Entropy production and isotropization in Yang-Mills theory with use of quantum distribution function

We investigate thermalization process in relativistic heavy ion collisions in terms of the Husimi-Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang-Mills field theory with the phenomenological initial field configuration known as the McLerran-Venugopalan model in a non-expanding geometry, which has instabilty triggered by initial field fluctuations. HW-entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov-Sina\"i rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around $1$ fm/c in the present calculation in the non-expanding geometry.Comment: 17 pages, 5 figure

Cosmological Magnetic Field: a fossil of density perturbations in the early universe

The origin of the substantial magnetic fields that are found in galaxies and on even larger scales, such as in clusters of galaxies, is yet unclear. If the second-order couplings between photons and electrons are considered, then cosmological density fluctuations, which explain the large scale structure of the universe, can also produce magnetic fields on cosmological scales before the epoch of recombination. By evaluating the power spectrum of these cosmological magnetic fields on a range of scales, we show here that magnetic fields of 10^{-18.1} gauss are generated at a 1 megaparsec scale and can be even stronger at smaller scales (10^{-14.1} gauss at 10 kiloparsecpc). These fields are large enough to seed magnetic fields in galaxies and may therefore have affected primordial star formation in the early universe.Comment: 11 pages, 3 figures, accepted draft for publication in Science. Edited version and supporting online material are available at: http://www.sciencemag.org/cgi/content/abstract/311/5762/82

Entropy production in quantum Yang-Mills mechanics in semi-classical approximation

We discuss thermalization of isolated quantum systems by using the Husimi-Wehrl entropy evaluated in the semiclassical treatment. The Husimi-Wehrl entropy is the Wehrl entropy obtained by using the Husimi function for the phase space distribution. The time evolution of the Husimi function is given by smearing the Wigner function, whose time evolution is obtained in the semiclassical approximation. We show the efficiency and usefullness of this semiclassical treatment in describing entropy production of a couple of quantum mechanical systems, whose classical counter systems are known to be chaotic. We propose two methods to evaluate the time evolution of the Husimi-Wehrl entropy, the test-particle method and the two-step Monte-Carlo method. We demonstrate the characteristics of the two methods by numerical calculations, and show that the simultaneous application of the two methods ensures the reliability of the results of the Husimi-Wehrl entropy at a given time.Comment: 11 pages, 8 figure

Biermann Mechanism in Primordial Supernova Remnant and Seed Magnetic Fields

We study generation of magnetic fields by the Biermann mechanism in the pair-instability supernovae explosions of first stars. The Biermann mechanism produces magnetic fields in the shocked region between the bubble and interstellar medium (ISM), even if magnetic fields are absent initially. We perform a series of two-dimensional magnetohydrodynamic simulations with the Biermann term and estimate the amplitude and total energy of the produced magnetic fields. We find that magnetic fields with amplitude $10^{-14}-10^{-17}$ G are generated inside the bubble, though the amount of magnetic fields generated depend on specific values of initial conditions. This corresponds to magnetic fields of $10^{28}-10^{31}$ erg per each supernova remnant, which is strong enough to be the seed magnetic field for galactic and/or interstellar dynamo.Comment: 12 pages, 3 figure