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Quantum response to classical transitions.
1Department of Physics, George Mason University, Fairfax, Virginia 22030, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
Quantum systems mirror classical transitions in parameter changes, not time, revealing universal behavior. Critical points in quantum eigenstates highlight boundaries between localized and ballistic regimes in the kicked Harper model.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Condensed matter physics
Background:
- The kicked Harper model exhibits complex dynamics across its two-dimensional parameter space.
- Understanding the relationship between quantum and classical systems is crucial in quantum chaos.
Purpose of the Study:
- To demonstrate quantum fingerprints of all classical transitions within the kicked Harper model's parameter space.
- To investigate the universality of the quantum-classical relationship concerning parameter changes.
Main Methods:
- Exploiting the two-dimensional parameter space of the kicked Harper model.
- Analyzing quantum and classical system dynamics across localized, critical, and ballistic regimes.
Main Results:
- Quantum systems follow classical systems in parameter response but not in time.
- A universal relationship between quantum and classical systems is observed when measured by parameter change response.
- Critical points in quantum eigenstates are identified within classically diffusive regimes, marking boundaries between ballistic and localized patches.
Conclusions:
- The study reveals universal quantum-classical correspondence in parameter response, irrespective of the dynamical regime.
- Quantum fingerprints of classical transitions are identified, offering insights into quantum chaos.
- The existence of critical points in quantum eigenstates surviving the semiclassical limit provides novel insights into the quantum-classical boundary.