The theory of stochastic dynamics of an inhomogeneous quantum system is being explored in this work by calculating the decay rate from a metastable state of a Brownian particle under the influence of quantum state-dependent friction and diffusion. We begin with the appropriate c-number...

By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Q=1−q defined...

We deal with the 3D inviscid Leray-α model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves conservation of energy. The result holds for the initial...

We study the influence of multiplicative random external perturbation on the Selkov model exhibiting limit cycles. The dynamics are described by stochastic differential equations. The numerically computed ensemble averages of the concentrations exhibit temporal localization of the limit cycles...

In this work, we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power-law tail. The proposed circuit design is a variant of a recently introduced one based on a differential equation with both multiplicative and additive noises. Here,...

A multiplicative noise and an additive noise are introduced in the kinetic model of Smolen–Baxter–Byrne [P. Smolen, D.A. Baxter, J.H. Byrne, Amer. J. Physiol. Cell. Physiol. 274 (1998) 531], in which the expression of gene is controlled by protein concentration of transcriptional activator....

We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model...

We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow algebraically with time before the dissipative time scale...