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Universal relationship between a quantum phase transition and instability points of classical systems
1Centre of Theoretical Physics and School of Physics, University of the Witwatersrand, P.O. Wits 2050, Johannesburg, South Africa.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
This study reveals a universal link between quantum phase transitions and classical mechanics. Exceptional points in quantum spectra correspond to singularities in classical actions, both exhibiting instability and sensitivity that can lead to chaos.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Chaos theory
Background:
- Phase transitions in quantum systems are associated with spectral degeneracies.
- Classical systems can exhibit singularities in their action at specific points.
Purpose of the Study:
- To investigate the direct and universal relationship between quantum exceptional points and classical action singularities.
- To identify common features driving instability and chaos in both domains.
Main Methods:
- Analysis of the quantum spectrum during phase transitions.
- Investigation of the classical action near homoclinic points of separatrices.
- Comparative analysis of analytic structures and stability properties.
Main Results:
- A direct and universal relationship is established between exceptional points and classical singularities.
- Both phenomena share an analytic structure leading to instability.
- This instability generically results in the onset of chaos under perturbation.
Conclusions:
- The findings provide a unified perspective on phase transitions and classical dynamics.
- Understanding these connections is crucial for predicting chaotic behavior in complex systems.
- This research bridges fundamental concepts in quantum and classical physics.