Mathematical Sciences: Some Problems in Statistical Mechanics

首席研究员将继续研究统计力学中的各种问题。特别是，他将研究铁磁性的海森堡模型，以表明在低温下，该模型的自由能近似于完美玻色气体的自由能。他还将研究具有短程相互作用的高密度经典气体模型和多体库仑系统的基态能量。统计力学的基本目标是通过粒子之间微观相互作用的知识来获得多粒子系统的大尺度热力学行为。首席研究员将验证几个关于气体的近似理论，这些理论适用于涉及超流体和超导的现象。

The principal investigator will continue his studies of various problems in statistical mechanics. In particular, he will study the Heisenberg model for ferromagnetism, in order to show that at low temperature the free energy of this model approximates the free energy of a perfect Bose gas. He will also work on models of high density classical gases with short-range interaction and on ground state energies of many-body Coulomb systems. The basic aim of statistical mechanics is to obtain the large scale thermodynamic behavior of a many-particle system from a knowledge of the microscopic interactions between the particles. The principal investigator will validate several approximate theories concerning gases that have applicability to phenomena involving superfluidity and superconductivity.