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Updated: Jul 1, 2025
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.0K
Multifractal dimensions for orthogonal-to-unitary crossover ensemble.
Ayana Sarkar1, Ashutosh Dheer1, Santosh Kumar1
1Department of Physics, Shiv Nadar Institution of Eminence (SNIoE), Gautam Buddha Nagar, Uttar Pradesh 201314, India.
Chaos (Woodbury, N.Y.)
|March 12, 2024
Summary
This study introduces new formulas for multifractal dimensions in quantum systems, aiding the analysis of system ergodicity. These findings help distinguish quantum system behaviors and analyze crossovers effectively.
Area of Science:
- Quantum mechanics
- Statistical physics
- Complex systems analysis
Background:
- Multifractal analysis characterizes quantum system eigenstates.
- Eigenvectors of random matrices model ergodic states.
- Finite-size effects in multifractal dimensions reveal system properties.
Purpose of the Study:
- Provide semi-analytical expressions for multifractal dimensions in orthogonal-to-unitary crossover ensembles.
- Introduce shifted and scaled multifractal dimensions to study crossovers.
- Apply these measures to complex quantum systems.
Main Methods:
- Derivation of semi-analytical expressions for multifractal dimensions.
- Monte Carlo simulations of crossover random matrix models.
- Analysis of quantum kicked rotor, Sinai billiard, and spin-chain models.
Main Results:
- Semi-analytical expressions for ensemble-averaged multifractal dimensions derived.
- Shifted and scaled multifractal dimensions effectively distinguish orthogonal and unitary limits.
- Results accurately capture multifractal dimensions in system crossovers.
Conclusions:
- The developed multifractal dimension measures are effective for studying orthogonal-to-unitary crossovers in quantum systems.
- These findings offer a valuable tool for analyzing ergodicity and localization in complex quantum models.
- The approach is validated across diverse physical systems, demonstrating broad applicability.
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