2,516 research outputs found
Excitation of hydrogen molecule by electron impact, III - Singlet-triplet excitations
Exchange excitation of hydrogen molecule by electron impact from ground to triplet electronic stat
Chemical Enrichment at High Redshifts
We have tried to understand the recent observations related to metallicity in
Ly forest clouds in the framework of the two component model suggested
by Chiba & Nath (1997). We find that even if the mini-halos were chemically
enriched by an earlier generation of stars, to have [C/H] -2.5, the
number of C IV lines with column density , contributed by the
mini-halos, at the redshift of 3, would be only about 10% of the total number
of lines, for a chemical enrichment rate of in the galaxies.
Recently reported absence of heavy element lines associated with most of the Ly
lines with H I column density between and by Lu et al (1998), if correct, gives an upper limit on [C/H]=-3.7,
not only in the mini-halos, but also in the outer parts of galactic halos. This
is consistent with the results of numerical simulations, according to which,
the chemical elements associated with the Ly clouds are formed in situ
in clouds, rather than in an earlier generation of stars. However, the mean
value of for the column density ratio of C IV and H I,
determined by Cowie and Songaila (1998) for low Lyman alpha optical depths,
implies an abundance of [C/H] =-2.5 in mini-halos as well as in most of the
region in galactic halos, presumably enriched by an earlier generation of
stars. The redshift and column density distribution of C IV has been shown to
be in reasonable agreement with the observations.Comment: 23 pages, 6 figures, To appear in Astrophysical Journa
A Calogero-Sutherland Type Model For Branched Polymers
We show that a Calogero-Sutherland type model with anharmonic interactions of
fourth and sixth orders leads to the matrix model corresponding to the branched
polymers. We also show that by suitably modifying this model one can also
obtain N-particle problems which are connected to matrix models corresponding
to the pure gravity phase as well as corresponding to the transition point
between the soap bubble and the branched polymer phase.Comment: 6 pages, no figure
Local Identities Involving Jacobi Elliptic Functions
We derive a number of local identities of arbitrary rank involving Jacobi
elliptic functions and use them to obtain several new results. First, we
present an alternative, simpler derivation of the cyclic identities discovered
by us recently, along with an extension to several new cyclic identities of
arbitrary rank. Second, we obtain a generalization to cyclic identities in
which successive terms have a multiplicative phase factor exp(2i\pi/s), where s
is any integer. Third, we systematize the local identities by deriving four
local ``master identities'' analogous to the master identities for the cyclic
sums discussed by us previously. Fourth, we point out that many of the local
identities can be thought of as exact discretizations of standard nonlinear
differential equations satisfied by the Jacobian elliptic functions. Finally,
we obtain explicit answers for a number of definite integrals and simpler forms
for several indefinite integrals involving Jacobi elliptic functions.Comment: 47 page
Methods for Generating Quasi-Exactly Solvable Potentials
We describe three different methods for generating quasi-exactly solvable
potentials, for which a finite number of eigenstates are analytically known.
The three methods are respectively based on (i) a polynomial ansatz for wave
functions; (ii) point canonical transformations; (iii) supersymmetric quantum
mechanics. The methods are rather general and give considerably richer results
than those available in the current literature.Comment: 12 pages, LaTe
Estimating the spectral gap of a trace-class Markov operator
The utility of a Markov chain Monte Carlo algorithm is, in large part,
determined by the size of the spectral gap of the corresponding Markov
operator. However, calculating (and even approximating) the spectral gaps of
practical Monte Carlo Markov chains in statistics has proven to be an extremely
difficult and often insurmountable task, especially when these chains move on
continuous state spaces. In this paper, a method for accurate estimation of the
spectral gap is developed for general state space Markov chains whose operators
are non-negative and trace-class. The method is based on the fact that the
second largest eigenvalue (and hence the spectral gap) of such operators can be
bounded above and below by simple functions of the power sums of the
eigenvalues. These power sums often have nice integral representations. A
classical Monte Carlo method is proposed to estimate these integrals, and a
simple sufficient condition for finite variance is provided. This leads to
asymptotically valid confidence intervals for the second largest eigenvalue
(and the spectral gap) of the Markov operator. In contrast with previously
existing techniques, our method is not based on a near-stationary version of
the Markov chain, which, paradoxically, cannot be obtained in a principled
manner without bounds on the spectral gap. On the other hand, it can be quite
expensive from a computational standpoint. The efficiency of the method is
studied both theoretically and empirically
One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations
We study the generalized Korteweg-DeVries equations derivable from the
Lagrangian: where the usual fields of the
generalized KdV equation are defined by . For an
arbitrary continuous parameter we find compacton solutions
to these equations which have the feature that their width is independent of
the amplitude. This generalizes previous results which considered . For
the exact compactons we find a relation between the energy, mass and velocity
of the solitons. We show that this relationship can also be obtained using a
variational method based on the principle of least action.Comment: Latex 4 pages and one figure available on reques
Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials
We obtain the exact nontopological soliton lattice solutions of the
Associated Lam\'e equation in different parameter regimes and compute the
corresponding energy for each of these solutions. We show that in specific
limits these solutions give rise to nontopological (pulse-like) single
solitons, as well as to different types of topological (kink-like) single
soliton solutions of the Associated Lam\'e equation. Following Manton, we also
compute, as an illustration, the asymptotic interaction energy between these
soliton solutions in one particular case. Finally, in specific limits, we
deduce the soliton lattices, as well as the topological single soliton
solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy
New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
Quantum mechanical potentials satisfying the property of shape invariance are
well known to be algebraically solvable. Using a scaling ansatz for the change
of parameters, we obtain a large class of new shape invariant potentials which
are reflectionless and possess an infinite number of bound states. They can be
viewed as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for energy eigenvalues,
eigenfunctions and transmission coefficients are given. Included in our
potentials as a special case is the self-similar potential recently discussed
by Shabat and Spiridonov.Comment: 8pages, Te
Truncated Harmonic Osillator and Parasupersymmetric Quantum Mechanics
We discuss in detail the parasupersymmetric quantum mechanics of arbitrary
order where the parasupersymmetry is between the normal bosons and those
corresponding to the truncated harmonic oscillator. We show that even though
the parasusy algebra is different from that of the usual parasusy quantum
mechanics, still the consequences of the two are identical. We further show
that the parasupersymmetric quantum mechanics of arbitrary order p can also be
rewritten in terms of p supercharges (i.e. all of which obey ).
However, the Hamiltonian cannot be expressed in a simple form in terms of the p
supercharges except in a special case. A model of conformal parasupersymmetry
is also discussed and it is shown that in this case, the p supercharges, the p
conformal supercharges along with Hamiltonian H, conformal generator K and
dilatation generator D form a closed algebra.Comment: 9 page
- …