Analytic study of a sequence of path integral approximations for simple quantum systems at low temperature

S. K. Kauffmann, J. Rafelski

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

The sequence of Feynman-Trotter approximations to the thermal Feynman path integral for the simple harmonic oscillator is obtained in an easily analyzable closed form. While it converges pointwise at every non-zero temperature to the quantum thermal propagator, the sequence manifests a highly non-uniform behaviour in the zero temperature limit-every one of its elements tends toward the classical ground state (static equilibrium). For high order elements of the sequence, there is an abrupt "collapse" from the quantum to the classical ground state with falling temperature, a phenomenon which bears a possibly misleading resemblance to a phase transition. It is shown that Feynman-Trotter sequences for many simple systems other than the harmonic oscillator also have all their elements tending to the classical static equilibrium state in the zero temperature limit.

Original languageEnglish (US)
Pages (from-to)157-162
Number of pages6
JournalZeitschrift für Physik C Particles and Fields
Volume24
Issue number2
DOIs
StatePublished - Jun 1 1984
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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