Related papers: Emergence of the Macroscopic Fourier Law from the …

The Fourier law of heat conduction describes heat diffusion in macroscopic systems. This physical law has been experimentally tested for a large class of physical systems. A natural question is to know whether it can be derived from the…

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's…

The onset of Fourier's law in a one-dimensional quantum system is addressed via a simple model of weakly coupled quantum systems in contact with thermal baths at their edges. Using analytical arguments we show that the crossover from the…

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first…

We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…

We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…

Diffusive scaling of position moments and a central limit theorem are obtained for the mean position of a quantum particle hopping on a cubic lattice and subject to a random potential consisting of a large static part and a small part that…

We consider a class of one-dimensional chains of weakly coupled many level systems. We present a theory which predicts energy diffusion within these chains for almost all initial states, if some concrete conditions on their Hamiltonians are…

Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…

We consider a tight-binding Schroedinger equation with time dependent diagonal noise, given as a function of a Markov process. This model was considered previously by Kang and Schenker (J. Stat. Phys., 134(5-6):1005, arXiv:0808.2784), who…

We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…

The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the…

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion…

A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are…

The porous media equation has been proposed as a phenomenological ``non-extensive'' generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming…

We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…

Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the…

We derive a new kinetic and a porous medium equations from the nonlinear Schr\"odinger equation with random potentials. The kinetic equation has a very similar form with the 4-wave turbulence kinetic equation in the wave turbulence theory.…

The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion…

I present a microscopic framework in which quantum phenomena emerge from particle-particle interactions governed by Newton's second law of motion. Within this approach, stationary states and quantized energy spectra arise naturally for the…