Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Abstract

We study the localization of energy in a nonlinear coupled system, exhibiting so-called breather modes, using quantized Hamilton dynamics (QHD). Already at the lowest order, which is only twice as complex as classical mechanics, this simple semiclassical method incorporates quantum-mechanical effects. The transition between the localized and delocalized regimes is instantaneous in classical mechanics, while it is gradual due to tunneling in both quantum mechanics and QHD. In contrast to classical mechanics, which predicts an abrupt appearance of breathers, quantum mechanics and QHD show an alternation of localized and delocalized behavior in the transient region. QHD includes zero-point energy that is reflected in a shifted energy asymptote for the localized states, providing another improvement on the classical perspective. By detailed analysis of the distribution and transfer of energy within classical mechanics, QHD, and quantum dynamics, we conclude that QHD is an efficient approach that accounts for moderate quantum effects and can be used to identify quantum breathers in large nonlinear systems.