Related papers: Time Scale and Completely Positive Dynamical Evolu…

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…

We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…

We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…

Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…

Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We…

A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…

We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to…

Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian…

The dynamics of an infinite system of point particles in $\mathbb{R}^d$, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of…

The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its…

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…

Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynamics of higher-order out-of-time-order…

We study special systems with infinitely many degrees of freedom with regard to dynamical evolution and fulfillment of constraint conditions. Attention is focused on establishing a meaningful functional framework, and for that purpose,…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

Our work deals with the dynamical system analysis of quintessence dark energy scalar field model with exponential potential. A dynamical system analysis has been applied at the background level. Using suitable transformation of variables,…

The description of an open quantum system's decay almost always requires several approximations as to remain tractable. Here, we first revisit the meaning, domain and seeming contradictions of a few of the most widely used of such…

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…