Related papers: Exact interpolation between Fick and Cattaneo diff…
Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave vector…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
Laplace's first law of errors, which states that the frequency of an error can be represented as an exponential function of the error magnitude, was overlooked for many decades but was recently shown to describe the statistical behavior of…
The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response…
Since the famous 1926 paper by Richardson, the relative diffusion of two particles in a turbulent liquid has attracted a lot of interest. The motion of a single particle on the other hand is usually considered not to be especially…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
The interplay of Umklapp scattering from a periodic potential and other scattering processes determine the conductivity of (quasi) one-dimensional metals. We show that the transport at finite temperature is qualitatively and quantitatively…
In nematic liquid crystals light is strongly scattered from director fluctuations. We are interested in the limit where the incoming light wave is scattered many times. Then, the light transport can be described by a diffusion equation for…
We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…
The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
We introduce a multi-species generalization of the hard-rod gas in which each species has a distinct effective length, and the repulsive scattering shift is set by the smaller of the two colliding rods. We argue that this model shares key…
We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a…
We propose a field-theoretic framework for ideal hydrodynamics of charged relativistic fluids formulated in terms of a complex scalar field defined on a spacelike hypersurface comoving with the fluid. In the normal phase, the dynamics of…
We consider a system of two kinetic equations modelling a multicellular system : The first equation governs the dynamics of cells, whereas the second kinetic equation governs the dynamics of the chemoattractant. For this system, we first…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We study a time-reversed hyperbolic heat conduction problem based upon the Maxwell--Cattaneo model of non-Fourier heat law. This heat and mass diffusion problem is a hyperbolic type equation for thermodynamics systems with thermal memory or…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time…