University of Washington
Quantum Dynamics in Rugged Energy Landscapes, and Additional Topics in Disordered Systems.
Degree: PhD, 2019, University of Washington
This thesis concerns the interplay of quantum mechanics with strong disorder, and the novel dynamical phases that are unique to disordered quantum systems. The results that we present apply to systems ranging from spin glasses to granular superconductors to quantum-computational problems. In the first part, we discuss the isolated quantum dynamics of mean-field spin glass models, using the random energy and p-spin models in a transverse field as tractable examples. We show that the low-energy configurations are organized into clusters separated by macroscopic Hamming distances, and that the tunneling amplitudes between clusters are exponentially suppressed. As a result, we find three distinct dynamical phases. At small transverse field, the system remains trapped within its starting cluster (trapped phase). At intermediate transverse field, the system tunnels between clusters (tunneling phase). At large transverse field, the system is excited out of clusters (excitation phase). We describe the similarities and differences between the trapped phase and a many-body localized phase. We also discuss at length the implications for quantum-computational approaches to ``matching'' problems, in which one solution to a computational problem is used as a starting point to find others. Only in the tunneling phase can quantum dynamics solve the matching problem. Although necessarily exponentially slow in system size, it may be exponentially faster than simple classical algorithms. In the second part, we discuss interfering directed paths in disordered media. Important physical realizations are hopping conduction in semiconductors, spin glasses at high temperature, and granular D-wave superconductors. Sign order, defined as the directed path sum having greater probability of being positive than negative at large distance, is a characterization of the role of interference with implications for the response of systems to a magnetic field. We show that path sums are necessarily sign-disordered in two dimensions but may be sign-ordered in three dimensions. Building on this result, we study the behavior of granular D-wave superconductors and show that the superconductivity is enhanced by a magnetic field, even beyond the directed-path regime.
Advisors/Committee Members: Laumann, Christopher (advisor).
Subjects/Keywords: Directed polymers; Disordered systems; Quantum computing; Spin glasses; Superconductivity; Condensed matter physics; Statistical physics; Quantum physics; Physics
to Zotero / EndNote / Reference
APA (6th Edition):
Baldwin, C. (2019). Quantum Dynamics in Rugged Energy Landscapes, and Additional Topics in Disordered Systems. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/43442
Chicago Manual of Style (16th Edition):
Baldwin, Christopher. “Quantum Dynamics in Rugged Energy Landscapes, and Additional Topics in Disordered Systems.” 2019. Doctoral Dissertation, University of Washington. Accessed March 20, 2019.
MLA Handbook (7th Edition):
Baldwin, Christopher. “Quantum Dynamics in Rugged Energy Landscapes, and Additional Topics in Disordered Systems.” 2019. Web. 20 Mar 2019.
Baldwin C. Quantum Dynamics in Rugged Energy Landscapes, and Additional Topics in Disordered Systems. [Internet] [Doctoral dissertation]. University of Washington; 2019. [cited 2019 Mar 20].
Available from: http://hdl.handle.net/1773/43442.
Council of Science Editors:
Baldwin C. Quantum Dynamics in Rugged Energy Landscapes, and Additional Topics in Disordered Systems. [Doctoral Dissertation]. University of Washington; 2019. Available from: http://hdl.handle.net/1773/43442