Electric circuit networks equivalent to chaotic quantum billiards

Details Electric circuit networks equivalent to chaotic quantum billiards Electric circuit networks equivalent to chaotic quantum billiards

2004-11-15

arxiv.org/abs/quant-ph/0411100v1

Physics

Quantum Physics

9 pages, 7 figures

Scientific paper

10.1103/PhysRevE.71.046205

We formulate two types of electric RLC resonance network equivalent to quantum billiards. In the network of inductors grounded by capacitors squared resonant frequencies are eigenvalues of the quantum billiard. In the network of capacitors grounded by inductors squared resonant frequencies are given by inverse eigen values of the billiard. In both cases local voltages play role of the wave function of the quantum billiard. However as different from quantum billiards there is a heat power because of resistance of the inductors. In the equivalent chaotic billiards we derive the distribution of the heat power which well describes numerical statistics.

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