Ergodicity breaking and localization.

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Se p 19 99 Supersymmetry approach in the field theory of ergodicity breaking transitions ∗

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...

Weak-ergodicity Breaking in Mean-field Spin-glass Models

Non-Markovian Brownian dynamics and nonergodicity.

We report the breaking of ergodicity for a class of generalized, Brownian motion obeying a non-Markovian dynamics being driven by a generalized Langevin equation (GLE). This very feature originates from a vanishing of the effective friction. A novel quantity b (being uniquely determined from the corresponding memory friction kernel gamma(t)of the GLE) is introduced as a parameter that is capabl...

Ergodicity breaking and parametric resonances in systems with long-range interactions.

We explore the mechanism responsible for the ergodicity breaking in systems with long-range forces. In thermodynamic limit such systems do not evolve to the Boltzmann-Gibbs equilibrium, but become trapped in an out-of-equilibrium quasi-stationary-state. Nevertheless, we show that if the initial distribution satisfies a specific constraint-a generalized virial condition-the quasistationary state...