Time evolution in the multi-component dynamical Keldysh models

M. N. Kiselev

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arXiv · 2610.38338

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 $Z_2$ 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.

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M. N. Kiselev. 2026-10-28. Time evolution in the multi-component dynamical Keldysh models. https://arxiv.org/abs/2610.38338

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