Regensburg 2022 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 4: Many-Body Quantum Dynamics 1 (joint session DY/TT)

TT 4.10: Talk

Monday, September 5, 2022, 12:30–12:45, H20

Towards a dictionary between JT gravity and periodic orbit theory — •Torsten Weber, Fabian Haneder, Juan-Diego Urbina, and Klaus Richter — University of Regensburg, Germany

Periodic orbit theory is a far reaching development of the semiclassical methods where the most fundamental signatures of the quantum nature of closed systems, like the discreteness of their energy spectrum, emerges from interference between amplitudes constructed from the classical properties of periodic solutions [1]. This conceptual basis, leading to the celebrated Gutzwiller trace formula, has provided impressive achievements from quantum transport to atomic physics and multi-particle scattering. In particular, together with the necessary existence of periodic orbit bunching in ergodic systems, it has lead to an understading of the emergence of universal spectral correlations in chaotic systems, the BGS conjecture [2].

We report our progress in studying how a loss of information (characterized by a coarse graining of classical bunches of orbits) at the level of the trace formula implies the emergence of genus-like expansions with formally the same structure as the solution of JT quantum gravity found in [3]. Our work thus gives convincing hints toward a possible dictionary between quantum-gravitational and periodic orbit objects and concepts.

[1] See e.g. F. Haake, Quantum Signatures of Chaos, Springer, 2000

[3] S. Müller et al., Phys. Rev. E 72, 046207 (2005)

[3] P. Saad, S. Shenker, D. Stanford, arXiv:1903.11115