scholarly journals On Quantum Statistical Mechanics: A Study Guide

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Wladyslaw Adam Majewski
Keyword(s):  
Statistical Mechanics ◽  
Statistical Physics ◽  
Algebraic Approach ◽  
Quantum Statistical Mechanics ◽  
Quantum Correlations ◽  
New Formalism ◽  
Mathematical Structures ◽  
Infinite Dimensional ◽  
Quantum Statistical ◽  
Large Quantum

We provide 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 statistical mechanics, quantum field theory, and quantum correlations are discussed.

scholarly journals Entanglement and algebraic independence in fermion systems

2014 ◽  
Vol 12 (02) ◽  
pp. 1461002 ◽  
Author(s):  
Fabio Benatti ◽  
Roberto Floreanini
Keyword(s):  
Statistical Mechanics ◽  
Algebraic Independence ◽  
Algebraic Approach ◽  
Quantum Statistical Mechanics ◽  
Creation And Annihilation Operators ◽  
Fermion Systems ◽  
Quantum Statistical ◽  
Local Observables ◽  
Typical Instance ◽  
Algebraic Formulation

In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between operators from subalgebras localized in spatially disjoint regions. While this algebraic approach is straightforward for bosons, in the case of fermions it is subtler since one has to distinguish between micro-causality, that is the anti-commutativity of the basic creation and annihilation operators, and algebraic independence that is the commutativity of local observables. We argue that a consistent algebraic formulation of separability and entanglement should be compatible with micro-causality rather than with algebraic independence.

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