711 research outputs found
Wick's Theorem for non-symmetric normal ordered products and contractions
We consider arbitrary splits of field operators into two parts, and use the
corresponding definition of normal ordering introduced by Evans and Steer. In
this case the normal ordered products and contractions have none of the special
symmetry properties assumed in existing proofs of Wick's theorem. Despite this,
we prove that Wick's theorem still holds in its usual form as long as the
contraction is a c-number. Wick's theorem is thus shown to be much more general
than existing derivations suggest, and we discuss possible simplifying
applications of this result.Comment: 17 page
Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy
We use simulated maps of the cosmic microwave background anisotropy to
quantify the ability of different statistical tests to discriminate between
Gaussian and non-Gaussian models. Despite the central limit theorem on large
angular scales, both the genus and extrema correlation are able to discriminate
between Gaussian models and a semi-analytic texture model selected as a
physically motivated non-Gaussian model. When run on the COBE 4-year CMB maps,
both tests prefer the Gaussian model. Although the bispectrum has comparable
statistical power when computed on the full sky, once a Galactic cut is imposed
on the data the bispectrum loses the ability to discriminate between models.
Off-diagonal elements of the bispectrum are comparable to the diagonal elements
for the non-Gaussian texture model and must be included to obtain maximum
statistical power.Comment: Accepted for publication in ApJ; 20 pages, 6 figures, uses AASTeX
v5.
How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate
We discuss the dynamics of a quantum phase transition in a spin-1
Bose-Einstein condensate when it is driven from the magnetized
broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We
determine where the condensate goes out of equilibrium as it approaches the
critical point, and compute the condensate magnetization at the critical point.
This is done within a quantum Kibble-Zurek scheme traditionally employed in the
context of symmetry-breaking quantum phase transitions. Then we study the
influence of the nonequilibrium dynamics near a critical point on the
condensate magnetization. In particular, when the quench stops at the critical
point, nonlinear oscillations of magnetization occur. They are characterized by
a period and an amplitude that are inversely proportional. If we keep driving
the condensate far away from the critical point through the unmagnetized
``symmetric'' polar phase, the amplitude of magnetization oscillations slowly
decreases reaching a non-zero asymptotic value. That process is described by
the equation that can be mapped onto the classical mechanical problem of a
particle moving under the influence of harmonic and ``anti-friction'' forces
whose interplay leads to surprisingly simple fixed-amplitude oscillations. We
obtain several scaling results relating the condensate magnetization to the
quench rate, and verify numerically all analytical predictions.Comment: 15 pages, 11 figures, final version accepted in NJP (slight changes
with respect to the former submission
A study of global monopole in Lyra geometry
A class of exact static solution around a global monopole resulting from the
breaking of a global S0(3) symmetry is obtained in the context of Lyra
geometry. Our solution is shown to possess an interesting feature like
wormholes space-time. It has been shown that the global monopole exerts no
gravitational force on surrounding non-relativistic matter.Comment: 6 pages, Published in Mod.Phys.Lett.A19:2785-2790,200
Defect Production in Slow First Order Phase Transitions
We study the formation of vortices in a U(1) gauge theory following a
first-order transition proceeding by bubble nucleation, in particular the
effect of a low velocity of expansion of the bubble walls. To do this, we use a
two-dimensional model in which bubbles are nucleated at random points in a
plane and at random times and then expand at some velocity .
Within each bubble, the phase angle is assigned one of three discrete values.
When bubbles collide, magnetic `fluxons' appear: if the phases are different, a
fluxon--anti-fluxon pair is formed. These fluxons are eventually trapped in
three-bubble collisions when they may annihilate or form quantized vortices. We
study in particular the effect of changing the bubble expansion speed on the
vortex density and the extent of vortex--anti-vortex correlation.Comment: 13 pages, RevTeX, 15 uuencoded postscript figure
Global monopole in scalar tensor theory
The well known monopole solution of Barriola and Vilenkin (BV) resulting from
the breaking of a global SO(3) symmetry is extended in general relativity along
with a zero mass scalar field and also in Brans-Dicke(BD) theory of gravity.In
the case of BD theory, the behaviour of spacetime and other variables such as
BD scalar field and the monopole energy density have been studied
numerically.For monopole along with a zero mass scalar field, exact solutions
are obtained and depending upon the choice of arbitary parameters, the
solutions either reduce to the BV case or to a pure scalar field solution as
special cases.It is interesting to note that unlike the BV case the global
monopole in the BD theory does exert gravitational pull on a test particle
moving in its spacetime.Comment: 12 pages LaTex, 3 postscript figures, Communicated to
Class.Quant.Gra
How does the geodesic rule really work for global symmetry breaking first order phase transitions?
The chain of events usually understood to lead to the formation of
topological defects during phase transitions is known as the Kibble mechanism.
A central component of the mechanism is the so-called ``geodesic rule''.
Although in the Abelian Higgs model the validity of the geodesic rule has been
questioned recently, it is known to be valid on energetic grounds for a global
U(1) symmetry breaking transition. However, even for these globally symmetric
models no dynamical analisys of the rule has been carried to this date, and
some points as to how events proceed still remain obscure. This paper tries to
clarify the dynamics of the geodesic rule in the context of a global U(1)
model. With an appropriate ansatz for the field modulus we find a family of
analytical expressions, phase walls, that accounts for both geodesic and
nongeodesic configurations. We then show how the latter ones are unstable and
decay into the former by nucleating pairs of defects. Finnally, we try to give
a physical perspective of how the geodesic rule might really work in these
transitions.Comment: 10 pages, 9 multiple figre
Where are the Hedgehogs in Nematics?
In experiments which take a liquid crystal rapidly from the isotropic to the
nematic phase, a dense tangle of defects is formed. In nematics, there are in
principle both line and point defects (``hedgehogs''), but no point defects are
observed until the defect network has coarsened appreciably. In this letter the
expected density of point defects is shown to be extremely low, approximately
per initially correlated domain, as result of the topology
(specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)
Gravitational Field of a Global Monopole in a Modified Gravity
In this paper we analyze the gravitational field of a global monopole in the
context of gravity. More precisely, we show that the field equations
obtained are expressed in terms of . Since we are
dealing with a spherically symmetric system, we assume that is a
function of the radial coordinate only. Moreover, adopting the weak field
approximation, we can provide all components of the metric tensor. A comparison
with the corresponding results obtained in General Relativity and in the
Brans-Dicke theory is also made.Comment: 9 pages, work presented in the 8th Alexander Friedmann International
Seminar on Gravitation and Cosmology, in Rio de Janeiro, 30/05 to 03/06/201
Nucleation of vortices by rapid thermal quench
We show that vortex nucleation in superfluid He by rapid thermal quench
in the presence of superflow is dominated by a transverse instability of the
moving normal-superfluid interface. Exact expressions for the instability
threshold as a function of supercurrent density and the front velocity are
found. The results are verified by numerical solution of the Ginzburg-Landau
equation.Comment: 4 Pages, 4 Figure, submitted to Phys. Rev. Let
- âŠ