Fractals, similarity, intermediate asymptotics

Zel’dovich, Yakov Borisovich; Соколов, Д. Д.

doi:10.1070/pu1985v028n07abeh003873

Cited by 50 publications

(25 citation statements)

References 3 publications

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“…We can compute this force by using the integrals (28)(29)(30) given in & 2 and the macroscopic quantities (42-45), we obtain…”

Section: Photon-electron Scatteringmentioning

confidence: 99%

Dynamics of relativistic interacting gases: from a kinetic to a fluid description

Uzan

1998

Class. Quantum Grav.

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Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this equation to obtain an effective macroscopic description. This formalism will be useful to study the cosmic microwave background non-perturbatively in inhomogeneous cosmologies. It should also be useful for the study of the dynamics of the early universe and can be applied, if one considers fluids of galaxies, to the study of structure formation.Pacs : 98.80.Hw, 04.20.Cv

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“…We can compute this force by using the integrals (28)(29)(30) given in & 2 and the macroscopic quantities (42-45), we obtain…”

Section: Photon-electron Scatteringmentioning

confidence: 99%

Dynamics of relativistic interacting gases: from a kinetic to a fluid description

Uzan

1998

Class. Quantum Grav.

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“…Analytic solutions can be obtained by the standard method of characteristics for the recoil (n) and induced recoil (n 2 ) terms individually, and they consist of photons moving down the frequency axes at a speed proportional to x 2 for the recoil term (Arons 1971; and at a speed proportional to the x 2 n for the induced recoil term (Zel'Dovich & Levich 1969;Syunyaev 1971). To get the linear solution, we can just substitute n(x) = n BB (x) on the righthand side of Eq.…”

Section: New Solution Of Kompaneets Equation For Comptonization Of Phmentioning

confidence: 99%

Does Bose-Einstein condensation of CMB photons cancelμdistortions created by dissipation of sound waves in the early Universe?

Khatri

Sunyaev

Chluba

2012

A&A

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The difference in the adiabatic indices of photons and non-relativistic baryonic matter in the early Universe causes the electron temperature to be slightly lower than the radiation temperature. Comptonization of photons with colder electrons results in the transfer of energy from photons to electrons and ions, owing to the recoil effect (spontaneous and induced). Thermalization of photons with a colder plasma results in the accumulation of photons in the Rayleigh-Jeans tail, aided by stimulated recoil, while the higher frequency spectrum tries to approach Planck spectrum at the electron temperature T final γ = T e < T initial γ ; i.e., Bose-Einstein condensation of photons occurs. We find new solutions of the Kompaneets equation describing this effect. No actual condensate is, in reality, possible since the process is very slow and photons drifting to low frequencies are efficiently absorbed by bremsstrahlung and double Compton processes. The spectral distortions created by Bose-Einstein condensation of photons are within an order of magnitude (for the present range of allowed cosmological parameters), with exactly the same spectrum but opposite in sign, of those created by diffusion damping of the acoustic waves on small scales corresponding to comoving wavenumbers 45 < k < 10 4 Mpc −1 . The initial perturbations on these scales are completely unobservable today due to their being erased completely by Silk damping. There is partial cancellation of these two distortions, leading to suppression of μ distortions expected in the standard model of cosmology. The net distortion depends on the scalar power index n s and its running dn s /d ln k, and may vanish for special values of parameters, for example, for a running spectrum with, n s = 1, dn s /d ln k = −0.038. We arrive at an intriguing conclusion: even a null result, non-detection of μ-type distortion at a sensitivity of 10 −9 , gives a quantitative measure of the primordial small-scale power spectrum.

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“…To complete the overall academic research, experiments on BEC of photons were required. For several reasons there are few theoretical works devoted to this phenomenon (see, for example [17][18][19]). Indeed, when it comes to Bose-Einstein condensation, the possibility of such phenomena in gases as the simplest physical systems was studied first.…”

Section: Introductionmentioning

confidence: 99%

Coexistence of photonic and atomic Bose-Einstein condensates in ideal atomic gases

Boichenko¹,

Slyusarenko²

2015

Condens. Matter Phys.

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We have studied conditions of photon Bose-Einstein condensate formation that is in thermodynamic equilibrium with ideal gas of two-level Bose atoms below the degeneracy temperature. Equations describing thermodynamic equilibrium in the system were formulated; critical temperatures and densities of photonic and atomic gas subsystems were obtained analytically. Coexistence conditions of these photonic and atomic Bose-Einstein condensates were found. There was predicted the possibility of an abrupt type of photon condensation in the presence of Bose condensate of ground-state atoms: it was shown that the slightest decrease of the temperature could cause a significant gathering of photons in the condensate. This case could be treated as a simple model of the situation known as "stopped light" in cold atomic gas. We also showed how population inversion of atomic levels can be created by lowering the temperature. The latter situation looks promising for light accumulation in atomic vapor at very low temperatures.

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Fractals, similarity, intermediate asymptotics

Cited by 50 publications

References 3 publications

Dynamics of relativistic interacting gases: from a kinetic to a fluid description

Dynamics of relativistic interacting gases: from a kinetic to a fluid description

Does Bose-Einstein condensation of CMB photons cancelμdistortions created by dissipation of sound waves in the early Universe?

Coexistence of photonic and atomic Bose-Einstein condensates in ideal atomic gases

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