Topological singularities and transport in kicked Harper model.

Area of Science:

• Quantum chaos
• Condensed matter physics
• Topological physics

Background:

• The kicked Harper model is a paradigmatic system for studying quantum chaos.
• Understanding the interplay between topology and dynamics is crucial in various quantum systems.

Purpose of the Study:

• To investigate the quasienergy spectrum of the kicked Harper model.
• To explore the nature and location of degeneracies and singularities.
• To establish correlations between transport properties and topological characteristics.

Main Methods:

• Analysis of the quasienergy spectrum.
• Identification of diabolic crossings and exceptional points.
• Analytical continuation of the kicking parameter into the complex plane.
• Correlation analysis between spectral features and kinetic energy/wave packet localization.

Main Results:

• The quasienergy spectrum exhibits diabolic crossings, primarily on the symmetry line.
• Diabolic crossing locations coincide with kinetic energy maxima.
• Exceptional point singularities are identified in the complex parameter plane.
• The positions of exceptional points correlate with quantum wave packet localization.

Conclusions:

• Diabolic crossings and exceptional points are key spectral features of the kicked Harper model.
• A strong link exists between the system's transport properties and its topological characteristics.
• This work provides insights into the quantum dynamics and topological phases of periodically driven systems.