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A semiclassical trace formula for the canonical partition function of one dimensional systems

We present a semiclassical trace formula for the canonical partition function of an arbitrary one-dimensional system. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density operator in the coherent state representation. The formalism is valid in the low temperature limit, presenting accurate results in this regime. As illustrations we consider a quartic Hamiltonian that can not be split into kinetic and potential parts, and a system with two local minima.
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