Distribution of lowest eigenvalue in k-body bosonic random matrix ensembles

N.D. Chavda, Priyanka Rao, V.K.B. Kota and Manan Vyas

Physica A: Statistical Mechanics and its Applications, 2025, vol. 677, issue C

Abstract: We present numerical investigations demonstrating the result that the distribution of the lowest eigenvalue of finite many-boson systems (say we have m number of bosons) with k-body interactions, modeled by Bosonic Embedded Gaussian Orthogonal [BEGOE(k)] and Unitary [BEGUE(k)] random matrix Ensembles of k-body interactions, exhibits a smooth transition from Gaussian like (for k=1) to a modified Gumbel like (for intermediate values of k) to the well-known Tracy–Widom distribution (for k=m) form. We also provide ansatz for centroids and variances of the lowest eigenvalue distributions. In addition, we show that the distribution of normalized spacing between the lowest and next lowest eigenvalues exhibits a transition from Wigner’s surmise (for k=1) to Poisson (for intermediate k values with k≤m/2) to Wigner’s surmise (starting from k=m/2 to k=m) form. We analyze these transitions as a function of q parameter defining q-normal distribution for eigenvalue densities.

Keywords: Extreme values statistics; Tracy–widom distribution; Gumbel distribution; k-body random matrix ensembles; Interacting boson systems; q-normal distribution (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:677:y:2025:i:c:s0378437125005266

DOI: 10.1016/j.physa.2025.130874

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