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Classical versus quantum structure of the scattering probability matrix: chaotic waveguides.
G A Luna-Acosta1, J A Méndez-Bermúdez, P Seba
1Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
Summary
We define the classical scattering probability matrix (SPM) for quantum waveguides. Its structure predicts quantum transport properties, offering insights beyond classical Poincaré maps.
Area of Science:
- Quantum chaos
- Condensed matter physics
- Waveguide theory
Background:
- The scattering probability matrix (SPM) describes quantum scattering phenomena.
- Understanding quantum transport in waveguides is crucial for device applications.
- Hamiltonian chaos in quantum systems presents complex dynamics.
Purpose of the Study:
- To define and investigate the classical counterpart of the quantum scattering probability matrix (SPM).
- To compare the classical and quantum structures of the SPM in two-dimensional waveguides.
- To explore the predictive power of classical SPM for quantum transport properties.
Main Methods:
- Definition of the classical scattering probability matrix (SPM) for M propagating modes.
- Comparative analysis of quantum and classical SPM structures in chaotic waveguides.
- Utilizing Poincaré maps for dynamical information extraction.
Main Results:
- The classical SPM structure successfully predicts the global structure of the quantum SPM.
- Classical dynamics provide insights into quantum transport properties of waveguides.
- The SPM offers additional dynamical information compared to Poincaré maps.
Conclusions:
- Classical dynamics can effectively predict quantum transport phenomena in waveguides.
- The SPM is a valuable tool for understanding complex dynamics in quantum systems.
- This work bridges classical and quantum descriptions of scattering in waveguides.