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Quantum Simulation Quantum Thermodynamics

Weyl-Wigner Representation of Canonical Equilibrium States

arXiv
Authors: F. Nicacio

Year

2020

Paper ID

18211

Status

Preprint

Abstract Read

~2 min

Abstract Words

97

Citations

N/A

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.

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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.11674 [2] arXiv https://arxiv.org/abs/2012.11674 [3] Publisher https://arxiv.org/abs/2012.11674

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