Abstract
We determine the rate with which finitely multiple approximations in the Feynman formula converge to the exact expression for the equilibrium density operator of a harmonic oscillator in the linear τ-quantization. We obtain an explicit analytic expression for a finitely multiple approximation of the equilibrium density operator and the related Wigner function. We show that in the class of τ-quantizations, the equilibrium Wigner function of a harmonic oscillator is positive definite only in the case of the Weyl quantization.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 1, pp. 122–137, July, 2012.
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Orlov, Y.N., Sakbaev, V.Z. & Smolyanov, O.G. Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian. Theor Math Phys 172, 987–1000 (2012). https://doi.org/10.1007/s11232-012-0090-x
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DOI: https://doi.org/10.1007/s11232-012-0090-x