Mean-field approximation of quantum systems and classical limit

被引：37

作者：

Graffi, S ^{[1
]}

Martinez, A

Pulvirenti, M

机构：

[1] Univ Bologna, Dipartmento Matemat, I-40126 Bologna, Italy

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2003年 / 13卷 / 01期

关键词：

mean field approximation; classical limit; Vlasov equation; Hartree equation;

D O I：

10.1142/S0218202503002386

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that, for a smooth two-body potential, the quantum mean-field approximation to the nonlinear Schrodinger equation of the Hartree type is stable at the classical limit h --> 0, yielding the classical Vlasov equation.

引用

页码：59 / 73

页数：15

共 50 条

[21] Mean-Field Limit and Semiclassical Expansion of a Quantum Particle System
Federica Pezzotti
Mario Pulvirenti
[J]. Annales Henri Poincaré, 2009, 10 : 145 - 187
[22] THE MEAN-FIELD LIMIT OF QUANTUM BOSE GASES AT POSITIVE TEMPERATURE
Froehlich, Juerg
Knowles, Antti
Schlein, Benjamin
Sohinger, Vedran
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, : 955 - 1030
[23] Memory effects in classical and quantum mean-field disordered models
L. F. Cugliandolo
G. Lozano
H. Lozza
[J]. The European Physical Journal B - Condensed Matter and Complex Systems, 2004, 41 : 87 - 96
[24] Memory effects in classical and quantum mean-field disordered models
Cugliandolo, L
Lozano, G
Lozza, H
[J]. EUROPEAN PHYSICAL JOURNAL B, 2004, 41 (01): : 87 - 96
[25] The mean-field approximation in quantum electrodynamics: The no-photon case
Hainzl, Christian
Lewin, Mathieu
Solovej, Jan Philip
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2007, 60 (04) : 546 - 596
[26] Quantized mean-field approximation
Brooksby, C
Prezhdo, OV
[J]. CHEMICAL PHYSICS LETTERS, 2001, 346 (5-6) : 463 - 469
[27] Pickl's proof of the quantum mean-field limit and quantum Klimontovich solutions
Ben Porat, Immanuel
Golse, Francois
[J]. LETTERS IN MATHEMATICAL PHYSICS, 2024, 114 (02)
[28] Mean-field theory of the transverse-field Ising spin glass in the classical limit
Li, MS
Walasek, K
Cieplak, M
[J]. PHYSICAL REVIEW B, 1997, 56 (18): : 11715 - 11720
[29] Pickl’s proof of the quantum mean-field limit and quantum Klimontovich solutions
Immanuel Ben Porat
François Golse
[J]. Letters in Mathematical Physics, 114
[30] Instantaneous control of interacting particle systems in the mean-field limit
Burger, Martin
Pinnau, Rene
Totzeck, Claudia
Tse, Oliver
Roth, Andreas
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 405

← 1 2 3 4 5 →