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Parametric correlations versus fidelity decay: the symmetry breaking case
H Kohler1, T Nagao, H-J Stöckmann
1Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juana de la Cruz 3, Cantoblanco, ES-28049 Madrid, Spain. hkohler@icmm.csic.es
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
We derived formulas for fidelity decay and energy correlations in random matrix systems with broken time-reversal symmetry. A simple relationship between these quantities was found, and fidelity freeze was observed across different spin systems.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter physics
Background:
- Random matrix theory (RMT) is crucial for understanding complex quantum systems.
- Time-reversal symmetry (TRS) plays a significant role in the behavior of quantum Hamiltonians.
- Perturbations can break fundamental symmetries, altering system dynamics.
Purpose of the Study:
- To derive formulas for fidelity decay and parametric energy correlations.
- To investigate these quantities in RMT ensembles with broken TRS.
- To explore the relationship between fidelity decay and energy correlations.
Main Methods:
- Analytical derivation of formulas.
- Analysis of random matrix ensembles.
- Investigating the impact of symmetry-breaking perturbations.
Main Results:
- Formulas for fidelity decay and parametric energy correlations are provided.
- A simple relation between fidelity decay and energy correlations is established, similar to symmetry-conserving cases.
- Fidelity freeze phenomenon is observed for systems with both even and odd spin.
Conclusions:
- The established relation between fidelity decay and energy correlations holds even when TRS is broken.
- Fidelity freeze is a robust feature, independent of spin parity in these systems.
- The findings offer insights into the dynamics of quantum systems under symmetry-breaking conditions.
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