Mathematical Background of 1/f Fluctuations
- Brain Functions Laboratory, Inc. 4259-3 Nagatsuta, Midori-ku, Yokohama, JAPAN 226-8510 (Japan)
Energy of harmonic oscillators in equilibrium decays exponentially in time when they are coupled in quadratic forms in amplitudes. In reality, however, their Hamiltonian includes higher-order coupling terms. Not all of the higher-order coupling terms contribute to the energy decay of oscillators after averaging over reservoir oscillators, and we find that one of the lowest higher-order terms makes a finite contribution to the energy decay. This effect is equivalently represented by a modified coupling coefficient of quadratic coupling terms. This modification works as a positive feedback to the action-reaction process between oscillators. Eventually the modified coupling terms generate 1/f fluctuations in energy partition among oscillators in equilibrium. It is concluded that 1/f type of energy partition is observable with harmonic oscillators if they obey the Bose-Einstein statistics regardless of whether the collective system is classical or quantum mechanical regime.
- OSTI ID:
- 21304852
- Journal Information:
- AIP Conference Proceedings, Vol. 1129, Issue 1; Conference: ICNF-2009: 20. international conference on noise and fluctuations, Pisa (Italy), 14-19 Jun 2009; Other Information: DOI: 10.1063/1.3140479; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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