Related papers: Conservation Laws and Integrability of a One-dimen…
Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by…
The ergodicity postulate, a foundational pillar of Gibbsian statistical mechanics predicts that a periodically driven (Floquet) system in the absence of any conservation law heats to a featureless `infinite temperature' state. Here, we…
We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden "quasiconservation laws", in which certain higher…
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…
We introduce a two-dimensional walk model in which a random walker can only move on the first quarter of a two-dimensional plane. We calculate the partition function of this walk model using a transfer matrix method and show that the model…
Density matrix embedding theory (Phys. Rev. Lett. 109, 186404 (2012)) and density embedding theory ((Phys. Rev. B 89, 035140 (2014)) have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work,…
We have studied dimerized spin systems by realizing the cluster expansion to high order. We have extended our previous dimer expansion for one-dimensional systems to cover weakly interacting chains for a quantitative description of three…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…
The diffraction of fast atoms at crystal surfaces is ideal for a detailed investigation of the surface electronic density. However, instead of sharp diffraction spots, most experiments show elongated streaks characteristic of inelastic…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…
Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating…
We study driven particle systems with excluded volume interactions on a two-lane ladder with periodic boundaries, using Monte Carlo simulation, cluster mean-field theory, and numerical solution of the master equation. Particles in one lane…
We construct a non reversible exclusion process with Bernoulli product invariant measure and having, in the diffusive hydrodynamic scaling, a non symmetric diffusion matrix, that can be explicitly computed. The antisymmetric part does not…
Diffusion of particles in complex fluids and gels is difficult to describe and often lies beyond the scope of the classical Stokes-Einstein relation. One of the main lines of research over the past few decades has sought to relate…
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of…
As a generalization of deterministic, nonlinear conservative dynamical systems, a notion of {\em canonical conservative dynamics} with respect to a positive, differentiable stationary density $\rho(x)$ is introduced: $\dot{x}=j(x)$ in which…
A typical linear open system is often defined as a component of a larger conservative one. For instance, a dielectric medium, defined by its frequency dependent electric permittivity and magnetic permeability is a part of a conservative…