Quantum-mechanical nonperturbative response of driven chaotic mesoscopic systems

Area of Science:

• Quantum Mechanics
• Nonlinear Dynamics
• Statistical Physics

Background:

• Time-dependent Hamiltonians with periodic driving are crucial for understanding quantum system responses.
• Classical dynamics exhibiting chaos and its power spectrum influence system behavior.
• Linear Response Theory (LRT) traditionally predicts system response based on driving frequency and amplitude.

Purpose of the Study:

• To investigate the validity of classical and quantum-mechanical Linear Response Theory (LRT) for chaotic systems under periodic driving.
• To identify and define a nonperturbative regime where LRT breaks down.
• To explore quantum nonperturbative effects on system response beyond the predictions of LRT.

Main Methods:

• Analysis of a time-dependent Hamiltonian with periodic driving, H(Q,P;x(t)) = Asin(Omegat).
• Numerical demonstration of LRT failure in a defined nonperturbative regime (Omega, A space).
• Investigation of quantum nonperturbative effects for driving amplitudes A > A(prt) (approximately Planck's constant / 2pi).

Main Results:

• LRT predicts a response dependent on driving frequency (Omega) relative to the classical power spectrum cutoff (omega(cl)), independent of driving amplitude (A).
• A nonperturbative regime is identified where LRT fails, particularly for driving amplitudes A > A(prt).
• Quantum nonperturbative effects can induce a strong system response even for Omega > omega(cl), contradicting LRT predictions.

Conclusions:

• Linear Response Theory is insufficient for describing the dynamics of chaotic quantum systems in the nonperturbative regime.
• Quantum nonperturbative effects play a significant role in determining system response at high driving amplitudes and frequencies.
• The study highlights the limitations of perturbative approaches and the importance of considering quantum effects beyond LRT.