Geometry and probability on the noncommutative 2-torus in a magnetic field

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI:10.1134/s0040577924080105

M. N. Hounkonnou, F. Melong

引用次数: 0

Abstract

We describe the geometric and probabilistic properties of a noncommutative \(2\)-torus in a magnetic field. We study the volume invariance, integrated scalar curvature, and the volume form by using the operator method of perturbation by an inner derivation of the magnetic Laplacian operator on the noncommutative \(2\)-torus. We then analyze the magnetic stochastic process describing the motion of a particle subject to a uniform magnetic field on the noncommutative \(2\)-torus, and discuss the related main properties.

查看原文本刊更多论文

磁场中的非交换 2-Torus 上的几何与概率

摘要我们描述了磁场中非交换（2\）-torus 的几何和概率性质。我们通过对非交换（2）-torus 上的磁拉普拉斯算子进行内推导，利用扰动算子法研究了体积不变性、积分标量曲率和体积形式。然后，我们分析了描述非交换（2）弦上受均匀磁场作用的粒子运动的磁随机过程，并讨论了相关的主要性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.