We review results on GKSL-type equations with multi-modal generators which are quadratic
in bosonic or fermionic creation and annihilation operators. General forms of such equations …

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a
standard assumption across all of the physical sciences. The Gibbs state is determined just …

A nonlinear Markov evolution is a dynamical system generated by a measure-valued
ordinary differential equation with the specific feature of preserving positivity. This feature …

The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-
free subalgebra is established providing a natural decomposition of a Markovian open …

Förster and modified Redfield theories play one of the central roles in the description of
excitation energy transfer in molecular systems. However, in the present state, these …

In this paper, we study a unified approach for quantum Markov chains (QMCs). A new
quantum Markov property that generalizes the old one, is discussed. We introduce Markov …

The Redfield equation describes the dynamics of a quantum system weakly coupled to one
or more reservoirs and is widely used in theory of open quantum system. However, the …

In these notes we treat problems related to that part of quantum probability dealing with the
theory of dilations of semigroups of completely positive mappings on a unital C∗–algebra …

A three-level quantum system interacting with non-equilibrium environment is investigated.
The stationary state of the system is found (both for non-coherent and coherent environment) …

The classical probability theory initiated by Kolmogorov and its quantum counterpart,
pioneered by von Neumann, were created at about the same time in the 1930s, but …