 0004292725 scopus 로고    scopus 로고
    • Transport in Nanostructures
    • D.K. Ferry S.M. Goodnick Transport in Nanostructures 1997 Cambridge Univ. Press
    • (1997)
    • Ferry, D.K.1    Goodnick, S.M.2
  • 17
    • 0031161337 scopus 로고    scopus 로고
    • Oscillatory perturbations of the Navier–Stokes equations
    • E. Grenier Oscillatory perturbations of the Navier–Stokes equations J. Math. Pures Appl. 76 1997 477 498
    • (1997) J. Math. Pures Appl. , vol.76 , pp. 477-498
    • Grenier, E.1
  • 18
    • 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
  • 19
    • 0039176090 scopus 로고
    • Théorie spectrale pour des opérateurs globalement elliptiques
    • B. Helffer Théorie spectrale pour des opérateurs globalement elliptiques Astérisque 112 1984
    • (1984) Astérisque , vol.112
    • Helffer, B.1
  • 20
    • 12844283991 scopus 로고    scopus 로고
    • Hypoelliptic Estimates and Spectral Theory for Fokker–Planck Operators and Witten Laplacians
    • B. Helffer F. Nier Hypoelliptic Estimates and Spectral Theory for Fokker–Planck Operators and Witten Laplacians Lecture Notes in Math. vol. 1862 2005 Springer-Verlag Berlin
    • (2005)
    • Helffer, B.1    Nier, F.2
  • 21
    • 0001390467 scopus 로고
    • Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
    • B. Helffer D. Robert Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles J. Funct. Anal. 53 3 1983 246 268
    • (1983) J. Funct. Anal. , vol.53 , Issue.3 , pp. 246-268
    • Helffer, B.1    Robert, D.2
  • 22
    • 0003668851 scopus 로고
    • The Analysis of Linear Partial Differential Operators
    • L. Hörmander The Analysis of Linear Partial Differential Operators 1985 Springer
    • (1985)
    • Hörmander, L.1
  • 23
    • 0038586145 scopus 로고    scopus 로고
    • Nonlinear geometrical optics for oscillatory wave trains with a continuous oscillatory spectrum
    • D. Lannes Nonlinear geometrical optics for oscillatory wave trains with a continuous oscillatory spectrum Adv. Differential Equations 6 6 2001 731 768
    • (2001) Adv. Differential Equations , vol.6 , Issue.6 , pp. 731-768
    • Lannes, D.1
  • 24
    • 0003506615 scopus 로고
    • Almost Periodic Functions and Differential Equations
    • B.M. Levitan V.V. Zhikov Almost Periodic Functions and Differential Equations 1982 Cambridge Univ. Press
    • (1982)
    • Levitan, B.M.1    Zhikov, V.V.2
  • 25
    • 0003483212 scopus 로고
    • Multiphase Averaging for Classical Systems. With Applications to Adiabatic Theorems
    • P. Lochak C. Meunier Multiphase Averaging for Classical Systems. With Applications to Adiabatic Theorems Appl. Math. Sci. vol. 72 1988 Springer-Verlag
    • (1988)
    • Lochak, P.1    Meunier, C.2
  • 26
    • 0003994041 scopus 로고    scopus 로고
    • An Introduction to Semiclassical and Microlocal Analysis
    • A. Martinez An Introduction to Semiclassical and Microlocal Analysis Universitext 2002 Springer-Verlag New York
    • (2002)
    • Martinez, A.1
  • 27
    • 0037222786 scopus 로고    scopus 로고
    • Averaging theorems for conservative systems and the weakly compressible Euler equations
    • G. Métivier S. Schochet Averaging theorems for conservative systems and the weakly compressible Euler equations J. Differential Equations 187 1 2003 106 183
    • (2003) J. Differential Equations , vol.187 , Issue.1 , pp. 106-183
    • Métivier, G.1    Schochet, S.2
  • 28
    • 2542585356 scopus 로고    scopus 로고
    • Adiabatic approximation of the Schrödinger–Poisson system with a partial confinement: The stationary case
    • O. Pinaud Adiabatic approximation of the Schrödinger–Poisson system with a partial confinement: The stationary case J. Math. Phys. 45 5 2004 2029 2050
    • (2004) J. Math. Phys. , vol.45 , Issue.5 , pp. 2029-2050
    • Pinaud, O.1
  • 29
    • 0003687441 scopus 로고
    • Methods of Modern Mathematical Physics
    • M. Reed B. Simon Methods of Modern Mathematical Physics 1975 Academic Press New York, San Francisco, London
    • (1975)
    • Reed, M.1    Simon, B.2
  • 30
    • 0003957366 scopus 로고
    • Averaging Methods in Nonlinear Dynamical Systems
    • J.A. Sanders F. Verhulst Averaging Methods in Nonlinear Dynamical Systems Appl. Math. Sci. vol. 59 1985 Springer-Verlag
    • (1985)
    • Sanders, J.A.1    Verhulst, F.2
  • 31
    • 43949155251 scopus 로고
    • Fast singular limits of hyperbolic PDEs
    • S. Schochet Fast singular limits of hyperbolic PDEs J. Differential Equations 114 2 1994 476 512
    • (1994) J. Differential Equations , vol.114 , Issue.2 , pp. 476-512
    • Schochet, S.1
  • 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
  • 33
    • 2942630584 scopus 로고    scopus 로고
    • Adiabatic Perturbation Theory in Quantum Dynamics
    • S. Teufel Adiabatic Perturbation Theory in Quantum Dynamics Lecture Notes in Math. vol. 1821 2003 Springer-Verlag Berlin
    • (2003)
    • Teufel, S.1
  • 34
    • 85120256586 scopus 로고    scopus 로고
    • W.-M. Wang, Pure point spectrum of the Floquet Hamiltonian for the quantum harmonic oscillator under time quasi-periodic perturbations, preprint
  • 35
    • 85120272254 scopus 로고    scopus 로고
    • W.-M. Wang, Quasi-periodic solutions of nonlinearly perturbed quantum harmonic oscillator, preprint
  • 36
    • 0004021335 scopus 로고
    • Functional analysis
    • K. Yosida Functional analysis Grundlehren Math. Wiss. in Einzeldarstellungen vol. 123 1968 Springer
    • (1968)
    • Yosida, K.1


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