201 research outputs found
Finite-Dimensional Bicomplex Hilbert Spaces
This paper is a detailed study of finite-dimensional modules defined on
bicomplex numbers. A number of results are proved on bicomplex square matrices,
linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces,
including the spectral decomposition theorem. Applications to concepts relevant
to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page
Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines
Here we briefly report on results of self-consistent numerical modeling of a
differentially rotating force-free magnetosphere of an aligned rotator. We show
that differential rotation of the open field line zone is significant for
adjusting of the global structure of the magnetosphere to the current density
flowing through the polar cap cascades. We argue that for most pulsars
stationary cascades in the polar cap can not support stationary force-free
configurations of the magnetosphere.Comment: 5 pages, 4 figures. Presented at the conference "Isolated Neutron
Stars: from the Interior to the Surface", London, April 24-28, 2006; to
appear in Astrophysics and Space Science. Significantly revised version, a
mistake found by ourselfs in the numerical code was corrected, all presented
results are obtained with the correct version of the cod
The influence of fractional diffusion in Fisher-KPP equations
We study the Fisher-KPP equation where the Laplacian is replaced by the
generator of a Feller semigroup with power decaying kernel, an important
example being the fractional Laplacian. In contrast with the case of the stan-
dard Laplacian where the stable state invades the unstable one at constant
speed, we prove that with fractional diffusion, generated for instance by a
stable L\'evy process, the front position is exponential in time. Our results
provide a mathe- matically rigorous justification of numerous heuristics about
this model
Adjustment of the electric current in pulsar magnetospheres and origin of subpulse modulation
The subpulse modulation of pulsar radio emission goes to prove that the
plasma flow in the open field line tube breaks into isolated narrow streams. I
propose a model which attributes formation of streams to the process of the
electric current adjustment in the magnetosphere. A mismatch between the
magnetospheric current distribution and the current injected by the polar cap
accelerator gives rise to reverse plasma flows in the magnetosphere. The
reverse flow shields the electric field in the polar gap and thus shuts up the
plasma production process. I assume that a circulating system of streams is
formed such that the upward streams are produced in narrow gaps separated by
downward streams. The electric drift is small in this model because the
potential drop in narrow gaps is small. The gaps have to drift because by the
time a downward stream reaches the star surface and shields the electric field,
the corresponding gap has to shift. The transverse size of the streams is
determined by the condition that the potential drop in the gaps is sufficient
for the pair production. This yields the radius of the stream roughly 10% of
the polar cap radius, which makes it possible to fit in the observed
morphological features such as the "carousel" with 10-20 subbeams and the
system of the core - two nested cone beams.Comment: 8 pages, 1 figur
On the role of the current loss in radio pulsar evolution
The aim of this article is to draw attention to the importance of the
electric current loss in the energy output of radio pulsars. We remind that
even the losses attributed to the magneto-dipole radiation of a pulsar in
vacuum can be written as a result of an Ampere force action of the electric
currens flowing over the neutron star surface (Michel, 1991, Beskin et al.,
1993). It is this force that is responsible for the transfer of angular
momentum of a neutron star to an outgoing magneto-dipole wave. If a pulsar is
surrounded by plasma, and there is no longitudinal current in its
magnetosphere, there is no energy loss (Beskin et al., 1993, Mestel et al.,
1999). It is the longitudinal current closing within the pulsar polar cap that
exerts the retardation torque acting on the neutron star. This torque can be
determined if the structure of longitudinal current is known. Here we remind of
the solution by Beskin, Gurevitch & Istomin (1993) and discuss the validity of
such an assumption. The behavior of the recently observed "part-time job"
pulsar B1931+24 can be naturally explained within the model of current loss
while the magneto-dipole model faces difficulties.Comment: 4 pages, to appear in Astrophysics and Space Science, Special Issue:
Isolated Neutron Stars. In the replaced paper we amended several misprints
(coefficients in equations 12,14,15) and removed the excessive explanation
for the boundary condition (4
Stochastic excitation of acoustic modes in stars
For more than ten years, solar-like oscillations have been detected and
frequencies measured for a growing number of stars with various characteristics
(e.g. different evolutionary stages, effective temperatures, gravities, metal
abundances ...).
Excitation of such oscillations is attributed to turbulent convection and
takes place in the uppermost part of the convective envelope. Since the
pioneering work of Goldreich & Keely (1977), more sophisticated theoretical
models of stochastic excitation were developed, which differ from each other
both by the way turbulent convection is modeled and by the assumed sources of
excitation. We review here these different models and their underlying
approximations and assumptions.
We emphasize how the computed mode excitation rates crucially depend on the
way turbulent convection is described but also on the stratification and the
metal abundance of the upper layers of the star. In turn we will show how the
seismic measurements collected so far allow us to infer properties of turbulent
convection in stars.Comment: Notes associated with a lecture given during the fall school
organized by the CNRS and held in St-Flour (France) 20-24 October 2008 ; 39
pages ; 11 figure
"The fruits of independence": Satyajit Ray, Indian nationhood and the spectre of empire
Challenging the longstanding consensus that Satyajit Ray's work is largely free of ideological concerns and notable only for its humanistic richness, this article shows with reference to representations of British colonialism and Indian nationhood that Ray's films and stories are marked deeply and consistently by a distinctively Bengali variety of liberalism. Drawn from an ongoing biographical project, it commences with an overview of the nationalist milieu in which Ray grew up and emphasizes the preoccupation with colonialism and nationalism that marked his earliest unfilmed scripts. It then shows with case studies of Kanchanjangha (1962), Charulata (1964), First Class Kamra (First-Class Compartment, 1981), Pratidwandi (The Adversary, 1970), Shatranj ke Khilari (The Chess Players, 1977), Agantuk (The Stranger, 1991) and Robertsoner Ruby (Robertson's Ruby, 1992) how Ray's mature work continued to combine a strongly anti-colonial viewpoint with a shifting perspective on Indian nationhood and an unequivocal commitment to cultural cosmopolitanism. Analysing how Ray articulated his ideological positions through the quintessentially liberal device of complexly staged debates that were apparently free, but in fact closed by the scenarist/director on ideologically specific notes, this article concludes that Ray's reputation as an all-forgiving, ‘everybody-has-his-reasons’ humanist is based on simplistic or even tendentious readings of his work
An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes
The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n≥2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance
Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV
A search for pair-production of supersymmetric particles under the assumption
that R-parity is violated via a dominant LQDbar coupling has been performed
using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV.
The observed candidate events in the data are in agreement with the Standard
Model expectation. This result is translated into lower limits on the masses of
charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for
m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81
GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the
95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure
New Phase-coherent Measurements of Pulsar Braking Indices
Pulsar braking indices offer insight into the physics that underlies pulsar
spin-down. Only five braking indices have been measured via phase-coherent
timing; all measured values are less than 3, the value expected from magnetic
dipole radiation. Here we present new measurements for three of the five pulsar
braking indices, obtained with phase-coherent timing for PSRs J1846-0258
(n=2.65+/-0.01), B1509-58 (n=2.839+/-0.001) and B0540-69 (n=2.140+/-0.009). We
discuss the implications of these results and possible physical explanations
for them.Comment: 7 pages, 5 figures. To be published in the proceedings of the
conference "Isolated Neutron Stars: from the Interior to the Surface" (April
24-28, 2006, London, UK), eds. D. Page, R. Turolla, & S. Zan
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