标题： 规范平衡态的威尔-维格纳表示 显示英文标题

标题： Weyl-Wigner Representation of Canonical Equilibrium States

摘要： 规范热平衡量子态的Weyl-Wigner表示通过Heisenberg和元射算子的Weyl-Wigner符号的Wick旋转获得，适用于整个二次哈密顿量类。 在Wick映射下描述了这些幺正算子固有的经典结构的行为，揭示出热平衡态完全由一个复辛矩阵确定，该矩阵决定了其所有热力学性质。 分析了四类哈密顿动力学（抛物型、椭圆型、双曲型和螺旋型）。 推导并比较了半经典和高温近似与经典和/或二次行为。 显示英文摘要

摘要： The Weyl-Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the Weyl-Wigner symbols of Heisenberg and metaplectic operators. The behavior of classical structures inherently associated to these unitaries is described under the Wick mapping, unveiling that a thermal equilibrium state is fully determined by a complex symplectic matrix, which sets all of its thermodynamical properties. The four categories of Hamiltonian dynamics (Parabolic, Elliptic, Hyperbolic, and Loxodromic) are analyzed. Semiclassical and high temperature approximations are derived and compared to the classical and/or quadratic behavior.