Analyzing the dependence of finite-fold approximations of the harmonic oscillator equilibrium density matrix and of the Wigner function on the quantization prescription

DOI10.1007/s11232-015-0311-1zbMath1325.81076OpenAlexW1416907031MaRDI QIDQ746993

Yu. N. Orlov, L. A. Borisov

Publication date: 22 October 2015

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-015-0311-1

zbMATH Keywords

density matrixharmonic oscillatorChernoff theoremFeynman approximationquantization rule

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Schrödinger and Feynman-Kac semigroups (47D08)

Related Items (5)

Cauchy problem for a new aggregation-fragmentation model in the case of equal reaction rate constants ⋮ Generalized evolution equation of Wigner function for an arbitrary linear quantization ⋮ Chernoff equivalence for shift operators, generating coherent states in quantum optics ⋮ On the inversion formula of linear quantization and the evolution equation for the Wigner function ⋮ On the generalization of moyal equation for an arbitrary linear quantization

Cites Work

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• Rate of convergence of Feynman approximations of semigroups generated by the oscillator Hamiltonian
• Feynman formulas as a method of averaging random Hamiltonians
• Chernoff's theorem and discrete time approximations of Brownian motion on manifolds
• Note on product formulas for operator semigroups
• Hamiltonian Feynman path integrals via the Chernoff formula
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• An Operator Calculus Having Applications in Quantum Electrodynamics

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