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In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
By using large-scale molecular dynamics simulations, the dynamics of two-dimensional (2D) supercooled liquids turns out to be dependent on the system size, while the size dependence is not pronounced in three dimensional (3D) systems. It is…
We discuss spontaneous breaking of continuum symmetries, whose generators do explicitly depend on the spacetime coordinates. We clarify the relation between broken symmetries and elastic variables at both zero and finite temperatures,…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
In this work, we introduce long range version of the extended Hubbard model. The system is defined on a non-uniform lattice. We show that the system is integrable. The ground state, the ground state energies, the energy spectrum are also…
We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite…
We illustrate the scope of Time Dependent Density Functional Theory (TDDFT) for strongly correlated (lattice) models out of equilibrium. Using the exact many body time evolution, we reverse engineer the exact exchange correlation (xc)…
In this paper we consider some concepts of exponential splitting for nonautonomous linear discrete-time systems. These concepts are generalizations of some well-known concepts of (uniform and nonuniform) exponential dichotomies. Connections…
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
Results of the idealized mode-coupling theory for the structural relaxation in suspensions of hard-sphere colloidal particles are presented and discussed with regard to recent light scattering experiments. The structural relaxation becomes…
We describe an exactly solvable model which illustrates the Fluctuation Theorem and other predictions for systems evolving far from equilibrium. Our model describes a particle dragged by a spring through a thermal environment. The rate at…
Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output…
In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
We consider the strength-duration relationship in one-dimensional spatially extended excitable media. In a previous study [Idris and Biktashev 2008] set out to separate initial (or boundary) conditions leading to propagation wave solutions…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…