Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTime-fractional kinetic equation for the non-Markovian kinetic processes
120
0
0.0
(
0
)
Authors
E. Aydiner
Ask ChatGPT about the research
No Arabic abstract
In this study, we analytically formulated the path integral representation of the conditional probabilities for non-Markovian kinetic processes in terms of the free energy of the thermodynamic system. We carry out analytically the time-fractional kinetic equations for these processes. Thus, in a simple way, we generalize path integral solutions of the Markovian to the non-Markovian cases. We conclude that these pedagogical results can be applied to some physical problems such as the deformed ion channels, internet networks and non-equilibrium phase transition problems.
rate research
Read More
73 -
A. V. Chechkin
, V. Yu. Gonchar (Institute for Theoretical Physics
, n Kharkov. Institute for Single Crystals
1999
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equations of the Brownian motion theory and contain symmetric fractional derivatives over velocity and space, respectively. With the help of these equations we study analytically the processes of linear relaxation in a force - free case and for linear oscillator. For a weakly damped oscillator we also get kinetic equation for the distribution in slow variables. Linear relaxation processes are also studied numerically by solving corresponding Langevin equations with the source which is a discrete - time approximation to a white Levy noise. Numerical and analytical results agree quantitatively.
We obtain a kinetic description of spatially averaged dynamics of particle systems. Spatial averaging is one of the three types of averaging relevant within the Irwing-Kirkwood procedure (IKP), a general method for deriving macroscopic equations from molecular models. The other two types, ensemble averaging and time averaging, have been extensively studied, while spatial averaging is relatively less understood. We show that the average density, linear momentum, and kinetic energy used in IKP can be obtained from a single average quantity, called the generating function. A kinetic equation for the generating function is obtained and tested numerically on Lennard-Jones oscillator chains.
The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time $n$. Few results are known for the persistence $P_0(n)$ in discrete time, except the large time behavior which is characterized by the nontrivial constant $theta$ through $P_0(n)sim theta^n$. Using a modified version of the Independent Interval Approximation (IIA) that we developed before, we are able to calculate $P_0(n)$ analytically in $z$-transform space in terms of the autocorrelation function $A(n)$. If $A(n)to0$ as $ntoinfty$, we extract $theta$ numerically, while if $A(n)=0$, for finite $n>N$, we find $theta$ exactly (within the IIA). We apply our results to three special cases: the nearest neighbor-correlated first order moving average process where $A(n)=0$ for $ n>1$, the double exponential-correlated second order autoregressive process where $A(n)=c_1lambda_1^n+c_2lambda_2^n$, and power law-correlated variables where $A(n)sim n^{-mu}$. Apart from the power-law case when $mu<5$, we find excellent agreement with simulations.
The article is devoted to the dynamics of systems with an anomalous scaling near a critical point. The fractional stochastic equation of a Lanvevin type with the $varphi^3$ nonlinearity is considered. By analogy with the model A the field theoretic model is built, and its propagators are calculated. The nonlocality of the new action functional in the coordinate representation is caused by the involving of the fractional spatial derivative. It is proved that the new model is multiplicatively renormalizable, the Gell-Man-Low function in the one-loop approximation is evaluted. The existence of the scaling behavior in the framework of the $varepsilon$-expansion for a superdiffusion is established.
The system of nonlinear Langevin equations was obtained by using Hamiltonians operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
