69,990 research outputs found
Reverse Shock Emission as a Probe of GRB Ejecta
We calculate the reverse shock (RS) synchrotron emission in the optical and
the radio wavelength bands from electron-positron pair enriched gamma-ray burst
ejecta with the goal of determining the pair content of GRBs using early time
observations. We take into account an extensive number of physical effects that
influence radiation from the reverse-shock heated GRB ejecta. We find that
optical/IR flux depends very weakly on the number of pairs in the ejecta, and
there is no unique signature of ejecta pair enrichment if observations are
confined to a single wavelength band. It may be possible to determine if the
number of pairs per proton in the ejecta is > 100 by using observations in
optical and radio bands; the ratio of flux in the optical and radio at the peak
of each respective reverse-shock light curve is dependent on the number of
pairs per proton. We also find that over a large parameter space, RS emission
is expected to be very weak; GRB 990123 seems to have been an exceptional burst
in that only a very small fraction of the parameter space produces optical
flashes this bright. Also, it is often the case that the optical flux from the
forward shock is brighter than the reverse shock flux at deceleration. This
could be another possible reason for the paucity of prompt optical flashes with
a rapidly declining light curve at early times as was seen in 990123 and
021211. Some of these results are a generalization of similar results reported
in Nakar & Piran (2004).Comment: 12 pages, 6 figures, 2 tables, accepted to MNRA
Modelling temporal and spatial features of collaboration network
The collaboration network is an example of a social network which has both
non-trivial temporal and spatial dependence. Based on the observations of
collaborations in Physical Review Letters, a model of collaboration network is
proposed which correctly reproduces the time evolution of the link length
distributions, clustering coefficients, degree distributions and assortative
property of real data to a large extent.Comment: 8 pages, 10 figures; follow up work on arXiv.org/physics/0511181;
accepted for publication in IJMP
Canonical representation for electrons and its application to the Hubbard model
A new representation for electrons is introduced, in which the electron
operators are written in terms of a spinless fermion and the Pauli operators.
This representation is canonical, invertible and constraint-free. Importantly,
it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard
model is reduced to a form in which the exchange interaction emerges simply by
decoupling the Pauli subsystem from the spinless fermion bath. This exchange
correctly reproduces the large superexchange. Also derived, for
, is the Hamiltonian to study Nagaoka ferromagnetism. In this
representation, the infinite- Hubbard problem becomes elegant and easier to
handle. Interestingly, the ferromagnetism in Hubbard model is found to be
related to the gauge invariance of the spinless fermions. Generalization of
this representation for the multicomponent fermions, a new representation for
bosons, the notion of a `soft-core' fermion, and some interesting unitary
transformations are introduced and discussed in the appendices.Comment: 10+ pages, 3 Figure
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