40 research outputs found
CMB map derived from the WMAP data through Harmonic Internal Linear Combination
We are presenting an Internal Linear Combination (ILC) CMB map, in which the
foreground is reduced through harmonic variance minimization. We have derived
our method by converting a general form of pixel-space approach into spherical
harmonic space, maintaining full correspondence. By working in spherical
harmonic space, spatial variability of linear weights is incorporated in a
self-contained manner and our linear weights are continuous functions of
position over the entire sky. The full correspondence to pixel-space approach
enables straightforward physical interpretation on our approach. In variance
minimization of a linear combination map, the existence of a cross term between
residual foregrounds and CMB makes the linear combination of minimum variance
differ from that of minimum foreground. We have developed an iterative
foreground reduction method, where perturbative correction is made for the
cross term. Our CMB map derived from the WMAP data is in better agreement with
the WMAP best-fit CDM model than the WMAP team's Internal Linear
Combination map. We find that our method's capacity to clean foreground is
limited by the availability of enough spherical harmonic coefficients of good
Signal-to-Noise Ratio (SNR).Comment: The whole sky CMB map, which is derived from the WMAP 5 year data
through our method, is available in HEALPix FITS format at
http://www.nbi.dk/~jkim/hilc The paper with higher resolution images also
available at http://www.nbi.dk/~jkim/hil
Thermodynamic curvature measures interactions
Thermodynamic fluctuation theory originated with Einstein who inverted the
relation to express the number of states in terms of entropy:
. The theory's Gaussian approximation is discussed in most
statistical mechanics texts. I review work showing how to go beyond the
Gaussian approximation by adding covariance, conservation, and consistency.
This generalization leads to a fundamentally new object: the thermodynamic
Riemannian curvature scalar , a thermodynamic invariant. I argue that
is related to the correlation length and suggest that the sign of
corresponds to whether the interparticle interactions are effectively
attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27
Single-Particle Density of States of a Superconductor with a Spatially Varying Gap and Phase Fluctuations
Recent experiments have shown that the superconducting energy gap in some
cuprates is spatially inhomogeneous. Motivated by these experiments, and using
exact diagonalization of a model d-wave Hamiltonian, combined with Monte Carlo
simulations of a Ginzburg-Landau free energy functional, we have calculated the
single-particle density of states LDOS of a model high-T
superconductor as a function of temperature. Our calculations include both
quenched disorder in the pairing potential and thermal fluctuations in both
phase and amplitude of the superconducting gap. Most of our calculations assume
two types of superconducting regions: , with a small gap and large
superfluid density, and , with the opposite. If the regions are
randomly embedded in an host, the LDOS on the sites still has
a sharp coherence peak at , but the component does not, in
agreement with experiment. An ordered arrangement of regions leads to
oscillations in the LDOS as a function of energy. The model leads to a
superconducting transition temperature well below the pseudogap
temperature , and has a spatially varying gap at very low , both
consistent with experiments in underdoped Bi2212. Our calculated
LDOS shows coherence peaks for , in agreement with previous work considering phase but not amplitude
fluctuations in a homogeneous superconductor. Well above , the gap in the
LDOS disappears.Comment: 37 pages, 12 figures. Accepted by Phys. Rev. B. Scheduled Issue: 01
Nov 200
Conformal Scalar Propagation on the Schwarzschild Black-Hole Geometry
The vacuum activity generated by the curvature of the Schwarzschild
black-hole geometry close to the event horizon is studied for the case of a
massless, conformal scalar field. The associated approximation to the unknown,
exact propagator in the Hartle-Hawking vacuum state for small values of the
radial coordinate above results in an analytic expression which
manifestly features its dependence on the background space-time geometry. This
approximation to the Hartle-Hawking scalar propagator on the Schwarzschild
black-hole geometry is, for that matter, distinct from all other. It is shown
that the stated approximation is valid for physical distances which range from
the event horizon to values which are orders of magnitude above the scale
within which quantum and backreaction effects are comparatively pronounced. An
expression is obtained for the renormalised in the
Hartle-Hawking vacuum state which reproduces the established results on the
event horizon and in that segment of the exterior geometry within which the
approximation is valid. In contrast to previous results the stated expression
has the superior feature of being entirely analytic. The effect of the
manifold's causal structure to scalar propagation is also studied.Comment: 34 pages, 2 figures. Published on line on October 16, 2009 and due to
appear in print in Gen.Rel.Gra
Precise bounds on the Higgs boson mass
We study the renormalization group evolution of the Higgs quartic coupling
and the Higgs mass in the Standard Model. The one loop
equation for is non linear and it is of the Riccati type which we
numerically and analytically solve in the energy range where
