Heisenberg Dynamics for Non Self-Adjoint Hamiltonians: Symmetries and Derivations

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2022-12-19 DOI:10.1007/s11040-022-09443-4

F. Bagarello

引用次数: 2

Abstract

In some recent literature the role of non self-adjoint Hamiltonians, \(H\ne H^\dagger \), is often considered in connection with gain-loss systems. The dynamics for these systems is, most of the times, given in terms of a Schrödinger equation. In this paper we rather focus on the Heisenberg-like picture of quantum mechanics, stressing the (few) similarities and the (many) differences with respected to the standard Heisenberg picture for systems driven by self-adjoint Hamiltonians. In particular, the role of the symmetries, *-derivations and integrals of motion is discussed.

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非自伴随哈密顿量的Heisenberg动力学:对称性和推导

在最近的一些文献中，非自伴随哈密顿量\(H\ne H^\dagger \)的作用经常被认为与得失系统有关。大多数情况下，这些系统的动力学是用Schrödinger方程给出的。在本文中，我们将重点放在量子力学的类海森堡图像上，强调由自伴随哈密顿量驱动的系统与标准海森堡图像的(少数)相似和(许多)不同。特别讨论了运动的对称性、*导数和积分的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.