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...

This paper is devoted to investigate the stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation. First, the viscoelastic force is approximated as equivalent stiffness and damping terms, and the original system is replaced by a system...

In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker–Planck equation, and the expressions of stationary probability density function and mean first-passage...

The present paper is devoted to the numerical solution of the Fokker–Planck (FP) equation associated to the Duffing oscillator driven by colored noise. We propose an improved discretization of the standard FP operator-splitting method which renders the scheme unconditionally stable. This...

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation...

This paper is to continue our study on complex beam–beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam–beam interaction model with random forcing [Physica A 336 (2004) 347–360]. The random noise is taken as the form of...

In recent years, many studies have been devoted to complex differential equations (CDE), which appear in very important applications in physics and engineering. This paper aims to investigate one such CDE, containing a random forcing term:...