dorsal/arxiv
View SchemaIrreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
| Authors | Sandor Varro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610184 |
| URL | https://arxiv.org/abs/quant-ph/0610184 |
| DOI | 10.1088/0031-8949/75/2/008 |
| Journal | Physica Scripta, Vol. 75, pp 160-169 (2007) |
Abstract
It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it Planck variable) whose distribution is just the Bose distribution yielding the Planck law of black-body radiation. The fractional part is the dark part (we call is dark variable) with a continuous distribution, which is, of course, not observed in the experiments. It is proved that the Bose distribution is infinitely divisible, and the irreducible decomposition of it is given. The Planck variable can be decomposed into an infinite sum of independent binary random variables representing the binary photons (more accurately photo-molecules or photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons follow the Fermi statistics. Consequently, the black-body radiation can be viewed as a mixture of statistically and thermodynamically independent fermion gases consisting of binary photons. The binary photons give a natural tool for the dyadic expansion of arbitrary (but not coherent) ordinary photon excitations. It is shown that the binary photons have wave-particle fluctuations of fermions. These fluctuations combine to give the wave-particle fluctuations of the original bosonic photons expressed by the Einstein fluctuation formula.
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"abstract": "It is shown that the energy of a mode of a classical chaotic field, following\nthe continuous exponential distribution as a classical random variable, can be\nuniquely decomposed into a sum of its fractional part and of its integer part.\nThe integer part is a discrete random variable (we call it Planck variable)\nwhose distribution is just the Bose distribution yielding the Planck law of\nblack-body radiation. The fractional part is the dark part (we call is dark\nvariable) with a continuous distribution, which is, of course, not observed in\nthe experiments. It is proved that the Bose distribution is infinitely\ndivisible, and the irreducible decomposition of it is given. The Planck\nvariable can be decomposed into an infinite sum of independent binary random\nvariables representing the binary photons (more accurately photo-molecules or\nphoto-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons\nfollow the Fermi statistics. Consequently, the black-body radiation can be\nviewed as a mixture of statistically and thermodynamically independent fermion\ngases consisting of binary photons. The binary photons give a natural tool for\nthe dyadic expansion of arbitrary (but not coherent) ordinary photon\nexcitations. It is shown that the binary photons have wave-particle\nfluctuations of fermions. These fluctuations combine to give the wave-particle\nfluctuations of the original bosonic photons expressed by the Einstein\nfluctuation formula.",
"arxiv_id": "quant-ph/0610184",
"authors": [
"Sandor Varro"
],
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"doi": "10.1088/0031-8949/75/2/008",
"journal_ref": "Physica Scripta, Vol. 75, pp 160-169 (2007)",
"title": "Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation",
"url": "https://arxiv.org/abs/quant-ph/0610184"
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