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Weak ergodicity breaking and quantum scars in constrained quantum systems

Turner, Christopher Jack (2019) Weak ergodicity breaking and quantum scars in constrained quantum systems. PhD thesis, University of Leeds.

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Abstract

The success of statistical mechanics in describing complex quantum systems rests upon typicality properties such as ergodicity. Both integrable systems and the recently discovered many-body localisation show that these assumptions can be strongly violated in either finely tuned cases, or in the presence of quenched disorder. In this thesis, we uncover a qualitatively different form of ergodicity breaking, wherein a small number of atypical eigenstates are embedded throughout an otherwise thermalising spectrum. We call this a many-body quantum scar, in analogy to quantum scars in single-particle quantum chaos, where quantum scarred eigenfunctions concentrate around associated periodic classical trajectories. We demonstrate that many-body quantum scars can be found in an unusual model recently realised in a 51 Rydberg atom quantum simulator. The observed coherent oscillations following in a certain quench experiment are a consequence of the quantum scar. At the same time, the level statistics rules out conventional explanations such as integrability and many-body localisation. We develop an approximate method to construct scarred eigenstates, in order to describe their structure and physical properties. Additionally, we find a local perturbation which makes these non-equilibrium properties much more pronounced, with near perfect quantum revivals. At the same time the other eigenstates remain thermal. Our results suggest that many-body quantum scars forms a new class of quantum dynamics with unusual properties, which are realisable in current experiments.

Item Type: Thesis (PhD)
Keywords: quantum chaos, quantum dynamics, quantum information, ultra-cold atoms
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
Identification Number/EthosID: uk.bl.ethos.789439
Depositing User: Mr Christopher Jack Turner
Date Deposited: 08 Nov 2019 16:10
Last Modified: 18 Feb 2020 12:51
URI: http://etheses.whiterose.ac.uk/id/eprint/24812

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