Silvia Bartolucci, Fabio Caccioli, Francesco Caravelli, Pierpaolo Vivo
SciPost Phys. 11, 088 (2021) ·
published 4 November 2021

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We derive an approximate but explicit formula for the Mean First Passage Time
of a random walker between a source and a target node of a directed and
weighted network. The formula does not require any matrix inversion, and it
takes as only input the transition probabilities into the target node. It is
derived from the calculation of the average resolvent of a deformed ensemble of
random substochastic matrices $H=\langle H\rangle +\delta H$, with $\langle
H\rangle$ rank$1$ and nonnegative. The accuracy of the formula depends on the
spectral gap of the reduced transition matrix, and it is tested numerically on
several instances of (weighted) networks away from the high sparsity regime,
with an excellent agreement.
Salvatore F. E. Oliviero, Lorenzo Leone, Francesco Caravelli, Alioscia Hamma
SciPost Phys. 10, 076 (2021) ·
published 25 March 2021

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We present a systematic construction of probes into the dynamics of
isospectral ensembles of Hamiltonians by the notion of Isospectral twirling,
expanding the scopes and methods of ref.[1]. The relevant ensembles of
Hamiltonians are those defined by salient spectral probability distributions.
The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic
Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal
Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the
Isospectral twirling of several classes of important quantities in the analysis
of quantum manybody systems: Frame potentials, Loschmidt Echos, OTOCs,
Entanglement, Tripartite mutual information, coherence, distance to equilibrium
states, work in quantum batteries and extension to CPmaps. Moreover, we
perform averages in these ensembles by random matrix theory and show how these
quantities clearly separate chaotic quantum dynamics from non chaotic ones.