The classical β-ensembles with β proportional to 1/N: from loop equations to Dyson's disordered chain

PJ Forrester, G Mazzuca - Journal of Mathematical Physics, 2021‏ - pubs.aip.org
In the classical β-ensembles of random matrix theory, setting β= 2α/N and taking the N→∞
limit gives a statistical state depending on α. Using the loop equations for the classical β …

Differential identities for the structure function of some random matrix ensembles

PJ Forrester - Journal of Statistical Physics, 2021‏ - Springer
The structure function of a random matrix ensemble can be specified in terms of the
covariance of the linear statistics∑ j= 1 N eik 1 λ j,∑ j= 1 N e-ik 2 λ j for Hermitian matrices …

Turbulence hierarchy and multifractality in the integer quantum Hall transition

ALR Barbosa, THV de Lima, IRR González… - Physical Review Letters, 2022‏ - APS
We offer a new perspective on the problem of characterizing mesoscopic fluctuations in the
interplateau regions of the integer quantum Hall transition. We found that longitudinal and …

[HTML][HTML] Random density matrices: Closed form expressions for the variance of squared Hilbert-Schmidt distance

A Laha, S Kumar - Physics Letters A, 2024‏ - Elsevier
One of the fundamental aspects of quantum information theory is the study of distance
measures between quantum states. Hilbert-Schmidt distance serves as a convenient choice …

Computing marginal eigenvalue distributions for the Gaussian and Laguerre orthogonal ensembles

PJ Forrester, S Kumar, BJ Shen - arxiv preprint arxiv:2411.15635, 2024‏ - arxiv.org
The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix
theory, and the marginal eigenvalue distributions are basic observable quantities …

Entanglement spectrum statistics of a time reversal invariant spin chain system: insights from random matrix theory

A Sarkar, S Kumar - The European Physical Journal B, 2023‏ - Springer
The entanglement spectrum statistics (ESS) of a disordered and generalised time reversal
invariant XXZ model is inspected in the bipartite framework using exact finite-N results from …

Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance

A Laha, S Kumar - Physical Review E, 2023‏ - APS
One of the key issues in problems related to quantum information theory is concerned with
the distinguishability of quantum states. In this context, Bures distance serves as one of the …

Joint moments of a characteristic polynomial and its derivative for the circular β-ensemble

PJ Forrester - Probability and mathematical physics, 2022‏ - msp.org
The problem of calculating the scaled limit of the joint moments of the characteristic
polynomial, and the derivative of the characteristic polynomial, for matrices from the unitary …

Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance

S Kumar - Physical Review A, 2020‏ - APS
Hilbert-Schmidt distance is one of the prominent distance measures in quantum information
theory which finds applications in diverse problems, such as construction of entanglement …

Computation of marginal eigenvalue distributions in the Laguerre and Jacobi ensembles

PJ Forrester, S Kumar - arxiv preprint arxiv:2402.16069, 2024‏ - arxiv.org
We consider the problem of the exact computation of the marginal eigenvalue distributions
in the Laguerre and Jacobi $\beta $ ensembles. In the case $\beta= 1$ this is a question of …