We construct a delta-kicked model for the quantum ratchet effect. Two symmetric flashing potentials alternately act on a particle with a symmetric and homogeneous initial state of zero momentum. Ratchet currents emerge when quantum resonances are excited. We give some results and compare our...

We investigate a time-asymmetric delta-kicked model for the quantum ratchet effect, in which a flashing potential acts on a particle at unequal time intervals. Ratchet currents emerge when quantum resonances are excited. The currents in time-asymmetric models may be stronger than those found in...

A Parrondo game is a counterintuitive game where two losing games can be combined to form a winning game. We construct a quantum version of a Parrondo game based on a quantum ratchet effect for a delta-kicked model, which can be realized in optical lattices. A game set is presented and a quantum...

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether...

Most previous investigations on spatial Public Goods Game assume that individuals treat neighbors equivalently, which is in sharp contrast with realistic situations, where bias is ubiquitous. We construct a model to study how a selective investment mechanism affects the evolution of cooperation....

Time delay, accounting for constant incubation period or sojourn times in an infective state, widely exists in most biological systems like epidemiological models. However, the effect of time delay on spatial epidemic models is not well understood. In this paper, spatial pattern of an epidemic...

One of the central issues in epidemiology is the study of the distribution of disease. And time delay widely exists in the process of disease spread. Thus, in this paper, we presented an epidemic model with spatial diffusion and time delay. By mathematical analysis, we find two different types...