Weyl–Wigner representation of canonical equilibrium states

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