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Condensed Matter > Disordered Systems and Neural Networks

Title:Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

Abstract: We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the probability of finding the initial state after time $t$. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that $R(t)$ can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of $R(t)$ with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of $R(t\to\infty)=k$, finite in the thermodynamic limit $N\rightarrow\infty$, which approaches $k=R(t\to 0)$ in this limit.
Comments: 21 pages, 12 figures, 61 references
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
Journal reference: SciPost Phys. 6, 014 (2019)
DOI: 10.21468/SciPostPhys.6.1.014
Cite as: arXiv:1805.06472 [cond-mat.dis-nn]
  (or arXiv:1805.06472v4 [cond-mat.dis-nn] for this version)

Submission history

From: Ivan Khaymovich [view email]
[v1] Wed, 16 May 2018 18:00:22 UTC (440 KB)
[v2] Thu, 1 Nov 2018 17:05:18 UTC (483 KB)
[v3] Fri, 28 Dec 2018 12:37:22 UTC (547 KB)
[v4] Fri, 11 Jan 2019 07:25:07 UTC (548 KB)