Related papers: Time Evolution of Two-Level Systems Driven by Peri…
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover…
Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of…
Graphs offer a generic abstraction for modeling entities, and the interactions and relationships between them. Most real world graphs, such as social and cooperation networks evolve over time, and exploring their evolution may reveal…
We consider the dynamical system created by iterating a morphism of a projective variety defined over the field of fractions of a discrete valuation ring. We study the primitive period of a periodic point in this field in relation to the…
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
In this paper, we investigate the time evolution of entanglement entropy and mutual information for the spatially-infinite systems where we act with a primary operator on the vacuum state and then time-evolve it with the sequence of the…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
The dispersive interaction between a two-level atom and a quantized field is studied. We consider besides a time dependent linear amplification and dissipative processes. In order to solve the master equation for this system, we use…
In this letter we show how to perform a systematic perturbative approach for the mode-coupling theory. The results coincide with those obtained via the replica approach. The upper critical dimension turns out to be always 8 and the…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…