江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目: Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder
報告人: Francesco Ferraro
Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy, G. Galilei, University of Padova, Padova, Italy
報告時間: Thursday 24/10 at 19:30
報告地點: https://unipd.zoom.us/my/francesco.ferraro
報告摘要: We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as “annealed,” in contrast to quenched disorder in which couplings are fixed in time. We extend Dynamical Mean-Field Theory to accommodate annealed disorder and employ it to find the exact solution of the linear model in the limit of a large number of degrees of freedom. Our analysis yields analytical results for the non-stationary auto-correlation, the stationary variance, the power spectral density, and the phase diagram of the model. Interestingly, some unexpected features emerge upon changing the correlation time of the interactions. The stationary variance of the system and the critical variance of the disorder are generally found to be a non-monotonic function of the correlation time of the interactions. We also find that in some cases a re-entrant phase transition takes place when this correlation time is varied.