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PreprintCC BY 4.0arXiv

Time evolution in the multi-component dynamical Keldysh models

  • M. N. Kiselev
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Abstract

We construct a time evolution operator for a dynamical quantum models with a multi-component random Gaussian field characterized by a long correlation time. We analyze three paradigmatic cases: non-Abelian SU(2) symmetry class for the three-component Gaussian noise and Abelian symmetry classes U(1) and Z2 for the two- and one-component noises correspondingly. Starting with a limiting case of the infinite correlation time (Keldysh model) we shown that statistics of the two-component random field with a non-zero mean is described by the Rice distribution. We derived and solved the system of coupled linear differential equations for the exact diagonal and off-diagonal single-particle Green's functions. We showed how the finite time correlation in Keldysh models are accounted by a continuous fractions method.

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Cite

BibTeXRIS
BibTeX
@misc{kiselev2026time,
  title = {{Time evolution in the multi-component dynamical Keldysh models}},
  author = {M. N. Kiselev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38338},
  eprint = {2610.38338},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38338},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Time evolution in the multi-component dynamical Keldysh models
AU  - M. N. Kiselev
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38338
UR  - https://arxiv.org/abs/2610.38338
AB  - We construct a time evolution operator for a dynamical quantum models with a multi-component random Gaussian field characterized by a long correlation time. We analyze three paradigmatic cases: non-Abelian SU(2) symmetry class for the three-component Gaussian noise and Abelian symmetry classes U(1) and Z_2 for the two- and one-component noises correspondingly. Starting with a limiting case of the infinite correlation time (Keldysh model) we shown that statistics of the two-component random field with a non-zero mean is described by the Rice distribution. We derived and solved the system of coupled linear differential equations for the exact diagonal and off-diagonal single-particle Green's functions. We showed how the finite time correlation in Keldysh models are accounted by a continuous fractions method.
ER  -