Related papers: Universal late-time dynamics in isolated one-dimen…
We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…
A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal…
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate…
It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the…
The low-energy physics of (quasi)degenerate one-dimensional systems is typically understood as the particle-like dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly non-trivial when the ground states…
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…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a…
The dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics. While the evolution is in general intractable in all its details, relevant observables can become…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored,…
The non-equilibrium spin dynamics of a one-dimensional system of repulsively interacting fermions is studied by means of density-matrix renormalization-group simulations. We focus on the short-time decay of the oscillation amplitudes of the…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
The integrable system is constrained strictly by the conservation law during the time evolution, and the nearly integrable system or nonintegrable system is also constrained by the conserved parameters (like the constants of motion) with…
Recent experimental and theoretical progress as well as the prospect of commercially viable quantum technologies have inspired great interest in the study of open quantum systems and their dynamics. Many open quantum systems are well…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…