相关论文: Bipartite Mean Field Spin Systems. Existence and S…

Collaborative multi-agent robotic systems where agents coordinate by modifying a shared environment often result in undesired dynamical couplings that complicate the analysis and experiments when solving a specific problem or task.…

We consider a quasiclassical model that allows us to simulate the process of spin diffusion and relaxation in the presence of a highly nonuniform magnetic field. The energy of the slow relaxing spins flows to the fast relaxing spins due to…

We prove an upper bound on the maximal rate at which a Hamiltonian interaction can generate entanglement in a bipartite system. The scaling of this bound as a function of the subsystem dimension on which the Hamiltonian acts nontrivially is…

We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is…

Redfield master equation was applied to study the dynamics of an ensemble of interacting pairs of unlike spins at room temperature. This spin quantum system is a workbench quantum model to analyze the relaxation dynamics of a heteronuclear…

We introduce a Hamiltonian for two interacting $su(2)$ spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin…

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual…

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

We study magnetic fluctuations in a system of interacting spins on a lattice at high temperatures and in the presence of a spatially varying magnetic field. Starting from a microscopic Hamiltonian we derive effective equations of motion for…

Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible…

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

We consider a quantum system S interacting sequentially with independent systems E_m, m=1,2,... Before interacting, each E_m is in a possibly random state, and each interaction is characterized by an interaction time and an interaction…

We investigate the zero-temperature and the finite-temperature properties of the two-dimensional antiferromagnetic quantum spin system composed of the s=1/2 and s=1 spins. The spin excitation spectrum as well as the thermodynamic quantities…

This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…

We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a…

We present the full analysis of the normal state of the spin-fermion model near the antiferromagnetic instability in two dimensions. This model describes low-energy fermions interacting with their own collective spin fluctuations, which…

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

We describe a simple model of heterogeneous, interacting agents making decisions between $n\ge 2$ discrete choices. For a special class of interactions, our model is the mean field description of random-field Potts-like models, and is…

In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will…

All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a…