Free fermions and α-determinantal processes
Abstract
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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- April 2019
- DOI:
- 10.1088/1751-8121/ab0ebd
- arXiv:
- arXiv:1811.11556
- Bibcode:
- 2019JPhA...52p5202D
- Keywords:
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- Mathematical Physics;
- Condensed Matter - Quantum Gases;
- Mathematics - Probability;
- Quantum Physics
- E-Print:
- 22 pages, 7 figures