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Wave functions with localizations on classical periodic orbits in weakly perturbed quantum billiards
1Department of Electrophysics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, 30050 Taiwan. ccliu@cc.nctu.edu.tw
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
Summary
Researchers studied quantum wave functions in circular billiards, finding they localize on classical periodic orbits (POs). Coherent states reveal these localizations, aiding the study of quantum vortex structures.
Area of Science:
- Quantum mechanics
- Mathematical physics
- Classical mechanics
Background:
- Quantum wave functions in billiards exhibit complex behaviors.
- Understanding localization phenomena is key to quantum chaos.
- Classical periodic orbits (POs) offer insights into quantum systems.
Purpose of the Study:
- To analytically investigate quantum wave function localization on classical POs in circular billiards.
- To construct coherent states for analyzing mesoscopic eigenstates.
- To explore the application of these states in studying quantum vortex structures.
Main Methods:
- Analytical investigation of quantum wave functions.
- Construction of coherent states as superpositions of nearly degenerate eigenstates.
- Mathematical expression of mesoscopic eigenstates in perturbed systems.
Main Results:
- Coherent states were successfully constructed and found to localize around single classical POs.
- Mesoscopic eigenstates in weakly perturbed systems were analytically expressed and localized on ensembles of POs.
- The constructed coherent states provide a tool for analyzing quantum vortex structures.
Conclusions:
- Quantum wave functions in circular billiards can be localized on classical periodic orbits.
- Coherent states are effective tools for understanding quantum localization and eigenstates.
- This approach facilitates the study of quantum phenomena like vortex structures.
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