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Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

by G. De Tomasi, M. Amini, S. Bera, I. M. Khaymovich, V. E. Kravtsov

This Submission thread is now published as SciPost Phys. 6, 014 (2019)

Submission summary

As Contributors: Mohsen Amini · Ivan Khaymovich
Arxiv Link: https://arxiv.org/abs/1805.06472v4 (pdf)
Date accepted: 2019-01-22
Date submitted: 2019-01-14 01:00
Submitted by: Khaymovich, Ivan
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical

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.

Ontology / Topics

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Random matrix theory (RMT)

Published as SciPost Phys. 6, 014 (2019)



Author comments upon resubmission

Dear Editor,

We are grateful to all the Referees for their comments and efforts in order to improve our manuscript.
Hereby we resubmit the manuscript with all requested changes.

Sincerely yours,
Giuseppe De Tomasi, Mohsen Amini, Soumya Bera , Ivan M. Khaymovich and Vladimir E. Kravtsov.

List of changes

1) Page 3: the comment about Ref. [12] has been corrected according to the suggestion of the Referee 2 and the corresponding reference [13] has been added.
2) Page 3: the footnote referring to arXiv:1812.10283 (Ref. [15]) has been added according to the optional suggestion of the Referee 2.
3) The relevant recent references [14, 25-28] have been added with the corresponding comments in pages 3, 18.
4) Some minor language corrections have been included throughout the text.

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