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Statistical description of eigenfunctions in chaotic and weakly disordered systems beyond universality
Juan Diego Urbina1, Klaus Richter
1Institute for Physics of Complex Systems, The Weizmann Institute of Science, 76100 Rehovot, Israel. jdurbinag@unal.edu.co
We developed a new semiclassical method for quantum system eigenfunction statistics, improving upon existing theories. This approach reveals novel oscillatory contributions relevant to Coulomb blockade physics.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter physics
Background:
- Eigenfunction statistics in chaotic and disordered quantum systems are typically analyzed using random matrix theory and supersymmetry.
- Existing semiclassical methods have limitations in fully describing these statistics.
Purpose of the Study:
- To introduce a novel semiclassical approach for analyzing eigenfunction statistics.
- To extend beyond the limitations of random matrix theory and supersymmetry techniques.
- To provide a more comprehensive understanding of quantum system behavior.
Main Methods:
- Generalizing Berry's random wave model.
- Incorporating a semiclassical representation of spatial two-point correlations.
- Deriving closed expressions for wave-function averages using universal coefficients and classical paths.
Main Results:
- Developed a semiclassical approach that surpasses existing methods.
- Derived closed expressions for arbitrary wave-function averages.
- Identified novel oscillatory contributions beyond standard supersymmetry results.
Conclusions:
- The new semiclassical approach offers a powerful tool for studying quantum systems.
- The identified oscillatory contributions have demonstrable physical relevance, particularly in Coulomb blockade phenomena.
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