Signatures of Discrete Breathers in Coherent State Quantum

TL;DR

This paper investigates quantum signatures of discrete breathers in coherent states, revealing a complex interplay of localized and delocalized behaviors, including tunneling phenomena and mode transitions in non-linear quantum systems.

Contribution

It introduces a quantum analysis of discrete breathers using coherent states, highlighting the transition regions and new tunneling modes absent in classical descriptions.

Findings

Eigenstates exhibit avoided crossings between tunneling and non-tunneling modes.

High non-linearity regions show dominance of tunneling modes with new high order tunneling modes emerging.

Transient regions contain modes that are neither purely tunneling nor non-tunneling, indicating smooth transitions.

Abstract

Discrete breathers (DBs) -- a spatial time-periodic localization of energy -- are predicted in a large variety of non-linear systems. Motivated by the conceptual bridging of the DBs phenomena in classical and quantum mechanical representation, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in a phase space -- a coherent state. We show that in contrast to a point in a phase space that can exhibit either delocalized or localized motion, a coherent state can show signatures of a quantum equivalent of both localized and delocalized behavior. In classical mechanics, the separation between the energy regions of localized and delocalized motion is a point. In quantum mechanics, this point becomes a transient region, in which both tunneling and non-tunneling modes are present. Furthermore, the transient region contains modes that cannot be characterized as either, because the transition from non-tunneling to tunneling modes is smooth. With a further analysis we document four intriguing observations: 1. Considered as a function of coupling, the eigenstates go through avoided crossings between tunneling and non-tunneling modes. 2. The dominance of tunneling modes in high non-linearity region is compromised by an appearance of new types of modes -- high order tunneling modes. These modes are similar to the tunneling modes but have attributes of non-tunneling modes. ...