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Quantum Physics
Title: Weyl-Wigner Representation of Canonical Equilibrium States
(Submitted on 21 Dec 2020 (v1), last revised 12 Jan 2021 (this version, v2))
Abstract: 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.
Submission history
From: Fernando Nicacio Prof. Dr. [view email][v1] Mon, 21 Dec 2020 20:41:28 GMT (195kb,D)
[v2] Tue, 12 Jan 2021 13:54:16 GMT (195kb,D)
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