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

Area of Science:

• Quantum physics
• Nonlinear dynamics
• Condensed matter theory

Background:

• Discrete time quantum walks are unitary maps on coupled two-level systems.
• Linear quantum walks with flat bands exhibit localized states and lack transport.
• Nonlinearities introduce complex dynamics not present in linear systems.

Purpose of the Study:

• Investigate excitation dynamics in a nonlinear discrete time quantum walk.
• Analyze the properties of localized states in the nonlinear regime.
• Explore the impact of nonlinearity on transport and localization.

Main Methods:

• Studied a nonlinear discrete time quantum walk model.
• Analyzed the behavior of solitary excitations.
• Investigated stationary and moving breather solutions.
• Examined spatial localization properties and velocity dependence.

Main Results:

• Identified a set of stationary and moving breathers.
• Breathers exhibit almost compact superexponential spatial tails.
• At maximum velocity, the moving breather becomes a compact bullet.
• Nonlinearity prevents resonances with plane waves due to absence of linear dispersion.

Conclusions:

• Nonlinear discrete time quantum walks support novel localized states (breathers).
• These breathers display unique localization properties, stronger than exponential.
• The system exhibits a transition to compact localized states (bullets) at high velocities.