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arXiv · 1904.02716

From ergodic to non-ergodic chaos in Rosenzweig-Porter model

M. Pino·J. Tabanera·P. Serna
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Abstract

The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus on several quantities that exhibit non-analytical behaviour and show that they obey the scaling hypothesis. Based on this, we argue that non-ergodic chaotic and ergodic regimes are separated by a continuous phase transition, similarly to the transition between non-ergodic chaotic and localized phases.

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M. Pino, J. Tabanera, P. Serna. 2019-04-04. From ergodic to non-ergodic chaos in Rosenzweig-Porter model. https://doi.org/10.1088/1751-8121%2Fab4b76

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