dorsal/arxiv
View SchemaInvitation to the "Spooky" Quantum Phase-Locking Effect and its Link to 1/F Fluctuations
| Authors | Michel Planat |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310082 |
| URL | https://arxiv.org/abs/quant-ph/0310082 |
Abstract
An overview of the concept of phase-locking at the non linear, geometric and quantum level is attempted, in relation to finite resolution measurements in a communication receiver and its 1/f noise. Sine functions, automorphic functions and cyclotomic arithmetic are respectively used as the relevant trigonometric tools. The common point of the three topics is found to be the Mangoldt function of prime number theory as the generator of low frequency noise in the coupling coefficient, the scattering coefficient and in quantum critical statistical states. Huyghens coupled pendulums, the Adler equation, the Arnold map, continued fraction expansions, discrete Mobius transformations, Ford circles, coherent and squeezed phase states, Ramanujan sums, the Riemann zeta function and Bost and Connes KMS states are some but a few concepts which are used synchronously in the paper.
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"abstract": "An overview of the concept of phase-locking at the non linear, geometric and\nquantum level is attempted, in relation to finite resolution measurements in a\ncommunication receiver and its 1/f noise. Sine functions, automorphic functions\nand cyclotomic arithmetic are respectively used as the relevant trigonometric\ntools. The common point of the three topics is found to be the Mangoldt\nfunction of prime number theory as the generator of low frequency noise in the\ncoupling coefficient, the scattering coefficient and in quantum critical\nstatistical states. Huyghens coupled pendulums, the Adler equation, the Arnold\nmap, continued fraction expansions, discrete Mobius transformations, Ford\ncircles, coherent and squeezed phase states, Ramanujan sums, the Riemann zeta\nfunction and Bost and Connes KMS states are some but a few concepts which are\nused synchronously in the paper.",
"arxiv_id": "quant-ph/0310082",
"authors": [
"Michel Planat"
],
"categories": [
"quant-ph"
],
"title": "Invitation to the \"Spooky\" Quantum Phase-Locking Effect and its Link to 1/F Fluctuations",
"url": "https://arxiv.org/abs/quant-ph/0310082"
},
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