2018/11/30 by Fabio Deelan Cunden, Satya N. Majumdar, Satya N Majumdar +2 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Excited state #Fermion #Kernel (algebra) #Limit (mathematics) #Mathematical functions and polynomials #Point (geometry) #Random Matrices and Applications #Scaling #Simple (philosophy) #cond-mat.quant-gas #math-ph #math.MP #math.PR #quant-ph
paper · pdf · doi:10.1088/1751-8121/ab0ebd
published as J. Phys. A: Math. Theor. 52, 165202 (2019) · 22 pages, 7 figures
openalex created_date 2018/12/11 · arxiv created 2019/02/26 · openalex publication_date 2019/03/11 · arxiv updated 2019/06/07 · openalex updated_date 2026/08/06
The -determinant is a one-parameter generalisation of the standard determinant, with corresponding to the determinant, and corresponding to the permanent. In this paper a simple limit procedure to construct -determinantal point processes out of fermionic processes is examined. The procedure is illustrated for a model of N free fermions in a harmonic potential. When the system is in the ground state, the rescaled correlation functions converge for large N to determinants (of the sine kernel in the bulk and the Airy kernel at the edges). We analyse the point processes associated to a special family of excited states of fermions and show that appropriate scaling limits generate -determinantal processes. Links with wave optics and other random matrix models are suggested.