Urbina, Juan Diego and Kelly, Michael and Richter, Klaus (2023) Periodic orbit theory of Bethe-integrable quantum systems: an <i>N</i>-particle Berry-Tabor trace formula. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 56 (21): 214001. ISSN 1751-8113, 1751-8121
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One of the fundamental results of semiclassical theory is the existence of trace formulae showing how spectra of quantum mechanical systems emerge from massive interference among amplitudes related with time-periodic structures of the corresponding classical limit. If it displays the properties of Hamiltonian integrability, this connection is given by the celebrated Berry-Tabor trace formula, and the periodic structures it is built on are tori supporting closed trajectories in phase space. Here we show how to extend this connection into the domain of quantum many-body systems displaying integrability in the sense of the Bethe ansatz, where a classical limit cannot be rigorously defined due to the presence of singular potentials. Formally following the original derivation of Berry and Tabor (1976 Proc. R. Soc. A 349 101), but applied to the Bethe equations without underlying classical structure, we obtain a many-particle trace formula for the density of states of N interacting bosons on a ring, the Lieb-Liniger model. Our semiclassical expressions are in excellent agreement with quantum mechanical results for N=2,3 N = 2 we relate our results to the quantization of billiards with mixed boundary conditions. Our work paves the way towards the treatment of the important class of integrable many-body systems by means of semiclassical trace formulae pioneered by Michael Berry in the single-particle context.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CLOSED ORBITS; semiclassical theory; Bethe ansatz; Hamiltonian integrability; Lieb-Liniger model; asymptotic analysis |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Feb 2024 10:47 |
| Last Modified: | 22 Feb 2024 10:47 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59072 |
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