Quantum ergodicity and energy flow in molecules

Abstract

We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.

PACS:

• 33.15.Hp
• 82.20.-w
• 82.40.-g
• 05.45.Mt
• 33.20-t
• 33.15.Bh

Keywords:

• quantum ergodicity transition
• random matrix theory
• local random matrix theory
• energy flow in molecules
• Anderson localization
• many-body localization
• disordered systems
• chemical reaction rate theory

Acknowledgements

Part of this article was written while the author was a Senior Fellow at the Freiburg Institute for Advanced Study (FRIAS). The author thanks Gerhard Stock in particular for his hospitality and for many stimulating discussions on energy flow in molecules. The author has enjoyed many discussions and collaboration on the topic of quantum ergodicity and energy flow with Johnson Agbo, Hiroshi Fujisaki, Martin Gruebele, Ken Jordan, Srihari Keshavamurthy, Tamiki Komatsuzaki, John Straub, Mikito Toda, David Wales and Peter Wolynes.

Disclosure statement

No potential conflict of interest was reported by the author.

Funding

Support from NSF CHE-1361776 is gratefully acknowledged.