Chaotic and ballistic dynamics in time-driven quasiperiodic lattices

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Nonlinear dynamics

Background:

• Understanding the behavior of particles in disordered or complex potentials is crucial.
• Nonequilibrium systems offer insights into fundamental physical processes.
• Quasiperiodic systems, like those based on the Fibonacci sequence, exhibit unique properties distinct from periodic or random systems.

Purpose of the Study:

• To investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice.
• To identify and explain the origins of complex transient behaviors observed in such systems.
• To compare the dynamics in quasiperiodic lattices with those in periodic and fully randomized lattices.

Main Methods:

• Simulating the motion of classical particles in a one-dimensional driven quasiperiodic lattice.
• Analyzing the trajectories to identify distinct flight velocities and durations.
• Employing a hierarchical block decomposition analysis of the quasiperiodic lattice structure.

Main Results:

• Discovery of intricate transient dynamics characterized by extraordinarily long ballistic flights at distinct velocities.
• Identification of a hierarchy of block decompositions within the Fibonacci quasiperiodic lattice as the cause of these long flights.
• Demonstration that these dynamics differ significantly from those observed in periodic and fully randomized lattices.

Conclusions:

• The complex transient dynamics in driven quasiperiodic lattices are a direct consequence of their unique hierarchical structure.
• Ballistic flights are not random but are dictated by the specific decomposition of the quasiperiodic lattice.
• This study provides a new perspective on transport phenomena in disordered and quasiperiodic systems.