Mathematical problems of irreversible statistical mechanics for quantum systems. II: On the singularities of (Ψ(z)−z)−1 and the pseudo‐Markovian equation. Application to Lee model

1982 ◽  
Vol 23 (4) ◽  
pp. 652-658 ◽  
Author(s):  
M. Courbage
Keyword(s):  
Statistical Mechanics ◽  
Quantum Systems ◽  
Lee Model ◽  
Mathematical Problems

Statistical Mechanics: Entropy, Order Parameters, and Complexity

2021 ◽  
Author(s):  
James P. Sethna
Keyword(s):  
Statistical Mechanics ◽  
Topological Defects ◽  
Linear Response Theory ◽  
Continuous Phase ◽  
Quantum Systems ◽  
Order Parameters ◽  
Free Energies ◽  
Onset Of Chaos ◽  
The Social ◽  
Essential Insight

This text distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, active matter, and dynamical systems. Chapters address random walks, equilibrium systems, entropy, free energies, quantum systems, calculation and computation, order parameters and topological defects, correlations and linear response theory, and abrupt and continuous phase transitions. Exercises explore the enormous range of phenomena where statistical mechanics provides essential insight — from card shuffling to how cells avoid errors when copying DNA, from the arrow of time to animal flocking behavior, from the onset of chaos to fingerprints. The text is aimed at graduates, undergraduates, and researchers in mathematics, computer science, engineering, biology, and the social sciences as well as to physicists, chemists, and astrophysicists. As such, it focuses on those issues common to all of these fields, background in quantum mechanics, thermodynamics, and advanced physics should not be needed, although scientific sophistication and interest will be important.

QUASI-MODULAR SYMMETRY AND QUASI-HYPERGEOMETRIC FUNCTIONS IN QUANTUM STATISTICAL MECHANICS OF FRACTIONAL EXCLUSION STATISTICS

1999 ◽  
Vol 13 (29n30) ◽  
pp. 1039-1046 ◽  
Author(s):  
KAZUMOTO IGUCHI ◽  
KAZUHIKO AOMOTO
Keyword(s):  
Statistical Mechanics ◽  
Modular Group ◽  
Hypergeometric Functions ◽  
Chemical Potential ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Quantum Statistical ◽  
Physical Quantities

We investigate a novel symmetry in dualities of Wu's equation: wg(1+w)1-g=eβ(ε-μ) for a degenerate g-on gas with fractional exclusion statistics of g, where β=1/k B T, ∊ the energy, and μ the chemical potential of the system. We find that the particle–hole duality between g and 1/g and the supersymmetric duality between g and 1-g form a novel quasi-modular group of order six for Wu's equation. And we show that many physical quantities in quantum systems with the fractional exclusion statistics can be represented in terms of quasi-hypergeometric functions and that the quasi-modular symmetry acts on these functions.

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