Chaotic Dynamics in a Quantum Fermi-Pasta-Ulam Problem.

Alexander L Burin,Andrii O Maksymov,Ma'Ayan Schmidt,Il'Ya Ya Polishchuk

doi:10.3390/e21010051

Abstract

We investigate the emergence of chaotic dynamics in a quantum Fermi—Pasta—Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed.

Highlights

Understanding vibrational energy flow in molecules is one of the challenges in modern science and technology [1,2]
After seminal work by Stewart and McDonalds [11], it has been realized that the internal vibrational relaxation can be absent or proceed very slowly in small enough molecules and/or at low temperature
Theory was further extended combining random matrix theory methods [19,20,21] and Bose Statistics Triangle Rule approach [22,23,24] and this extension was reasonably consistent with the experimental observations [11]

Summary

Introduction

Understanding vibrational energy flow in molecules is one of the challenges in modern science and technology [1,2]. After seminal work by Stewart and McDonalds [11], it has been realized that the internal vibrational relaxation can be absent or proceed very slowly in small enough molecules and/or at low temperature. Based on these observations, the concept of localization of low energy anharmonic vibrational states of poly-atomic molecules within the manifold of harmonic product states of almost independent normal modes was put forward by Logan and Wolynes [12]. Theory was further extended combining random matrix theory methods [19,20,21] and Bose Statistics Triangle Rule approach [22,23,24] and this extension was reasonably consistent with the experimental observations [11]

Methods

Findings

Discussion

Conclusion