Quantum localization and quantum scrambling in molecular systems

My Ph.D. work can be summarized as studying vibrational energy redistribution in molecular systems. Two intertwined aspects of vibrational energy redistribution are studied in this thesis: quantum localization and quantum scrambling. Regarding the quantum localization, a toy model of inter-molecular energy transfer between two molecular fragments is studied numerically. I have successfully shown the “phase transition” between a region of facile energy transfer and a region limited by intramolecular energy redistribution, with the molecular anharmonicity serves as the order parameter. With collaborators, I have also extended the Logan-Wolynes theory for vibrational energy localization to the case of two-surface nonadiabatic systems. We numerically tested the theory with a toy model inspired by exciton energy transfer in bacteriochlorophyll dimers in the photo-synthesis process. We have found good agreement between numerical results with the approximate analytical theory. For the study of quantum scrambling, we have applied out-of-time-order correlation functions (OTOCs) to probe the quantum information scrambling in molecular vibrational systems. We have observed cases where quantum Lyapunov exponents agree with classical Lyapunov exponents and cases such quantum-classical correspondence breakdown because of quantum localization or Heisenberg’s uncertainty principle. We have also numerically tested a hypothesis about the bound on scrambling rate in molecular systems. We then revisited the classic problem of the relation of quantum scrambling and chemical reactions. We used OTOCs to study models of simple chemical reactions and found that the quantum Lyapunov exponent can approach the scrambling bound in the deep tunneling regime. We then compared quantum Lyapunov exponents with reaction rates in model systems and showed the intimate relation between scrambling and reaction events. For the final part of the thesis, we numerically investigated a toy model characterizing the quantum measurement process of photons. In the standard formalism of non-relativistic quantum mechanics, two distinct kinds of dynamics are invoked to explain experimental results: unitary evolution of the Schrodinger equation and irreversible wave function collapse upon measurement by detectors. Here we pursue the postulate that the irreversible wave function collapse process can be replaced by unitary evolution of the system-detector state with the Schrodinger equation, in the limit that the detector has many degrees of freedom. We show some fallacies in the standard argument against unitary evolution explaining measurement and discuss the implication of the current numerical results to the postulate.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Zhang, Chenghao

Contributors dc:contributor

• Gruebele, Martin
• Ceperley, David
• Wolynes, Peter Guy
• Makri, Nancy
• Abbamonte, Peter

• Molecular Vibration
• Quantum Scrambling
• Quantum Localization
• Local Random Matrix Theory

Statement dc:rights

• Copyright 2024, Chenghao Zhang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/124620

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F124620