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A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
We have attempted to describe the rapidity and transverse momentum spectra, simultaneously, of the hadrons produced in the Ultra-relativistic Nuclear Collisions. This we have tried to achieve in a single statistical thermal freeze-out model…
This paper uses Lie symmetry methods to analyze boundary crossing probabilities for a large class of diffusion processes. We show that if Fokker--Planck--Kolmogorov equation has non-trivial Lie symmetry, then boundary crossing identity…
A discussion is presented of results with identified particles at the Large Hadron Collider. Possible deviations from the standard statistical distributions are investigated by considering in detail results obtained using the Tsallis…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…
We discuss resonance recombination for quarks and show that it is compatible with quark and hadron distributions in local thermal equilibrium. We then calculate realistic heavy quark phase space distributions in heavy ion collisions using…
A model with non-uniform flow in the longitudinal direction is proposed for the relativistic heavy-ion collisions and compared with the 14.6 A GeV/c Si-Al and 10.8 A GeV/c Au-Au collision data. The stronger influence of transparency on the…
A heuristic approach for collisionless perpendicular diffusion of energetic particles is presented. Analytic forms for the corresponding diffusion coefficient are derived. The heuristic approach presented here explains the parameter $a^2$…
A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure…
We present algorithms to solve relativistic hydrodynamics in 3+1--dimensional situations without apparent symmetry to simplify the solution. In simulations of heavy--ion collisions, these numerical schemes have to deal with the physical…
The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The…
The transverse momentum distributions of the identified particles produced in small collision systems at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) have been analyzed by four models. The first two models…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
A relativistic kinetic Fokker-Planck equation that has been recently proposed in the physical literature is studied. It is shown that, in contrast to other existing relativistic models, the one considered in this paper is invariant under…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…