464 research outputs found
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
fm/c in the present calculation in the non-expanding geometry.Comment: 17 pages, 5 figure
Origami fold as algebraic graph rewriting
AbstractWe formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system (O,↬), where O is the set of abstract origamis and ↬ is a binary relation on O, that models fold. An abstract origami is a structure (Π,∽,≻), where Π is a set of faces constituting an origami, and ∽ and ≻ are binary relations on Π, each representing adjacency and superposition relations between the faces.We then address representation and transformation of abstract origamis and further reasoning about the construction for computational purposes. We present a labeled hypergraph of origami and define fold as algebraic graph transformation. The algebraic graph-theoretic formalism enables us to reason about origami in two separate domains of discourse, i.e. pure combinatorial domain where symbolic computation plays the main role and geometrical domain R×R. We detail the program language for the algebraic graph rewriting and graph rewriting algorithms for the fold, and show how fold is expressed by a set of graph rewrite rules
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
Study of entropy production in Yang-Mills theory with use of Husimi function
Understanding the thermalization process in a pure quantum system is a
challenge in theoretical physics. In this work, we explore possible
thermalization mechanism in Yang-Mills(YM) theory by using a positive
semi-definite quantum distribution function called a Husimi function which is
given by a coarse graining of the Wigner function within the minimum
uncertainty. Then entropy is defined in terms of the Husimi function, which is
called the Husimi-Wehrl(HW) entropy. We propose two numerical methods to
calculate the HW entropy. We find that it is feasible to apply the
semi-classical approximation with the use of classical YM equation. It should
be noted that the semi-classical approximation is valid in the systems of
physical interest including the early stage of heavy-ion collisions. Using a
product ansatz for the Husimi function, which is confirmed to reproduce the HW
entropy within 20% error (overestimate) for a few-body quantum system, we
succeed in a numerical evaluation of HW entropy of YM fields and show that it
surely has a finite value and increases in time.Comment: 7 pages, 5 figures, Proceeding of the 33rd International Symposium on
Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International
Conference Center, Kobe, Japa
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
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