Scalar and vector Keldysh models in the time domain

TL;DR

This paper introduces time-domain versions of the scalar and vector Keldysh models to describe disordered electron systems and two-level systems with fluctuating parameters, providing exact solutions and discussing applications in quantum dots and optical lattices.

Contribution

It develops time-dependent Keldysh models for disordered systems with long correlation times, including non-abelian cases, and connects these models to physical systems like quantum dots.

Findings

Exact solutions for time-dependent Keldysh models.

Description of TLS with fluctuating well depths and barriers.

Application to quantum dots and optical lattices.

Abstract

The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z_2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the planar Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. The case of simultaneous fluctuations of the well depth and barrier transparency is subject to non-abelian algebra. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed.