Eigenfunction statistics of Wishart Brownian ensembles

Shukla, Pragya

doi:10.1088/1751-8121/aa8bd7

Cited by 9 publications

(17 citation statements)

References 93 publications

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“…(6.14.21) in section 6.14 of [21], a hierarchical diffusion equation for R n can be derived by a direct integration of eq. (1) over N − n eigenvalues and entire eigenvector space (also see section 8 of [23] or [20,24,25] for more information). The specific case of R 1 (e) was discussed in detail in [15]; it varies at a scale Y ∼ N ∆ 2 e .…”

Section: Criticality Of Spectral Statistics and Eigenfunctionsmentioning

confidence: 99%

“…IPR-distribution or two-point wave-function correlations [6]. A complexity parameter based formulation for these measures is discussed in [15,20,25]. N .…”

Section: Criticality Of Spectral Statistics and Eigenfunctionsmentioning

confidence: 99%

“…Presence of disorder makes it necessary to consider an ensemble of such Hamiltonians; assuming the Gaussian disorder in on-site energies (and/or interaction strengths, hopping etc) and by representing the non-random matrix elements by a limiting Gaussian, the ensemble density, say ρ(H) with H as the Hamiltonian, was described in [15] by a multi-parametric Gaussian distribution, with uncorrelated or correlated matrix elements. Using the complexity parameter formulation discussed in detail in [16][17][18][19][20], the statistics of ρ(H) can then be mapped to that of a single parametric Brownian ensemble (BE) appearing between Poisson and Wigner-Dyson ensemble [20][21][22][23][24][25] (also equivalent to Rosenzweig-Porter model [26]). The mapping is achieved by identifying a rescaled complexity parameter of the BE with that of the disordered band.…”

Section: Introductionmentioning

confidence: 99%

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Disorder perturbed flat bands. II. Search for criticality

Shukla

2018

Phys. Rev. B

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We present a common mathematical formulation of the level statistics of a disordered tightbinding lattice, with one or many flat bands in clean limit, in which system specific details enters through a single parameter. The formulation, applicable to both single as well as many particle flat bands, indicates the possibility of two different types of critical statistics: one in weak disorder regime (below a system specific disorder strength) and insensitive of the disorder-strength, another in strong disorder regime and occurs at specific critical disorder strengths. The single parametric dependence however relates the statistics in the two regimes (notwithstanding different scattering conditions therein). This also helps in revealing an underlying universality of the statistics in weakly disordered flat bands, shared by a wide-range of other complex systems irrespective of the origin of their complexity.

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Section: Criticality Of Spectral Statistics and Eigenfunctionsmentioning

confidence: 99%

“…IPR-distribution or two-point wave-function correlations [6]. A complexity parameter based formulation for these measures is discussed in [15,20,25]. N .…”

Section: Criticality Of Spectral Statistics and Eigenfunctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Disorder perturbed flat bands. II. Search for criticality

Shukla

2018

Phys. Rev. B

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“…Consider an ensemble of N a × N rectangular matrices A(t) = √ f (A 0 + tV (t)) with f = (1 + γ t 2 ) −1 [8,9] with A 0 as a fixed matrix and γ as an arbitrary positive constant.…”

Section: B Wishart Orthogonal Ensemble (Woe)mentioning

confidence: 99%

“…multi-parameter dependent sparse random matrix ensembles, brownian ensembles etc [4][5][6][7]. The present study analyses the ensemble averaged mdos in the spectrum edge of a many particle system that consists of many non-interacting particles, with their fluctuation properties described by Gaussian or Wishart ensembles of both stationary/ non-stationary types [8,9].…”

Section: Introductionmentioning

confidence: 99%

Many body density of states in the edge of the spectrum: non-interacting limit

Shukla

2022

Preprint

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Spectral and strength statistics of chiral Brownian ensemble

Shukla¹

2021

J. Phys. A: Math. Theor.

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Multi-parametric chiral random matrix ensembles are important tools to analyze the statistical behavior of generic complex systems with chiral symmetry. A recent study (Mondal and Shukla 2020 Phys. Rev. E 102 032131) of the former maps them to the chiral Brownian ensemble (Ch-BE) that appears as a non-equilibrium state of a single parametric crossover between two stationary chiral Hermitian ensembles. This motivates us to pursue a detailed statistical investigation of the spectral and strength fluctuations of the Ch-BE, with a focus on their behavior near zero energy region. The information can then be used for a wide range of complex systems with chiral symmetry. Our analysis also reveals connections of Ch-BE to generalized Calogero Sutherland Hamiltonian (CSH) and Wishart ensembles. This along with already known connections of complex systems without chirality to CSH strongly hints the later to be the ‘backbone’ Hamiltonian governing the spectral dynamics of complex systems.

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Eigenfunction statistics of Wishart Brownian ensembles

Cited by 9 publications

References 93 publications

Disorder perturbed flat bands. II. Search for criticality

Disorder perturbed flat bands. II. Search for criticality

Many body density of states in the edge of the spectrum: non-interacting limit

Spectral and strength statistics of chiral Brownian ensemble

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