Spectral and strength statistics of chiral Brownian ensemble

Shukla, Pragya

doi:10.1088/1751-8121/abfffb

Cited by 2 publications

(2 citation statements)

References 64 publications

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“…+ c 0 (49) with constant c 0 determined by the initial state of the ensemble. Choosing initial condition with µ → ∞ corresponds to an ensemble of C-matrices with only first column elements as non-zero; this in turn gives Y 0 = c 0 .…”

Section: Numerical Verification Of Complexity Parameter Based Formula...mentioning

confidence: 99%

“…As the reduced density matrix of a random non-ergodic state belongs to a general class of multiparametric Wishart random matrix ensembles, it is necessary to have a prior information about the distribution of their Schmidt eigenvalues and thereby the average behavior of the entanglement measures. While changing system conditions can lead to a multiparametric variation of the ensemble, the latter's evolution in the matrix space is governed by a single functional, referred as the complexity parameter Y; this is briefly discussed in section 2.2 (with details given in [48,49]). This is followed by a derivation of Y dependent growth of the ensemble averaged entanglement entropy R 1 in section 3.1.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement dynamics of multi-parametric random states: a single parametric formulation

Shekhar¹,

Shukla²

2023

J. Phys. A: Math. Theor.

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A non-ergodic quantum state of a complex system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert space. An appropriate representation for the reduced density matrix of such a state is a generalized, multi-parametric Wishart ensemble with unit trace. Our theoretical analysis of these ensembles not only resolves the controversy about the growth rates of the average information entropies of the generic states but also leads to new insights in their entanglement dynamics. While the state itself is multi-parametric, we find that the growth of the average measures can be described in terms of an information-theoretic function, referred as the complexity parameter. The latter in turn leads to a common mathematical formulation of the measures for a wide range of states; it could also act as a possible tool for hierarchical arrangement of the entangled states of different systems.

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Section: Numerical Verification Of Complexity Parameter Based Formula...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Entanglement dynamics of multi-parametric random states: a single parametric formulation

Shekhar¹,

Shukla²

2023

J. Phys. A: Math. Theor.

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Spectral fluctuations of multiparametric complex matrix ensembles: evidence of a single parameter dependence

Ansari,

Shukla

2024

J. Phys. A: Math. Theor.

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We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of effective sparsity among the matrix elements, such ensembles can serve as good models for a wide range of phase transitions e.g. localization to delocalization in non-Hermitian systems or Hermitian to non-Hermitian one. Our analysis reveals a rich behavior hidden beneath the spectral statistics e.g. a crossover of the spectral statistics from Poisson to Ginibre universality class with changing variances for finite matrix size, an abrupt transition for infinite matrix size and the role of complexity parameter, a single functional of all system parameters, as a criteria to determine critical point. We also confirm the theoretical predictions in \cite{psgs, psnh}, regarding the universality of the spectral statistics in non-equilibrium regime of non-Hermitian systems characterized by the complexity parameter.

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Spectral and strength statistics of chiral Brownian ensemble

Cited by 2 publications

References 64 publications

Entanglement dynamics of multi-parametric random states: a single parametric formulation

Entanglement dynamics of multi-parametric random states: a single parametric formulation

Spectral fluctuations of multiparametric complex matrix ensembles: evidence of a single parameter dependence

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