Dynamical Phase Transitions, Caustics, and Quantum Dark Bands

• URL: http://arxiv.org/abs/2407.10529v1
• Date: Mon, 15 Jul 2024 08:37:13 GMT
• Title: Dynamical Phase Transitions, Caustics, and Quantum Dark Bands
• Authors: Valentin Link, Walter T. Strunz, D. H. J. O'Dell,
• Abstract summary: We show the connection to caustics forming in the Fock space representation of the many-body state over time. We propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide a new perspective on dynamical phase transitions (DPTs) in quantum systems by showing their connection to caustics forming in the Fock space representation of the many-body state over time. In this way we find an explanation for DPTs in a quantum spin system in terms of an everyday natural phenomenon: The dark band between the primary and seconday bows (caustics) in rainbows (Alexander's dark band). The DPT occurs when the Loschmidt echo crosses the switching line between the evanescent tails of two back-to-back Airy functions that dress neighbouring fold caustics in Fock space and is the time-dependent analogue of what is seen as a function of angle in the sky. The structural stability and universal properties of caustics, as described mathematically by catastrophe theory, suggests our analysis has wide applicability. Based on our thorough analytical understanding we propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.

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