Island myriads in periodic potentials.

Area of Science:

• Physics
• Quantum Mechanics
• Nonlinear Dynamics

Background:

• Periodic potentials in optical lattices are crucial for quantum simulations.
• Understanding phase space stability is key to controlling particle behavior.
• Hamiltonian models provide a framework for studying complex dynamical systems.

Purpose of the Study:

• To investigate the emergence of stability islands in square and hexagonal periodic potentials.
• To characterize the fractal structures, termed
• island myriads,
• and their relation to symmetries.
• To analyze the impact of these structures on particle transport properties.

Main Methods:

• Analysis of bidimensional Hamiltonian models of optical lattices.
• Numerical exploration of phase space dynamics.
• Investigation of systems with square, hexagonal, and rectangular tiling symmetries.

Main Results:

• Discovery of
• island myriads
• : fractal arrangements of stability islands in phase space.
• Isochronous orbits and varied periodic closures observed in the square lattice system, affecting transport.
• Attenuated
• myriads
• in the hexagonal lattice due to potential surface instabilities.

Conclusions:

• Symmetry plays a critical role in the formation and properties of stability islands.
• The breaking of symmetry, even slightly, disrupts the observed structures.
• Island myriads offer new insights into the complex dynamics and transport in optical lattice systems.