2 Networks of binary neurons 5 2.1 Neural information processing is noisy . . . . . . . . . . . . . 5 2.2 Stochastic binary neurons and networks . . . . . . . . . . . . . 11 2.2.1 Parallel dynamics: Little model . . . . . . . . . . . . . 13 2.2.2 Sequential dynamics . . . . . . . . . . . . . . . . . . . 13 2.3 Some properties of Markov processes . . . . . . . . . . . . . . 14 2.3.1 Eigenvalue s...

Pugh and Shub [PS3] have conjectured that essential accessibility implies ergodicity, for a C2, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C1+γ partially hyperbolic systems.

When a map is classically uniquely ergodic, it is expected that its quantization will posses quantum unique ergodicity. In this paper we give examples of Quantum Unique Ergodicity for the perturbed Kronecker map, and an upper bound for the rate of convergence.

The weak ergodicity breaking induced by quantum many-body scars (QMBSs) represents an intriguing concept that has received great attention in recent years due to its relation unusual nonequilibrium behavior. Here, we reveal this phenomenon can occur a particular regime of lattice gauge theory, where QMBSs emerge the presence extensive number local constraints. In particular, analyzing gauged Ki...

Ergodicity of the systems with Nosé-Hoover thermostat are studied. The dynamics of the heatbath variables are investigated and they can be periodic when the system has quick oscillation. The periodic behaviour of them causes the system to lose its ergodicity. The kinetic-moments method is also studied, and the heatbath variables in this method are found to be chaotic. The chaotic behaviour make...

Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will \inherit" the geometric ergo...

The supersymmetry (SUSY) self–consistent approximation for the model of non–equilibrium thermodynamic system with quenched disorder is derived by making use of generalized second Legendre transformation. The equations for adiabatic and isothermal susceptibilities, memory and field induced parameters and the temperature of ergodicity breaking transition are obtained on the basis of asymptotic an...

Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will \inherit" the geometric ergo...