On statistical mechanics in noncommutative spaces
S. A. Alavi
TL;DR
This paper develops quantum statistical mechanics frameworks for noncommutative spaces, extending classical ensembles to quantum systems with noncommuting coordinates, and illustrates with key physical examples.
Contribution
It introduces the formulation of microcanonical and canonical ensembles in noncommutative spaces, providing a foundation for noncommutative statistical mechanics.
Findings
Established ensemble theories in noncommutative settings
Analyzed electron in magnetic field within noncommutative space
Explored free particle and harmonic oscillator examples
Abstract
We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the framework of noncommutative statistical mechanics : (i). An electron in a magnetic field. (ii). A free particle in a box. (iii). A linear harmonic oscillator.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · advanced mathematical theories · Advanced Operator Algebra Research