is the mass of the top quark and GeV. We find that
depending on the value of the solution for
may have singularities or zeros and become negative in the
former energy range so the ultra violet cut off of the standard model should be
below the energy where the zero or singularity of occurs. We find
that for the Standard Model is valid in
the whole range . We consider two cases of the Higgs mass
relation to the parameters of the standard model: (a) the effective potential
method and (b) the tree level mass relations. The limits for
correspond to the following Higgs mass relation GeV. We also plot the dependence of the ultra violet cut
off on the value of the Higgs mass. We analyze the evolution of the vacuum
expectation value of the Higgs field and show that it depends on the value of
the Higgs mass. The pattern of the energy behavior of the VEV is different for
the cases (a) and (b). The behavior of , and
indicates the existence of a phase transition in the standard model. For the
effective potential this phase transition occurs at the mass range
GeV and for the tree level mass relations at GeV.Comment: 14 pages, 7 figures. Expanded the discussion of the Higgs mass
relation between the parameters of the Standard Model. Included the method of
the Higgs effective potentia
Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy
We consider spatially two dimensional Madelung fluid whose irrotational
motion reduces into the Schr\"odinger equation for a single free particle. In
this respect, we regard the former as a direct generalization of the latter,
allowing a rotational quantum flow. We then ask for the most likely wave
function possessing a given average energy by maximizing the Shannon
information entropy over the quantum probability density. We show that there
exists a class of solutions in which the wave function is self-trapped,
rotationally symmetric, spatially localized with finite support, and spinning
around its center, yet stationary. The stationarity comes from the balance
between the attractive quantum force field of a trapping quantum potential
generated by quantum probability density and the repulsive centrifugal force of
a rotating velocity vector field. We further show that there is a limiting case
where the wave function is non-spinning and yet still stationary. This special
state turns out to be the lowest stationary state of the ordinary Schr\"odinger
equation for a particle in a cylindrical tube classical potential.Comment: 19 page
General relativistic analysis of peculiar velocities
We give a careful general relativistic and (1+3)-covariant analysis of
cosmological peculiar velocities induced by matter density perturbations in the
presence of a cosmological constant. In our quasi-Newtonian approach,
constraint equations arise to maintain zero shear of the non-comoving
fundamental worldlines which define a Newtonian-like frame, and these lead to
the (1+3)-covariant dynamical equations, including a generalized Poisson-type
equation. We investigate the relation between peculiar velocity and peculiar
acceleration, finding the conditions under which they are aligned. In this case
we find (1+3)-covariant relativistic generalizations of well-known Newtonian
results.Comment: 8 pages, LaTeX2e (iopart); minor changes, matches version accepted
for publication by Classical and Quantum Gravit
Three routes to the exact asymptotics for the one-dimensional quantum walk
We demonstrate an alternative method for calculating the asymptotic behaviour
of the discrete one-coin quantum walk on the infinite line, via the Jacobi
polynomials that arise in the path integral representation. This is
significantly easier to use than the Darboux method. It also provides a single
integral representation for the wavefunction that works over the full range of
positions, including throughout the transitional range where the behaviour
changes from oscillatory to exponential. Previous analyses of this system have
run into difficulties in the transitional range, because the approximations on
which they were based break down here. The fact that there are two different
kinds of approach to this problem (Path Integral vs. Schr\"{o}dinger wave
mechanics) is ultimately a manifestation of the equivalence between the
path-integral formulation of quantum mechanics and the original formulation
developed in the 1920s. We discuss how and why our approach is related to the
two methods that have already been used to analyse these systems.Comment: 25 pages, AMS preprint format, 4 figures as encapsulated postscript.
Replaced because there were sign errors in equations (80) & (85) and Lemma 2
of the journal version (v3
Pure-state single-photon wave-packet generation by parametric down conversion in a distributed microcavity
We propose an optical parametric down conversion (PDC) scheme that does not
suffer a trade-off between the state-purity of single-photon wave-packets and
the rate of packet production. This is accomplished by modifying the PDC
process by using a microcavity to engineer the density of states of the optical
field at the PDC frequencies. The high-finesse cavity mode occupies a spectral
interval much narrower than the bandwidth of the pulsed pump laser field,
suppressing the spectral correlation, or entanglement, between signal and idler
photons. Spectral filtering of the field occurs prior to photon creation rather
than afterward as in most other schemes. Operator-Maxwell equations are solved
to find the Schmidt-mode decomposition of the two-photon states produced.
Greater than 99% pure-state packet production is predicted to be achievable.Comment: submitted for publicatio