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We consider a charged Brownian gas under the influence of external and non uniform electric, magnetic and mechanical fields, immersed in a non uniform bath temperature. With the collision time as an expansion parameter, we study the…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
The Brownian dynamics of the density operator for a quantum system interacting with a classical heat bath is described using a stochastic, non-linear Liouville equation obtained from a variational principle. The environment's degrees of…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
When analyzing the particle-like excitations in quantum field theory it is natural to regard the field mode corresponding to the particle momentum as an open quantum system, together with the opposite momentum mode. Provided that the state…
Our Recent advancements in stochastic processes have illuminated a paradox associated with the Einstein model of Brownian motion. The model predicts an infinite propagation speed, conflicting with the second law of thermodynamics. The…
Just at the beginning of quantum stochastic calculus Hudson and Parthasarathy proposed a quantum stochastic Schrodinger equation linked to dilations of quantum dynamical semigroups. Such an equation has found applications in physics, mainly…
The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes like decoherence, dissipation, particle creation, noise and fluctuation. We treat the case…
We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the…
The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…
Adsorption is a relevant process in many fields, such as product manufacturing or pollution remediation in porous materials. Adsorption takes place at the molecular scale, amenable to be modeled by Lagrangian numerical methods. We have…
We study the movement of the living organism in a band form towards the presence of chemical substrates based on a system of partial differential evolution equations. We incorporate Einstein's method of Brownian motion to deduce the…
We consider a linear Boltzmann equation that arises in a model for quantum friction. It describes a particle that is slowed down by the emission of bosons. We study the stochastic process generated by this Boltzmann equation and we show…
We investigate chains of interacting spinless fermions subject to a finite external field $F$ (also called Stark chains) and focus on the regime where the charge thermalization follows the subdiffusive hydrodynamics. First, we study reduced…
The Brownian motion of a single particle is a paradigmatic model of the nonequilibrium dynamics of dissipative systems. In the system-plus-reservoir approach, one can derive the particle's equations of motion from the reversible dynamics of…
A fully quantum treatment of Einstein's Brownian motion is given, showing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
The Green-Kubo relation, the Einstein relation, and the fluctuation-response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these…
Motivated by the wide range of applicability of the fluctuation and dissipation phenomena in non-equilibrium systems, we provide a universal study scheme for the dissipation of the energy and the corresponding Brownian motion analysis of…
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction…