The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE's main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems i...

Some 20 years ago, in a paper written jointly with Peter Mazur, we presented a discussion of the statistical mechanics of a coupled-oscil lator model of a heat bath. ~1) This model enabled us to obtain the quan tum mechanical form of the Langevin equat ion for a Brownian particle moving in an external potential. Ou r purpose here is to repeat this derivation, using a different, some would say s...

We propose a Langevin model with Coulomb friction. Through the analysis of the corresponding Fokker-Planck equation, we have obtained the steady velocity distribution function under the influence of the external field.

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations...

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. Here we study the simple Schnakenberg model consisting of two molecular species whose concentrations vary and three reversible reactions...

We investigate the Markov property of rough surfaces. Using stochastic analysis, we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy.

This chapter reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite stepsize algorithms, Fourier acceleration, and the relation of the Langevin equation to hybrid stochastic algorithms and hybrid Monte Carlo. Invited chapter to appear in the special supplement “Stochastic Quantiza...

I consider a Langevin equation with field-dependent kernels and investigate supersymmetry of the stochastic generating functional constructed from the Langevin equation. Moreover I describe the stochastic generating functional in terms of a superfield. In the superfield formalism, it becomes clear that the stochastic quantization method with the field-dependent kernel is equivalent to the path-...

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function, and then we study numerically the impact of time-correlated noise on the time evolution of a (1+1)-dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double...

The phase diffusion in a self-sustained oscillator, which produces oscillator’s spectral linewidth, is inherently governed by a nonlinear Langevin equation. Over past 40 years, the equation has been treated with linear approximation, rendering the nonlinearity’s effects unknown. Here we solve the nonlinear Langevin equation using the perturbation method borrowed from quantummechanics, and revea...