Related papers: On time-local generators of quantum evolution

We discuss fundamental features of the local expression for the entropy production rate of the nonequilibrium quantum dynamics of open systems and its relations to memory effects and the spectrum of the generator of the dynamics. Defining…

Entropy, and its temporal evolution, play a central role in the foundations of quantum theory and in modern quantum technologies. Here we study, in particular, the relations between the --- in general, non-Markovian --- evolution of an open…

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator…

These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…

An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input…

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…

The problem is considered of describing the dynamics of quantum systems generated by a nonlocal in time interaction. It is shown that the use of the Feynman approach to quantum theory in combination with the canonical approach allows one to…

Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical…

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…

Non-Markovian effects in quantum evolution appear when the system is strongly coupled to the environment and interacts with it for long periods of time. To include memory effects in the master equations, one usually incorporates time-local…

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body…

We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…

Open quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time…

Convolutionless and convolution master equations are the two mostly used physical descriptions of open quantum systems dynamics. We subject these equations to time deformations: local dilations and contractions of time scale. We prove that…

We address the problem of quantifying the non-Markovian character of quantum time-evolutions of general systems in contact with an environment. We introduce two different measures of non-Markovianity that exploit the specific traits of…

A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…

We study the concepts of complete positivity, positivity and non-Markovianity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the…

Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum…

We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…