Geodesic
Rate of convergence of Feynman approximations of semigroups generated by the~oscillator Hamiltonian
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 122-137

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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 $\tau$-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 $\tau$-quantizations, the equilibrium Wigner function of a harmonic oscillator is positive definite only in the case of the Weyl quantization.
Keywords: finitely multiple approximation, Chernoff theorem, linear quantization, harmonic oscillator, Wigner function.
Mots-clés : Feynman formula 
@article{TMF_2012_172_1_a7,
     author = {Yu. N. Orlov and V. Zh. Sakbaev and O. G. Smolyanov},
     title = {Rate of convergence of {Feynman} approximations of semigroups generated by the~oscillator {Hamiltonian}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {122--137},
     publisher = {mathdoc},
     volume = {172},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_1_a7/}
}
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Yu. N. Orlov; V. Zh. Sakbaev; O. G. Smolyanov. Rate of convergence of Feynman approximations of semigroups generated by the~oscillator Hamiltonian. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 122-137. http://geodesic.mathdoc.fr/item/TMF_2012_172_1_a7/