Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian

被引：10

作者：

Orlov, Yu N. ^{[1
]}

Sakbaev, V. Zh ^{[2
]}

Smolyanov, O. G. ^{[3
]}

机构：

[1] RAS, MV Keldysh Appl Math Inst, Moscow 117901, Russia

[2] Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow Oblast, Russia

[3] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2012年 / 172卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

finitely multiple approximation; Feynman formula; Chernoff theorem; linear quantization; harmonic oscillator; Wigner function; POSITION-DEPENDENT MASS; FORMULAS; PARTICLES; INTEGRALS;

D O I：

10.1007/s11232-012-0090-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We determine the rate with which finitely multiple approximations in the Feynman formula converge to the exact expression for the equilibrium density operator of a harmonic oscillator in the linear tau-quantization. We obtain an explicit analytic expression for a finitely multiple approximation of the equilibrium density operator and the related Wigner function. We show that in the class of tau-quantizations, the equilibrium Wigner function of a harmonic oscillator is positive definite only in the case of the Weyl quantization.

引用

页码：987 / 1000

页数：14

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