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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.