2018/11/05 by Phil Attard, Attard, Phil
Computer Science · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1811.02032
openalex publication_date 2018/11/05 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
The von Neumann trace form of quantum statistical mechanics is transformed to\nan integral over classical phase space. Formally exact expressions for the\nresultant position-momentum commutation function are given. A loop expansion\nfor wave function symmetrization is also given. The method is tested for\nquantum harmonic oscillators. For both the boson and fermion cases, the grand\npotential and the average energy obtained by numerical quadrature over\nclassical phase space are shown to agree with the known analytic results. A\nmean field approximation is given which is suitable for condensed matter, and\nwhich allows the quantum statistical mechanics of interacting particles to be\nobtained in classical phase space.\n