On quantum statistical mechanics; A study guide

@article{Majewski2016OnQS,
  title={On quantum statistical mechanics; A study guide},
  author={Wladyslaw A. Majewski},
  journal={arXiv: Mathematical Physics},
  year={2016}
}
  • W. Majewski
  • Published 24 August 2016
  • Physics
  • arXiv: Mathematical Physics
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems, and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite dimensional structures. As an illustration, a quantization of stochastic processes, new formalism for… 
On entropy for general quantum systems
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent
Integral and differential structures for quantum field theory
The aim of this work is to demonstrate the efficacy of the non-commutative calculus for quantum field theory. In so doing, we will consider the application of integrable and differential structures
Quantum Fokker–Planck Dynamics
The Fokker-Planck equation is a partial differential equation which is a key ingredient in many models in physics. This paper aims to obtain a quantum counterpart of Fokker-Planck dynamics, as a

References

SHOWING 1-10 OF 89 REFERENCES
Quantum correlations; quantum probability approach
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical
QUANTUM STOCHASTIC DYNAMICS II
We shortly review the progress in the domain of stochastic dynamics for quantum spin systems on a lattice. We also present some new results obtained in the framework of noncommutative ${\mathbb L}_p$
On Quantum Stochastic Dynamics and Noncommutative Lp Spaces
We show that using the thermodynamic limit, one can give a simple and natural construction of noncommutative Lp spaces for quantum systems on a lattice. Within this framework, we discuss the
On quantum stochastic dynamics and noncommutative $$\mathbb{L}_p $$ spaces
AbstractWe show that using the thermodynamic limit, one can give a simple and natural construction of noncommutative $$\mathbb{L}_p $$ spaces for quantum systems on a lattice. Within this framework,
On Applications of Orlicz Spaces to Statistical Physics
We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. The pair of Orlicz spaces we
Postulates for General Quantum Mechanics
We present in this paper a set of postulates for a physical system and deduce from these the main general features of the quantum theory of stationary states. Our theory is strictly operational in
Construction and Ergodicity of Dissipative Dynamics for Quantum Spin Systems on a Lattice
We show that for a large class of interactions there exist translation-invariant dissipative dynamics which satisfy the detailed balance condition (in the associated noncommutative symmetric space),
Quantum Stochastic Dynamics I : Spin Systems on a Lattice
In the context of non-commutative IL p spaces we discuss the conditions for existence and ergodicity of translation invariant stochastic spin ip and diiusion dynamics for quantum spin systems with
Integral and differential structures for quantum field theory
The aim of this work is to demonstrate the efficacy of the non-commutative calculus for quantum field theory. In so doing, we will consider the application of integrable and differential structures
Why Are Orlicz Spaces Useful for Statistical Physics
We review a new formalism based on Orlicz spaces for the description of large regular statistical systems. Our presentation includes both classical and quantum systems. This approach has the
...
1
2
3
4
5
...