Special Issue on Non-Ergodicity in dynamical systems
• 大类 : 物理 - 3区
• 小类 : 数学跨学科应用 - 3区
• 小类 : 物理：数学物理 - 3区
• 小类 : 物理：综合 - 3区
Physical properties of statistical systems are often determined under the assumption that the underlying dynamics is ergodic, so that one can replace time- with ensemble-averages and thereby make use of the powerful tools of equilibrium statistical mechanics. In the recent years, however, evidence has progressively accumulated both in classical and quantum physics that the evolution may remain localized within restricted areas of the phase space for arbitrarily large time, thereby giving rise to several nontrivial phenomena. In this sense, ergodicity breaking need not to extend to infinite time scales for being physically relevant: it can manifest itself as metastable or quasi-stationary states.
Glasses represent the most famous setup where lack of ergodicity has been recognized as a key element for the understanding of physical properties. In general, however, non-ergodic behaviour is not necessarily traced back to the presence of energetic or entropic barriers; it can also be due to dynamical effects which give rise to an effectively small coupling. This special issue is devoted to these latter effects, ranging from the lack of ergodicity observed in the the pioneering numerical experiment of Fermi, Pasta, Ulam and Tsingou, to the recent evidence of non-ergodic/bad metal behavior observed in the high temperature regimes of networks of Josephson junctions, which have opened venues for the search of novel dynamical features related to ergodic breaking in quantum and classical interacting many-body systems.
Understanding the dynamical mechanisms that lead to non-ergodicity remains, however, a difficult task, since no general tools exist to analyse them. This special issue is focused on this topic, aiming to collect recent advances in ergodicity breaking in dynamical systems, including many-body systems (classical and quantum) and stochastic processes. The two main goals are: a) to provide an interdisciplinary selection of novel results; b) to collect methods typically used within different scientific communities.
• Ergodicity and non-ergodicity in classical and quantum many-body systems
• Physical aspects of non-ergodic dynamics: slow relaxation, metastability and emergent phenomena
• Nekhoroshev estimates and adiabatic invariants in Hamiltonian systems
• continuous and discrete stochastic process
• many-body localization, metastability in quantum systems