Reducibility of the Linear Quantum Harmonic Oscillators Under Quasi-periodic Reversible Perturbation

被引：0

作者：

Lou, Zhaowei ^{[1
]}

Sun, Yingnan ^{[1
]}

Wu, Youchao ^{[2
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Sch Math, MIIT Key Lab Math Modelling & High Performance Com, Nanjing 211106, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 05期

基金：

芬兰科学院; 中国国家自然科学基金;

关键词：

Reducibility; Quantum harmonic oscillator; KAM; Reversible vector field; UNBOUNDED PERTURBATIONS; SCHRODINGER-EQUATION; KAM; SPECTRUM;

D O I：

10.1007/s12346-024-01067-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the reducibility of a class of linear coupled quantum harmonic oscillator systems under time quasi-periodic, non-Hamiltonian, reversible perturbations. This essentially means that for most values of the frequency vector, these systems can be reduced to autonomous reversible systems with constant coefficients with respect to time. Our proof relies on an application of Kolmogorov-Arnold-Moser (KAM) theory for infinite dimensional reversible systems.

引用

页数：28

共 30 条

[1] KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation [J].

Baldi, Pietro ;

Berti, Massimiliano ;

Montalto, Riccardo .

MATHEMATISCHE ANNALEN, 2014, 359 (1-2) :471-536

[2] Reducibility of 1-d Schrodinger equation with unbounded time quasiperiodic perturbations. III [J].

Bambusi, D. ;

Montalto, R. .

JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (12)

[3] Reducibility of 1-d Schrodinger Equation with Time Quasiperiodic Unbounded Perturbations, II [J].

Bambusi, D. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017, 353 (01) :353-378

[4] Time quasi-periodic unbounded perturbations of Schrodinger operators and KAM methods [J].

Bambusi, D ;

Graffi, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 219 (02) :465-480

[5]

Bambusi D, 2019, ANN HENRI POINCARE, V20, P1893, DOI 10.1007/s00023-019-00795-2

[6] REDUCIBILITY OF THE QUANTUM HARMONIC OSCILLATOR IN d-DIMENSIONS WITH POLYNOMIAL TIME-DEPENDENT PERTURBATION [J].

Bambusi, Dario ;

Grebert, Benoit ;

Maspero, Alberto ;

Robert, Didier .

ANALYSIS & PDE, 2018, 11 (03) :775-799

[7] REDUCIBILITY OF 1-D SCHRODINGER EQUATION WITH TIME QUASIPERIODIC UNBOUNDED PERTURBATIONS. I [J].

Bambusi, Dario .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (03) :1823-1865

[8] KAM for Reversible Derivative Wave Equations [J].

Berti, Massimiliano ;

Biasco, Luca ;

Procesi, Michela .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 212 (03) :905-955

[9]

COURANT R, 1953, METHODS MATH PHYS, V1

[10] On Reducibility of Schrodinger Equations with Quasiperiodic in Time Potentials [J].

Eliasson, Hakan L. ;

Kuksin, Sergei B. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 286 (01) :125-135

← 1 2 3 →