相关论文: Markov shift on non-commutative probability

The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra is established providing a naturaldecomposition of a Markovian open quantum system into its noiseless (decoherence-free) and irreducible…

We show that the scaled cumulant generating and large deviation function, associated to a two-state Markov process involving two processes, obey a symmetry relation reminiscent of the fluctuation theorem, independent from any conditions on…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

Building on a model recently proposed by F. Calogero, we postulate the existence of a coherent, long--range universal tremor affecting any stable and confined classical dynamical system. Deriving the characteristic fluctuative unit of…

We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a…

In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum…

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes…

We develop a general framework for the steady-state response of dissipative quantum systems. We concretely derive three different, but equivalent, forms of the quantum response function. We discuss for each of them the role of the…

We investigate some asymptotic properties of general Markov processes conditioned not to be absorbed by moving boundaries. We first give general criteria involving an exponential convergence towards the Q-process, that is the law of the…

We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact…

We present a comprehensive and up to date review on the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of quantum Markovian process as a generalization of the classical…

For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept…

Nonequilibrium statistical physics is concerned with a fundamental problem in physics, the phenomenon of irreversibility, which is not rigorously solved yet. Different approaches to the statistical mechanics of nonequilibrium processes are…

We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…

For a Markov and stationary stochastic process described by the well-known classical master equation, we introduce complex transition rates instead of real transition rates to study the pre-thermal oscillatory behaviour in complex…

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the…

We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…

We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the…

Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show that quantum Markov semigroups on the universal or reduced…

Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we…