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

Author

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

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.

Suggested Citation

  • Chavda, N.D. & Rao, Priyanka & Kota, V.K.B. & Vyas, Manan, 2025. "Distribution of lowest eigenvalue in k-body bosonic random matrix ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 677(C).
    • Handle: RePEc:eee:phsmap:v:677:y:2025:i:c:s0378437125005266
    DOI: 10.1016/j.physa.2025.130874
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    References listed on IDEAS

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    1. Chiani, Marco, 2014. "Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy–Widom distribution," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 69-81.
    2. Benedikt Fauseweh, 2024. "Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    3. Jean-Philippe Bouchaud & Marc Mezard, 1997. "Universality classes for extreme value statistics," Science & Finance (CFM) working paper archive 500043, Science & Finance, Capital Fund Management.
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