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Scaling near the quantum chaos border in interacting fermi systems
Song1
1Center for Theoretical Physics, Seoul National University, Seoul 151-742, Korea.
Summary
Quantum chaos emerges in interacting Fermi systems as interaction strength increases. This transition from nonchaotic to chaotic behavior is described by a universal scaling parameter, becoming sharper with higher excitation energy.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Interacting Fermi systems exhibit complex quantum behaviors.
- Understanding the transition to quantum chaos is crucial for characterizing these systems.
- Previous studies have explored quantum chaos in various models.
Purpose of the Study:
- To investigate the emergence of quantum chaos in interacting Fermi systems.
- To analyze the transition from nonchaotic to chaotic statistics.
- To identify the key parameters governing this transition.
Main Methods:
- Numerical calculations of the level spacing distribution P(s).
- Systematic variation of interaction strength (U) and excitation energy (epsilon).
- Analysis of the transition using a proposed scaling parameter Z.
Main Results:
- The level spacing distribution P(s) transitions from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) as U increases.
- This transition is characterized by a single scaling parameter Z = (U*epsilon(alpha) - u(0))*epsilon(1/(2*nu)).
- The exponent alpha is found to be broadly indecisive (0.9-2.0), while nu's finiteness suggests a sharp transition at higher epsilon.
Conclusions:
- A clear transition to quantum chaos is observed in interacting Fermi systems.
- The scaling parameter Z effectively describes the chaos transition.
- The transition sharpens with increasing excitation energy due to finite Fock space effects.
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