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Electric circuit networks equivalent to chaotic quantum billiards
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation, Astaf'Ev Pedagogical University, 89, Krasnoyarsk, 660049 Lebedeva, Russian Federation.
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation.
Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
2005 (English)In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 71, no 4Article in journal (Refereed) Published
Abstract [en]

We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics. © 2005 The American Physical Society.

Place, publisher, year, edition, pages
2005. Vol. 71, no 4
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-45484DOI: 10.1103/PhysRevE.71.046205OAI: diva2:266380
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-12

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Sadreev, Almas
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The Institute of TechnologyDepartment of Physics, Chemistry and Biology
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