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Ordered level spacing distribution in embedded random matrix ensembles

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Abstract

The probability distributions of the closest neighbour (CN) and farther neighbour (FN) spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded Gaussian orthogonal ensemble (GOE) of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a \(3 \times 3\) random matrix model and other related quantities by Srivastava et al, J. Phys. A: Math. Theor. 52, 025101 (2019). This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.

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Acknowledgements

One of the authors (NDC) thanks V K B Kota for useful discussions. PR and NDC acknowledge financial support from Science and Engineering Research Board, Department of Science and Technology (DST), Government of India (Project No.: EMR/2016/001327).

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Authors and Affiliations

  1. Department of Applied Physics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara,  390 001, India

    Priyanka Rao & N D Chavda

  2. HVHP Institute of Post Graduate Studies and Research, Kadi Sarva Vishwavidyalaya, Gandhinagar,  382 715, India

    H N Deota

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  1. Priyanka Rao
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  2. H N Deota
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  3. N D Chavda
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Correspondence to Priyanka Rao.

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Rao, P., Deota, H.N. & Chavda, N.D. Ordered level spacing distribution in embedded random matrix ensembles. Pramana - J Phys 95, 34 (2021). https://doi.org/10.1007/s12043-020-02066-w

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  • DOI: https://doi.org/10.1007/s12043-020-02066-w

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