Related papers: Tridiagonal Symmetries of Models of Nonequilibrium…
Discussed is relationship between nonlinearity and symmetry of dynamical models. The special stress is laid on essential, non-perturbative nonlinearity, when none linear background does exist. This is nonlinearity essentially different from…
In these lectures we give an overview of nonequilibrium stochastic systems. In particular we discuss in detail two models, the asymmetric exclusion process and a ballistic reaction model, that illustrate many general features of…
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…
We have found a family of solvable nineteen vertex model with statistical configurations invariant by the time reversal symmetry within a systematic study of the respective Yang-Baxter relation. The Boltzmann weights sit on a degree seven…
We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical"…
We consider Brownian motion on symmetric matrices of octonions, and study the law of the spectrum. Due to the fact that the octonion algebra is nonassociative, the dimension of the matrices plays a special role. We provide two specific…
We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha/n$ or $(1-\alpha)/n$ (resp. $\beta/n$…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
We study relaxation properties of two-body collisions in infinite spatial dimension. We show that this process exhibits multiscaling asymptotic behavior as the underlying distribution is characterized by an infinite set of nontrivial…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is based upon a sharp estimate on the relative…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
Boundary element methods provide powerful techniques for the analysis of problems involving coupled multi-physical response, especially in the linear case for which boundary-only formulations are possible. This paper presents the integral…
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with…
Entropy production and dynamical activity are two complementary aspects in nonequilibrium physics. The asymmetry of cross-correlation, serving as a distinctive feature of nonequilibrium, also finds widespread utility. In this Letter, we…
In recent decades, considerable research has been devoted to partial differential equations (PDEs) with dynamic boundary conditions. However, the physical interpretation of the parameters involved often remains unclear, which in turn limits…