Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles
- URL: http://arxiv.org/abs/2405.00190v1
- Date: Tue, 30 Apr 2024 20:44:31 GMT
- Title: Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles
- Authors: N. D. Chavda, Priyanka Rao, V. K. B. Kota, Manan Vyas,
- Abstract summary: We numerically study the distribution of the lowest eigenvalue of finite many-boson systems with $k$-body interactions.
Our results show the distribution exhibits a smooth transition from Gaussian like for $q$ close to 1 to a modified Gumbel like for intermediate values of $q$ to the well-known Tracy-Widom distribution for $q=0$.
- Score: 0.8999666725996978
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We numerically study the distribution of the lowest eigenvalue of finite many-boson systems with $k$-body interactions modeled by Bosonic Embedded Gaussian Orthogonal [BEGOE($k$)] and Unitary [BEGUE($k$)] random matrix Ensembles. Following the recently established result that the $q$-normal describes the smooth form of the eigenvalue density of the $k$-body embedded ensembles, the first four moments of the distribution of lowest eigenvalues have been analyzed as a function of the $q$ parameter, with $q \sim 1$ for $k = 1$ and $q = 0$ for $k = m$; $m$ being the number of bosons. Our results show the distribution exhibits a smooth transition from Gaussian like for $q$ close to 1 to a modified Gumbel like for intermediate values of $q$ to the well-known Tracy-Widom distribution for $q=0$.
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