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We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of…

This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit…

Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…

In a reaction-diffusion system, fluctuations in both diffusion and reaction events, have important effects on the steady-state statistics of the system. Here, we argue through extensive lattice simulations, mean-field type arguments, and…

Finite temperature lattice QCD is probed by varying the temporal boundary conditions of the fermions. We develop the emerging physical behavior in a study of the quenched case and subsequently present first results for a fully dynamical…

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…

The interplay between interactions and quenched disorder can result in rich dynamical quantum phenomena far from equilibrium, particularly when many-body localization prevents the system from full thermalization. With the aim of tackling…

We consider a Fermi liquid model with density-density as well as quadrupolar forward scattering interactions parametrized by the Landau parameters $F_0$ and $F_2$. Using bosonization and a decimation technique, we compute collective modes…

We study a discrete non-autonomous system whose autonomous counterpart (with the frozen bifurcation parameter) admits a saddle-node bifurcation, and in which the bifurcation parameter slowly changes in time and is characterized by a sweep…

We discuss relaxation in bosonic and fermionic many-particle systems. For integrable systems, the time evolution can cause a dephasing effect, leading for finite subsystems to certain steady states. We give an explicit derivation of those…

Collaboration between interconnected cyber-physical systems is becoming increasingly pervasive. Time-delays in communication channels between such systems are known to induce catastrophic failure modes, like high frequency oscillations in…

The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…

A fundamental problem of out-of-equilibrium physics is the speed at which the order parameter grows upon crossing a phase transition. Here, we investigate the dynamics of ordering in a Fermi gas undergoing a density-wave phase transition…

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain…

The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the…

Nonlinear dynamical systems with time delay are abundant in applications, but are notoriously difficult to analyse and predict because delay-induced effects strongly depend on the form of the nonlinearities involved, and on the exact way…

Time-evolution of open, dissipative quantum system is a stochastic process that consists of a series of quantum jumps that take place at random times. Between quantum jumps quantum system idles for some time in a particular quantum state.…

We consider the motion of a particle, taking into account its interaction with environmental degrees of freedom. The dephasing time is determined by the nature of the environment, and depends on the particle velocity. Our interest is in the…

Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…