相关论文: Cutoff Phenomenon for Cyclic Dynamics on Hypercube

We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time $N\ln(N)$. Then, we study the induced classical process on the real line and compute its atoms and density. This…

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…

The time irreversible evolution of the two-nucleus spin systems interacting with a magnetic field is analyzed in the framework of the subdynamics theory. The spin systems are determined by the H(1) and C(13) nuclei. The investigation is…

In the last decades the problem of metastability has been attacked on rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper. It is then useful to understand connections between different…

We couple a massive spin 2 particle to electromagnetism. By introducing new, redundant degrees of freedom using the Stueckelberg formalism, we extract an intrinsic, model independent UV cutoff of the effective field theory describing this…

We consider the most general single-spin-flip dynamics for the ferromagnetic Ising chain with nearest-neighbour influence and spin reversal symmetry. This dynamics is a two-parameter extension of Glauber dynamics corresponding respectively…

Motivated by recent prototypes of engineered atomic spin devices, we study a fully connected system of $N$ spins $1/2$, modeled by the Lipkin-Meshkov-Glick (LMG) model of a collective spin $s=N/2$ in the presence of Markovian dissipation…

The wavefunction of a single spin system in a prepared initial state evolves to equilibrium with a heat bath. The average spin $$q(t) = p_{\uparrow}(t) - p_{\downarrow}(t)$$ exhibits a characteristic time for this evolution. With the proper…

We give an example of a transient reversible Markov chain that almost surely has only a finite number of cutpoints. We explain how this is relevant to a conjecture of Diaconis and Freedman and a question of Kaimanovich. We also answer…

We evaluate the spin squeezing dynamics of N independent spin-1/2 particles with exchange symmetry. Each spin interacts with its own reservoir, and the reservoirs are independently and identical. The spin squeezing parameter is analytically…

This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…

We consider the irreducibility of switch-based Markov chains for the approximate uniform sampling of Hamiltonian cycles in a given undirected dense graph on $n$ vertices. As our main result, we show that every pair of Hamiltonian cycles in…

We study the simple random walk on trees and give estimates on the mixing and relaxation time. Relying on a recent characterization by Basu, Hermon and Peres, we give geometric criteria, which are easy to verify and allow to determine…

For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker-Planck dynamics involving an arbitrary force $F(x)$ and an arbitrary diffusion coefficient $D(x)$,…

We numerically investigate the stability of exceptional periodic classical trajectories in rather generic chaotic many-body systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates…

In this work, we study the driven-dissipative dynamics of a coherently-driven spin ensemble with a squeezed, superradiant decay. This decay consists of a sum of both raising and lowering collective spin operators with a tunable weight. The…

One-spin and two-spin in a thermodynamic limit spin-1/2 chain as open quantum systems are considered. The dynamics of system is generated by XX Heisenberg interaction and three-spin interaction (TSI) among all the nearest three spins in the…

We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold $X$. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting…

This paper establishes that an exactly optimal rule for Bayesian Quickest Change Detection (QCD) of Markov chains is a threshold test on the no change posterior. We also provide a computationally efficient scalar filter for the no change…

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…