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TMF, 1999, Volume 119, Number 2, Pages 308–331 (Mi tmf741)  

This article is cited in 4 scientific papers (total in 4 papers)

Low-temperature quasi-classical approximation for quantum macroscopic phenomena

V. S. Yarunin

Joint Institute for Nuclear Research

Abstract: Quantum systems with two distinct time scales for “fast” (quantum) and “slow” (quasi-classical) degrees of freedom with the respective frequencies $\Omega$ and $\omega\ll\Omega$ are considered. A general path-integral representation for a partition function involves ordinary coherent states for Bose and Fermi degrees of freedom as well as generalized coherent states for a nontrivial algebra of variables. Path-integral averaging over “fast” variables results in a nonlocal (in imaginary time) effective action for a “slow” (quasi-classical) variable, which becomes local in the low-temperature approximation. This low-temperature adiabatic path-integral approach, expressed by the inequality $\beta\Omega\gg1\gg\omega/\Omega$, yields an appropriate basis for a subsequent quasi-classical description. Theories of three complex condensed matter systems are developed with the “slow” and “fast” subsystems represented by localized and band electrons in the lattice Anderson model, by condensate and noncondensate bosons in the Bogoliubov model (with broken translational symmetry), and by soft-mode phonons and electrons induced in large molecules by an electron–phonon optical transition. The corresponding quantum macroscopic phenomena are the Kondo-type reorganization of the spectrum of correlated electrons, Bose condensation in nonuniform media, and chaotization of the phonon spectrum in molecules.

DOI: https://doi.org/10.4213/tmf741

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English version:
Theoretical and Mathematical Physics, 1999, 119:2, 640–659

Bibliographic databases:

Received: 02.10.1998

Citation: V. S. Yarunin, “Low-temperature quasi-classical approximation for quantum macroscopic phenomena”, TMF, 119:2 (1999), 308–331; Theoret. and Math. Phys., 119:2 (1999), 640–659

Citation in format AMSBIB
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\paper Low-temperature quasi-classical approximation for quantum macroscopic phenomena
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\jour Theoret. and Math. Phys.
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\vol 119
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\pages 640--659
\crossref{https://doi.org/10.1007/BF02557356}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Baranov, DB, “Trapped Bose condensate in a gravitational field”, JETP Letters, 71:6 (2000), 266  crossref  adsnasa  isi  scopus  scopus  scopus
    2. Baranov, D, “Gravity and light in trapped Bose-condensate”, Journal of Low Temperature Physics, 119:3–4 (2000), 461  crossref  adsnasa  isi
    3. Yarunin, VS, “Translationally noninvariant path integral for Bose–Einstein condensate”, Physics of Atomic Nuclei, 64:12 (2001), 2212  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    4. Correggi M., Falconi M., “Effective Potentials Generated By Field Interaction in the Quasi-Classical Limit”, Ann. Henri Poincare, 19:1 (2018), 189–235  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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