Related papers: A version of Aldous' spectral-gap conjecture for t…
The relaxation dynamics of zero range process (ZRP) has always been an interesting problem. In this study, we set up the relationship between ZRP and traps model, and investigate the slow dynamics of ZRP in the framework of traps model.…
We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. By analysing these equations in detail for the…
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…
It has been unknown in kinetic theory whether the linearized Boltzmann or Landau equation with soft potentials admits a spectral gap in the spatially inhomogeneous setting. Most of existing works indicate a negative answer because the…
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…
A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials such as the cuprate high temperature superconductors. Because of its unique momentum-space discrimination,…
Recent angle-resolved photoemission electron spectroscopy (ARPES) experiments demonstrate that the momentum dependence of the spectral gap in underdoped cuprates does not follow a pure $d$-wave form [H. Anzai et a., Nat. Comm. {\bf 4}, 1815…
Aldous and Fill conjectured that the maximum relaxation time for the random walk on a connected regular graph with $n$ vertices is $(1+o(1)) \frac{3n^2}{2\pi^2}$. This conjecture can be rephrased in terms of the spectral gap as follows: the…
One of the most intriguing aspects of cuprates is a large pseudogap coexisting with a high superconducting transition temperature. Here, we study pairing in the cuprates from electron-electron interactions by constructing the pair vertex…
It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage time (FPT). Although essential to…
We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Sz\'asz in connection with understanding heat conduction in a deterministic billiards model. The bound on the…
In this work, we consider the periodic impulse control of a system modeled as a set of linear differential equations. We define a matrix that governs the qualitative behavior of the controlled system. This matrix depends on the period and…
This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…
Recently, we have experimentally demonstrated a continuous loading mechanism for an optical dipole trap from a guided atomic beam [1]. The observed evolution of the number of atoms and temperature in the trap are consequences of the unusual…
We describe the spectral properties of underdoped cuprates as resulting from a momentum-dependent pseudogap in the normal state spectrum. Such a model accounts, within a BCS approach, for the doping dependence of the critical temperature…
We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
We consider zero-range processes in ${\mathbb{Z}}^d$ with site dependent jump rates. The rate for a particle jump from site $x$ to $y$ in ${\mathbb{Z}}^d$ is given by $\lambda_xg(k)p(y-x)$, where $p(\cdot)$ is a probability in…
For the almost Mathieu operator with a small coupling constant, for a series of spectral gaps, we describe the asymptotic locations of the gaps and get lower bounds for their lengths. The results are obtained by analysing a monodromy…
We give a lower bound on the spectral gap for a class of stochastic energy exchange models. In 2011, Grigo et al. introduced the model and showed that, for a class of stochastic energy exchange models with a uniformly positive rate…