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The exactly solvable Keldysh model of disordered electron system in a randomscattering field with extremely long correlation length is converted to thetime-dependent model with extremely long relaxation. The dynamical problem issolved for the ensemble of two-level systems (TLS) with fluctuating well depthshaving the discrete Z_2 symmetry. It is shown also that the symmetric TLS withfluctuating barrier transparency may be described in terms of the planarKeldysh model with dime-dependent random planar rotations in xy plane havingcontinuous SO(2) symmetry. The case of simultaneous fluctuations of the welldepth and barrier transparency is subject to non-abelian algebra. Applicationof this model to description of dynamic fluctuations in quantum dots andoptical lattices is discussed.

Scalar and vector Keldysh models in the time domain