Almost compact moving breathers with fine-tuned discrete time quantum walks

TL;DR

This paper investigates nonlinear discrete time quantum walks with flat band structures, revealing the existence of almost compact moving breathers with superexponential tails and a transition to fully compact bullets at maximum velocity.

Contribution

It introduces a novel class of nonlinear quantum walk solutions exhibiting nearly compact localized and moving breathers, including a fully compact bullet at maximum velocity.

Findings

Existence of stationary and moving breathers with superexponential tails

Moving breathers become fully compact bullets at maximum velocity

Nonlinear effects enable localized excitations without linear resonances

Abstract

Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band structure. The linear counterpart is, therefore, lacking transport, with exact solutions being compactly localized. A solitary entity of the nonlinear walk moving at velocity $v$ would therefore not suffer from resonances with small amplitude plane waves with identical phase velocity, due to the absence of the latter. That solitary excitation would also have to be localized stronger than exponential, due to the absence of a linear dispersion. We report on the existence of a set of stationary and moving breathers with almost compact superexponential spatial tails. At the limit of the largest velocity $v=1$ the moving breather turns into a completely compact bullet.