Thesis
Information-spreading and recurrence in finite-size quantum systems
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2025
- Thesis identifier
- T17477
- Person Identifier (Local)
- 202177159
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- Finite size closed systems are guaranteed to recur eventually. According to Poincaré’s recurrence theorem, recurrence is expected after a time scaling exponentially with the system volume. Low-amplitude recurrences are not covered by the theorem, but can be relevant for modern applications in quantum physics which depend on information to be delocalized in the system. The first part of this work is concerned with the investigation of such low-amplitude recurrences in quantum systems that can be set up in current day AMO systems, such as Rydberg arrays. Modifications to a toy Hamiltonian of hopping bosons are made and their impact on the scaling of the low-amplitude recurrence time with the system volume is investigated. Thereafter, the influence of interactions on this same scaling is analyzed in the system of an XXZ spin-½ chain. Both avenues show the possibility of generating superlinear scaling, which for low-amplitude recurrences is not inherently given and can be shown to not hold in the most simple setup. The origin of this superlinear scaling cannot be neatly tracked to either the spectral properties of the underlying Hamiltonian, nor to the dimensionality of the Hilbert space traced out by the initial-state evolution. It arises in situations associated with disorder in non-interacting cases, as well as in scrambling dynamics in the presence of interactions. Further investigating the origin of superlinear low-amplitude recurrence is the most promising continuation of this work. The second part of this work is concerned with the efficient delocalization of information in a quantum system. Following up an investigation in Clifford circuits by Kuriyattil et al. [1], this work contrasts the efficiency of dense and sparse long-range coupling models in delocalizing quantum information. Instead of a gate-based approach, this work considers quenches between translationally invariant quadratic fermionic Hamiltonians with dense or exponentially sparse long-range coupling. The tripartite mutual information after a short time evolution is investigated in order to check for the dynamical transition in decay exponents α observed in gate-based models of [1]. The differences to the gate-based models, as well as the models of intermediate sparsity between exponentially sparse and fully dense, which could also be used in gate-based experiments, are shown in this work as potential avenues for future investigation.
- Advisor / supervisor
- Kirkton, Peter
- Daley, Andrew
- Resource Type
- DOI
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PDF of thesis T17477 | 2025-10-15 | Public | Download |