2019/08/18 by Phil Attard, Attard, Phil
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1908.06373
openalex publication_date 2019/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial differential equation in temperature and space is given for this. The linear solution is obtained explicitly, which is valid at high and intermediate temperatures, or at low densities. An algorithm for solving the full non-linear problem is given. Symmetrization effects accounting for particle statistics are also written as a series of effective many-body potentials, of which the pair term is dominant at terrestrial densities. Casting these quantum functions as pair-wise additive, temperature-dependent, effective potentials enables the established techniques of classical statistical mechanics to be applied to quantum systems. The quantum Ornstein-Zernike equation is given as an example.