planck-->0 and classical-quantum correspondence in the kicked Harper model

Area of Science:

• Quantum chaos
• Condensed matter physics
• Mathematical physics

Background:

• The kicked Harper model is a paradigmatic system for studying quantum chaos.
• Understanding classical-quantum correspondence is crucial for bridging classical and quantum mechanics.

Purpose of the Study:

• To investigate classical-quantum correspondence in the kicked Harper model for small Planck's constant.
• To analyze the influence of symmetry on quantum transport phenomena.

Main Methods:

• Numerical simulations of the kicked Harper model.
• Analysis of quantum state evolution for varying Planck's constant values.
• Examination of transport properties in both symmetric and asymmetric cases.

Main Results:

• In the asymmetric case, quantum states exhibit classical diffusive and superdiffusive transitions independent of Planck's constant.
• In the symmetric case, Planck-independent behavior emerges for the renormalized parameter K/(2*Planck).
• The symmetric case reveals sharp transitions from integrable to nonintegrable transport, series of transitions at multiples of pi, and periodic transmission probability.

Conclusions:

• Classical-quantum correspondence in the kicked Harper model is robust, even at vanishing Planck's constant.
• Symmetry plays a critical role in shaping quantum transport, leading to distinct phenomena.
• The presence or absence of cantori significantly influences quantum dynamics, suggesting novel emergent features.