Semi-classical limit of a Schrodinger equation for a stratified material

被引：8

作者：

Bechouche, P ^{[1
]}

Poupaud, F ^{[1
]}

机构：

[1] Univ Nice, UMR 6621 CNRS, Lab JA Dieudonne, F-06108 Nice, France

来源：

MONATSHEFTE FUR MATHEMATIK | 2000年 / 129卷 / 04期

关键词：

semiclassical limit; Wigner means uses; Bloch waves; stratified material;

D O I：

10.1007/s006050050076

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the semi-classical limit of the dynamic of electrons in a stratified medium. The medium is assumed to be periodic in one direction and slowly varying in the other directions. In this case, a small parameter epsilon. is introduced and corresponds both to the Planck constant and to scaled lattice thickness. The limit behavior is studied by means of Wigner measures. The limit process is described by infinitely many transport (Vlasov) equations.

引用

页码：281 / 301

页数：21

共 50 条

[1] On the semi-classical limit for the nonlinear Schrodinger equation
Carles, Remi
[J]. STATIONARY AND TIME DEPENDENT GROSS-PITAEVSKII EQUATIONS, 2008, 473 : 105 - 127
[2] Semi-classical limit for the one dimensional nonlinear Schrodinger equation
Felmer, PL
Torres, JJ
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2002, 4 (03) : 481 - 512
[3] Semi-Classical Limit of a Schrödinger Equationfor a Stratified Material
Philippe Bechouche
Frédéric Poupaud
[J]. Monatshefte für Mathematik, 2000, 129 : 281 - 301
[4] Numerical simulation of the semi-classical limit of the focusing nonlinear Schrodinger equation
Bronski, JC
Kutz, JN
[J]. PHYSICS LETTERS A, 1999, 254 (06) : 325 - 336
[5] Semi-classical limit for radial non-linear Schrodinger equation
Castro, R
Felmer, PL
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 256 (02) : 411 - 435
[6] A numerical study of the semi-classical limit of the focusing nonlinear Schrodinger equation
Ceniceros, HD
Tian, FR
[J]. PHYSICS LETTERS A, 2002, 306 (01) : 25 - 34
[7] Stationary Schrodinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions
Arnold, Anton
Negulescu, Claudia
[J]. NUMERISCHE MATHEMATIK, 2018, 138 (02) : 501 - 536
[8] Existence and semi-classical limit of the least energy solution to a nonlinear Schrodinger equation with electromagnetic fields
Kurata, K
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2000, 41 (5-6) : 763 - 778
[9] On the semi-classical limit for the focusing nonlinear Schrodinger equation: sensitivity to analytic properties of the initial data
Clarke, SR
Miller, PD
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2002, 458 (2017): : 135 - 156
[10] Stationary Schrodinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point
Arnold, Anton
Doepfner, Kirian
[J]. CALCOLO, 2019, 57 (01)

← 1 2 3 4 5 →