Nondivergent classical response functions from uncertainty principle: quasiperiodic systems

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Classical dynamics

Background:

• Classical response functions often exhibit time-divergence.
• Establishing classical-quantum correspondence is crucial for understanding complex systems.

Purpose of the Study:

• To resolve time-divergence in classical response functions.
• To establish classical-quantum correspondence for quasiperiodic systems.

Main Methods:

• Phase-space averaging within the quantized uncertainty volume O(hn).
• Replacing microcanonical distribution density with quantized uniform distribution density.
• Numerical calculations for one- and two-dimensional systems.

Main Results:

• Time-divergence in linear and nonlinear classical response functions is eliminated.
• Agreement between quantum and classical expressions is achieved via Heisenberg's correspondence principle.
• Numerical results demonstrate good agreement between quantum and classical calculations.

Conclusions:

• Phase-space averaging within the quantized uncertainty volume is a viable method for classical-quantum correspondence.
• The approach is generalizable to systems with N degrees of freedom.
• This method provides a robust framework for studying response functions in quasiperiodic systems.