AN Kolmogorov and J. von Neumann proposed in the 30's two sets of axioms for the
mathematical modelling of random phenomena. In the classical (Kolmogorov) models one …

This article introduces a concept of subharmonic projections for a quantum Markov
semigroup, in view of characterizing the support projection of a stationary state in terms of …

Quantum dynamical semigroups QDS appeared for the first time in the physical literature
during the 1970s motivated by studies on the evolution of open systems. This class of …

The dynamics of Markovian open quantum systems are described by Lindblad master
equations, generating a quantum dynamical semigroup. An important concept for such …

Let be a quantum Markov semigroup on with a faithful normal invariant state ρ. The
decoherence-free subalgebra of is the biggest subalgebra of where the completely positive …

This article introduces a concept of transience and recurrence for a Quantum Markov
Semigroup and explores its main properties via the associated potential. We show that an …

Let be a uniformly continuous quantum Markov semigroup on with generator represented in
a standard GKSL form and a faithful normal invariant state ρ. In this note we give new …

This chapter focuses on the mathematical analysis of nonlinear quantum transport equations
that appear in the modeling of nano-scale semiconductor devices. We start with a brief …

We study a special class of generic quantum Markov semigroups, on the algebra of all
bounded operators on a Hilbert space, arising in the stochastic limit of a generic system …

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 …