Quantization of non-Hamiltonian and dissipative systems

被引：55

作者：

Tarasov, VE ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Skobeltsyn Inst Nucl Phys, Theoret High Energy Phys Dept, Moscow 119899, Russia

来源：

PHYSICS LETTERS A | 2001年 / 288卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

quantum mechanics; canonical quantization; quantum dissipative systems;

D O I：

10.1016/S0375-9601(01)00548-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables is a specific case of suggested quantization. This approach allows to define consistent quantization procedure for non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator with friction (generalized Lorenz-Rossler-Leipnik-Newton equation), the Fokker-Planck-type system and Lorenz-type system are considered. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：173 / 182

页数：10

共 50 条

[1] Quantization of Hamiltonian and non-Hamiltonian systems
Rashkovskiy, Sergey A.
COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2023, 15 (02): : 267 - 288
[2] Quantization of non-Hamiltonian physical systems
Bolivar, AO
PHYSICAL REVIEW A, 1998, 58 (06): : 4330 - 4335
[3] Semiclassical quantization of non-Hamiltonian dynamical systems without memory
Vol, E. D.
PHYSICAL REVIEW A, 2006, 73 (06):
[4] Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems
Barth, A. M.
Vagov, A.
Axt, V. M.
PHYSICAL REVIEW B, 2016, 94 (12)
[5] Nontwist non-Hamiltonian systems
Altmann, E. G.
Cristadoro, G.
Pazo, D.
PHYSICAL REVIEW E, 2006, 73 (05):
[6] NON-HAMILTONIAN SCHRODINGER SYSTEMS
Lucente, Sandra
Montefusco, Eugenio
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2013, 6 (03): : 761 - 770
[7] On the quantization of sectorially Hamiltonian dissipative systems
Castagnino, M.
Gadella, M.
Lara, L. P.
CHAOS SOLITONS & FRACTALS, 2009, 42 (01) : 94 - 100
[8] HAMILTONIAN DESCRIPTION AND QUANTIZATION OF DISSIPATIVE SYSTEMS
ENZ, CP
FOUNDATIONS OF PHYSICS, 1994, 24 (09) : 1281 - 1292
[9] Non-Hamiltonian molecular dynamics: Generalizing Hamiltonian phase space principles to non-Hamiltonian systems
Tuckerman, ME
Liu, Y
Ciccotti, G
Martyna, GJ
JOURNAL OF CHEMICAL PHYSICS, 2001, 115 (04): : 1678 - 1702
[10] THE STOCHASTIC APPROACH FOR NON-HAMILTONIAN SYSTEMS
TZANI, R
THEORETICAL AND MATHEMATICAL PHYSICS, 1994, 100 (01) : 916 - 920

← 1 2 3 4 5 →