Onset of universality in the dynamical mixing of a pure state
- URL: http://arxiv.org/abs/2109.10495v2
- Date: Sat, 12 Nov 2022 13:11:10 GMT
- Title: Onset of universality in the dynamical mixing of a pure state
- Authors: M. Carrera-N\'u\~nez, A. M. Mart\'inez-Arg\"uello, J. M. Torres, E. J.
Torres-Herrera
- Abstract summary: We study the time dynamics of random density matrices generated by evolving the same pure state.
We show that the spectral statistics of the resulting mixed state is well described by random matrix theory.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study the time dynamics of random density matrices generated by evolving
the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians.
We show that the spectral statistics of the resulting mixed state is well
described by random matrix theory (RMT) and undergoes a crossover from the GOE
to the Gaussian unitary ensemble (GUE) for short and large times respectively.
Using a semi-analytical treatment relying on a power series of the density
matrix as a function of time, we find that the crossover occurs in a
characteristic time that scales as the inverse of the Hilbert space dimension.
The RMT results are contrasted with a paradigmatic model of many-body
localization in the chaotic regime, where the GUE statistics is reached at
large times, while for short times the statistics strongly depends on the
peculiarity of the considered subspace.
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