THERMODYNAMICAL POTENTIALS OF CLASSICAL AND QUANTUM SYSTEMS

被引：4

作者：

Liu, Ruikuan ^{[1
]}

Ma, Tian ^{[1
]}

Wang, Shouhong ^{[2
]}

Yang, Jiayan ^{[3
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

[2] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[3] Southwest Med Univ, Sch Med Informat & Engn, Luzhou 646000, Sichuan, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 04期

基金：

美国国家科学基金会;

关键词：

Potential-descending principle; order parameters; control parameters; SO(3) symmetry; spinor representation; PVT system; N-component system; magnetic system; dielectric system; Bose-Einstein condensates (BEC); superfluid; superconductor; liquid helium-4; liquid helium-3; BOSE-EINSTEIN CONDENSATION; VORTEX; GAS;

D O I：

10.3934/dcdsb.2018214

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of the paper is to systematically introduce thermodynamic potentials for thermodynamic systems and Hamiltonian energies for quantum systems of condensates. The study is based on the rich previous work done by pioneers in the related fields. The main ingredients of the study consist of 1) SO(3) symmetry of thermodynamical potentials, 2) theory of fundamental interaction of particles, 3) the statistical theory of heat developed recently [23], 4) quantum rules for condensates that we postulate in Quantum Rule 4.1, and 5) the dynamical transition theory developed by Ma and Wang [20]. The statistical and quantum systems we study in this paper include conventional thermodynamic systems, thermodynamic systems of condensates, as well as quantum condensate systems. The potentials and Hamiltonian energies that we derive are based on first principles, and no mean-field theoretic expansions are used.

引用

页码：1411 / 1448

页数：38

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