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PreprintarXiv licencearXiv

Asymptotic analysis of the dynamical field-field correlation function of the impenetrable Bose gas

  • Frank Göhmann
  • Karol K. Kozlowski
  • Mikhail D. Minin
  • Alexander Weiße
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Abstract

We study the long-time, large-distance asymptotic behaviour of the two-point correlation function of fields of the impenetrable Bose gas in equilibrium states characterized by a quasi-momentum distribution (or filling fraction). This includes, in particular, the cases of Gibbs and generalized Gibbs ensembles. The overall structure of the asymptotic expansion depends on the number of Fermi points, those points for which the quasi-momentum distribution takes the value 1/2. The leading asymptotic behaviour is determined by a relaxation rate, a logarithmic correction term and an amplitude for which we provide simple and explicit expressions. In the case of two Fermi points the first sub-leading correction is calculated as well.

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Cite

BibTeXRIS
BibTeX
@misc{gohmann2026asymptotic,
  title = {{Asymptotic analysis of the dynamical field-field correlation function of the impenetrable Bose gas}},
  author = {Frank Göhmann and Karol K. Kozlowski and Mikhail D. Minin and Alexander Weiße},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08350},
  eprint = {2611.08350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08350},
}
RIS
TY  - UNPB
TI  - Asymptotic analysis of the dynamical field-field correlation function of the impenetrable Bose gas
AU  - Frank Göhmann
AU  - Karol K. Kozlowski
AU  - Mikhail D. Minin
AU  - Alexander Weiße
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08350
UR  - https://arxiv.org/abs/2611.08350
AB  - We study the long-time, large-distance asymptotic behaviour of the two-point correlation function of fields of the impenetrable Bose gas in equilibrium states characterized by a quasi-momentum distribution (or filling fraction). This includes, in particular, the cases of Gibbs and generalized Gibbs ensembles. The overall structure of the asymptotic expansion depends on the number of Fermi points, those points for which the quasi-momentum distribution takes the value 1/2. The leading asymptotic behaviour is determined by a relaxation rate, a logarithmic correction term and an amplitude for which we provide simple and explicit expressions. In the case of two Fermi points the first sub-leading correction is calculated as well.
ER  -