论文标题
规范平衡状态的Weyl-Wigner表示
Weyl-Wigner Representation of Canonical Equilibrium States
论文作者
论文摘要
通过Heisenberg的Weyl-Wigner符号和替代操作员的Weyl-Wigner符号，获得了整个二次汉密尔顿的典型热平衡量子状态的Weyl-Wigner表示。在灯芯映射下描述了与这些单位固有相关的经典结构的行为，并揭示了热平衡状态由复杂的符号矩阵完全确定，该基质设置了其所有热力学特性。分析了哈密顿动力学的四类（抛物线，椭圆形，双曲线和Loxodromic）。得出了半经典和高温近似值，并将其与经典和/或二次行为进行了比较。
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.
