Related papers: Weak-Memory Dynamics in Discrete Time
We study nonequilibrium cascades in which fragile bound or coherent structures are formed through intermediate states rather than by direct equilibration. Motivated by light-nuclei production in relativistic heavy-ion collisions and by…
We consider systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending on the past history of the process itself. Such coefficients…
Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: what other…
Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…
Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however,…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
We introduce history-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying Hamiltonian of the walker to include couplings with memory-keeping agents. We next numerically study the…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
A short-time dynamic approach to weak first order phase transitions is proposed. Taking the 2-dimensional Potts models as examples, from short-time behaviour of non-equilibrium relaxational processes starting from high temperature and zero…
We examine the emergence of dynamical memory effects in quantum processes having indefinite time direction and causal order. In particular, we focus on the class of phase-covariant qubit channels, which encompasses some of the most…
We consider the evolution of logistic maps under long-term memory. The memory effects are characterized by one parameter \alpha. If it equals to zero, any memory is absent. This leads to the ordinary discrete dynamical systems. For \alpha =…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
We investigate the quantum ratchet effect under the influence of weak dissipation which we treat within a Floquet-Markov master equation approach. A ratchet current emerges when all relevant symmetries are violated. Using time-reversal…
Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…
Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order $\alpha>0$, we obtain discrete maps with power-law memory.…
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…
We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown…