Related papers: Fluctuations for internal DLA on the Comb
The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as $(\ln t)^{2/3}$ with a…
The interplay of superconductivity and disorder generates a wealth of complex phenomena. In particular, the peculiar structure of diffusive electronic wavefunctions is predicted to increase the superconducting critical temperature in some…
We investigate charge fluctuations in the two-dimensional Hubbard model as a function of doping, interaction strength, next-nearest-neighbor hopping, and temperature within the eight-site dynamical cluster approximation. In the regime of…
Intracellular dynamics in living tissue are dominated by active transport driven by bioenergetic processes far from thermal equilibrium. Intracellular constituents typically execute persistent walks. In the limit of long mean-free paths,…
Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation…
We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is an LQG harmonic ball, which we constructed in a…
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $<x^2 > \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation…
We study the behavior of eight diffuse interstellar bands (DIBs) in different interstellar environments, as characterized by the fraction of hydrogen in molecular form [$f$(H$_2$)], with comparisons to the corresponding behavior of various…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
We construct an ionic lattice background in the framework of Einstein-Maxwell-dilaton theory in four dimensional space time. The optical conductivity of the dual field theory on the boundary is investigated. Due to the lattice effects, we…
I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys.…
A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…
We investigate the relation between thermodynamic and dynamic properties of an associating lattice gas (ALG) model. The ALG combines a three dimensional lattice gas with particles interacting through a soft core potential and orientational…
Heat transport in one-dimensional (1D) momentum-conserving lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in two-dimensional…
We study lattice trees (LTs) and animals (LAs) on the nearest-neighbor lattice $\mathbb{Z}^d$ in high dimensions. We prove that LTs and LAs display mean-field behavior above dimension $16$ and $17$, respectively. Such results have…
Uniform spanning trees are a statistical model obtained by taking the set of all spanning trees on a given graph (such as a portion of a cubic lattice in d dimensions), with equal probability for each distinct tree. Some properties of such…
We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the…
We introduce a phenomenological theory of dislocation motion appropriate for two dimensional lattices. A coarse grained description is proposed that involves as primitive variables local lattice rotation and Burgers vector densities along…
We describe theoretical models for the recent experimental observation of Macroscopic Quantum Self-Trapping (MQST) in the transverse dynamics of an ultracold bosonic gas in a 2D lattice. The pure mean-field model based on the solution of…
We analyze the equilibrium fluctuations of the density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow…