Langevin model corresponding to the Fokker-Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this cod...

Introduction: an alternative solution to the Schrodinger-Langevin equation is presented, where temporal dependence explained, assuming a Coulomb potential. Finally, trajectory equations are found. Objective: in this paper we contribute by presenting detailed and simple of Schrödinger-Langevin for Materials Methods: using appropriate ansatz, solve equation, finding expected values position momen...

In this paper, we study the diffusive limit of solutions to generalized Langevin equation (GLE) in a periodic potential. Under assumption quasi-Markovianity, obtain sharp longtime equilibration estimates for GLE using techniques from theory hypocoercivity. We then show asymptotic results effective diffusion coefficient small correlation time regime, as well overdamped and underdamped limits. Fi...

Complex probabilities arise in quantum systems where the euclidean action is complex, either because the couplings, or the field variables, are complex. Stochastic quantization using the Langevin equation allows one to study such systems, even though the probabilistic interpretation of the euclidean functional integral measure breaks down. The convergence of long time averages computed with the...

It is shown that all statistical properties of the generalized Langevin equation with Gaussian fluctuations are determined by a single, two-point correlation function. The resulting description corresponds with a stationary, Gaussian, non-Markovian process. Fokker-Planck-like equations are discussed, and it is explained how they can lead one to the erroneous conclusion that the process is nonst...

We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, wh...