Naslov
Spontaneous Ergodicity Breaking in Invariant Matrix Models

Autori
Franchini, Fabio

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Humboldt College: Science and educational challenges facing Europe in the next decade, On the occasion of the 250th anniversary of the birth of Alexander von Humboldt (1769-1859)

Mjesto i datum
Zagreb, Hrvatska, 10.10.2019. - 11.10.2019

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Random Matrices ; Ergodicity Breaking ; Spontaneous Symmetry Breaking

Sažetak
Many physical systems are ergodic, meaning that, over time, they sample most allowed physical states. Ergodicity is a central tenant for thermodynamics, as it provide meaning to the concept of equilibrium. However, certain systems are not ergodic and thus posses peculiar and important properties. Non-ergodic systems are typically harder to study. Here, we propose a new approach to the study of ergodicity breaking and localization, based on an abstract formulation that can disclose powerful computational techniques. Such formulation is grounded in the field of random matrix theory, but moves beyond the standard assumption that invariant models describe only extended (ergodic) systems. We show that deviations of the eigenvalue statistics from the Wigner-Dyson universality reflects itself on the eigenvector distribution. In particular, gaps in the eigenvalue density spontaneously break the rotational symmetry of the model to a smaller one, hence rendering the system not ergodic anymore. Models with log-normal weights, recently considered also in string theory models such as ABJM theories, show a critical eigenvalue distribution which indicates a critical breaking of the symmetry. While the main motivation for this approach is the description of the critical phase of a disordered conductive systems (Anderson Metal/Insulator transition), the underlying picture is very general: the spontaneous breaking of rotational symmetry corresponds to clustering of different physical degrees of freedom, which, not being equivalent anymore, prevent the exploration of the whole configurational space.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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