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Electric circuit networks equivalent to chaotic quantum billiards
Evgeny N Bulgakov1, Dmitrii N Maksimov, Almas F Sadreev
1Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia.
Summary
This study introduces electric RLC resonance networks as quantum billiard analogs. Researchers found that local voltages mimic wave functions, and derived a heat power distribution for these chaotic billiard models.
Area of Science:
- Physics
- Electrical Engineering
- Quantum Mechanics
Background:
- Quantum billiards are simplified models for quantum chaos.
- RLC resonance networks exhibit complex behaviors analogous to physical systems.
Purpose of the Study:
- To establish electric RLC resonance networks as physical analogs for quantum billiards.
- To investigate the relationship between network parameters and quantum billiard eigenvalues.
- To analyze the heat power distribution in these analog systems.
Main Methods:
- Analyzing two types of RLC resonance networks: inductor-capacitor and capacitor-inductor configurations.
- Mapping network eigenvalues to resonant frequencies and their inverses.
- Identifying local voltages as wave function analogs.
- Deriving and analyzing the heat power distribution.
Main Results:
- Resonant frequencies in inductor-capacitor networks correspond to quantum billiard eigenvalues.
- Inverse squared resonant frequencies in capacitor-inductor networks also map to eigenvalues.
- Local voltages in the networks function as quantum wave functions.
- A heat power distribution was derived and validated against numerical statistics for chaotic billiards.
Conclusions:
- Electric RLC networks provide a viable and experimentally accessible platform for studying quantum billiard phenomena.
- The presence of resistance introduces heat power, a factor absent in ideal quantum billiards.
- The derived heat power distribution accurately models the behavior of equivalent chaotic billiards.