Related papers: Generalized quantum Fokker-Planck, diffusion and S…
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the…
In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function…
We study Brownian motion driven with both conservative and nonconservative external forces. By using the thermodynamic approach of the theory of Brownian motion we obtain the Fokker-Planck equation and derive expressions for the Fluctuation…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals to the de Broglie…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
This article has to do with the derivation and solution of the Fokker--Planck equation associated to the momentum-independent Wigner function, of a particle subjected to a harmonic external field and immersed in a ohmic thermal bath of…
Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatial decoherence are special cases of an elegant class of Markovian quantum Brownian motion models that is invariant under linear symplectic transformations. Here we…
Simulating electron-nucleus coupled dynamics poses a non-trivial challenge and an important problem in the investigation of ultrafast processes involving coupled electronic and vibrational dynamics. Because irreversibility of the system…
A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem…
The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…
In this work, we analyze the relaxation of a classical spin interacting with a heat bath, starting from the fully dynamical Hamiltonian description. An analogous problem in the framework of generalized Langevin equation (GLE) with anomalous…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville…
On the basis of a coherent state representation of quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002);…
It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets…