dorsal/arxiv
View SchemaElectric circuit networks equivalent to chaotic quantum billiards
| Authors | Evgeny N. Bulgakov, Dmitrii N. Maksimov, Almas F. Sadreev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411100 |
| URL | https://arxiv.org/abs/quant-ph/0411100 |
| DOI | 10.1103/PhysRevE.71.046205 |
Abstract
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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"abstract": "We formulate two types of electric RLC resonance network equivalent to\nquantum billiards. In the network of inductors grounded by capacitors squared\nresonant frequencies are eigenvalues of the quantum billiard. In the network of\ncapacitors grounded by inductors squared resonant frequencies are given by\ninverse eigen values of the billiard. In both cases local voltages play role of\nthe wave function of the quantum billiard. However as different from quantum\nbilliards there is a heat power because of resistance of the inductors. In the\nequivalent chaotic billiards we derive the distribution of the heat power which\nwell describes numerical statistics.",
"arxiv_id": "quant-ph/0411100",
"authors": [
"Evgeny N. Bulgakov",
"Dmitrii N. Maksimov",
"Almas F. Sadreev"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.71.046205",
"title": "Electric circuit networks equivalent to chaotic quantum billiards",
"url": "https://arxiv.org/abs/quant-ph/0411100"
},
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