Related papers: A Kac Model with Exclusion
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…
Recent cosmological observations, such as the measurement of the primordial 4He abundance, CMB, and large scale structure, give preference to the existence of extra radiation component, Delta N_nu > 0. The extra radiation may be accounted…
We prove that the solution of the Kac analogue of Boltzmann's equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
In this paper, we study a system of $M$ particles interacting with a reservoir of $N$ particles, where $N >> M$, and compare this setup to one where the $M$-particle system interacts with a thermostat of infinite particles. Our goal is to…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
We study an extension of the standard model with one latticized extra dimension accessible to all fields. The model is characterized by the size of the extra dimension and the number of sites, and contains a tower of massive particles. At…
A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of…
The intrinsic excitation energy of fission fragments is dynamically evaluated in terms of the time dependent pairing equations. These equations are corroborated with two conditions. One of them fixes the number of particles and the another…
We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of $N$ particles, with the aim of quantifying how fast these degrees of freedom become chaotic in a time scale in…
For all $k$, we construct a bijection between the set of sequences of non-negative integers ${\bf a}=(a_i)_{i\in{\bf Z}_{\geq0}}$ satisfying $a_i+a_{i+1}+a_{i+2}\leq k$ and the set of rigged partitions $(\lambda,\rho)$. Here…
Inclusive single jet production in hadron collisions is considered. It is shown that the QCD parton model predicts a nonmonotonic dependence of the inclusive cross section on the fraction of the energy deposited in the jet registered, if it…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We extend the one-pair Cooper configuration towards Bardeen-Cooper-Schrieffer (BCS) model of superconductivity by adding one-by-one electron pairs to an energy layer where a small attraction acts. To do it, we solve Richardson's equations…
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…