14,418 research outputs found
An analysis of the noise reduction of orthotropic cylindrical shells Final report
Statistical energy and classical methods for calculating noise reduction of orthotropic cylindrical shell
Model of supersymmetric quantum field theory with broken parity symmetry
Recently, it was observed that self-interacting scalar quantum field theories
having a non-Hermitian interaction term of the form ,
where is a real positive parameter, are physically acceptable in the
sense that the energy spectrum is real and bounded below. Such theories possess
PT invariance, but they are not symmetric under parity reflection or time
reversal separately. This broken parity symmetry is manifested in a nonzero
value for , even if is an even integer. This paper extends
this idea to a two-dimensional supersymmetric quantum field theory whose
superpotential is . The resulting quantum
field theory exhibits a broken parity symmetry for all . However,
supersymmetry remains unbroken, which is verified by showing that the
ground-state energy density vanishes and that the fermion-boson mass ratio is
unity.Comment: 20 pages, REVTeX, 11 postscript figure
Non-perturbative calculations for the effective potential of the symmetric and non-Hermitian field theoretic model
We investigate the effective potential of the symmetric
field theory, perturbatively as well as non-perturbatively. For the
perturbative calculations, we first use normal ordering to obtain the first
order effective potential from which the predicted vacuum condensate vanishes
exponentially as in agreement with previous calculations. For the
higher orders, we employed the invariance of the bare parameters under the
change of the mass scale to fix the transformed form totally equivalent to
the original theory. The form so obtained up to is new and shows that all
the 1PI amplitudes are perurbative for both and regions. For
the intermediate region, we modified the fractal self-similar resummation
method to have a unique resummation formula for all values. This unique
formula is necessary because the effective potential is the generating
functional for all the 1PI amplitudes which can be obtained via and thus we can obtain an analytic calculation for the 1PI
amplitudes. Again, the resummed from of the effective potential is new and
interpolates the effective potential between the perturbative regions.
Moreover, the resummed effective potential agrees in spirit of previous
calculation concerning bound states.Comment: 20 page
Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset
The long-slit spectra obtained along the minor axis, offset major axis and
diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn
from a magnitude-limited sample studied before. The rotation curves, velocity
dispersion profiles and the H_3 and H_4 coefficients of the Hermite
decomposition of the line of sight velocity distribution are derived. The
radial profiles of the Hbeta, Mg, and Fe line strength indices are measured
too. In addition, the surface photometry of the central regions of a subsample
of 4 galaxies recently obtained with Hubble Space Telescope is presented. The
data will be used to construct dynamical models of the galaxies and study their
stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Conventional weak-coupling perturbation theory suffers from problems that
arise from resonant coupling of successive orders in the perturbation series.
Multiple-scale perturbation theory avoids such problems by implicitly
performing an infinite reordering and resummation of the conventional
perturbation series. Multiple-scale analysis provides a good description of the
classical anharmonic oscillator. Here, it is extended to study the Heisenberg
operator equations of motion for the quantum anharmonic oscillator. The
analysis yields a system of nonlinear operator differential equations, which is
solved exactly. The solution provides an operator mass renormalization of the
theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm
Quantum tunneling as a classical anomaly
Classical mechanics is a singular theory in that real-energy classical
particles can never enter classically forbidden regions. However, if one
regulates classical mechanics by allowing the energy E of a particle to be
complex, the particle exhibits quantum-like behavior: Complex-energy classical
particles can travel between classically allowed regions separated by potential
barriers. When Im(E) -> 0, the classical tunneling probabilities persist.
Hence, one can interpret quantum tunneling as an anomaly. A numerical
comparison of complex classical tunneling probabilities with quantum tunneling
probabilities leads to the conjecture that as ReE increases, complex classical
tunneling probabilities approach the corresponding quantum probabilities. Thus,
this work attempts to generalize the Bohr correspondence principle from
classically allowed to classically forbidden regions.Comment: 12 pages, 7 figure
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is
investigated. It is shown that for a given function w(x) the equation admits an
infinite set of polynomial solutions P(x). For polynomial solutions, this
nonlinear integral equation reduces to a finite set of coupled linear algebraic
equations for the coefficients of the polynomials. Interestingly, the set of
polynomial solutions is orthogonal with respect to the measure x w(x). The
nonlinear integral equation can be used to specify all orthogonal polynomials
in a simple and compact way. This integral equation provides a natural vehicle
for extending the theory of orthogonal polynomials into the complex domain.
Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex
domai
On the consistency of a non-Hermitian Yukawa interaction
We study different properties of an anti-Hermitian Yukawa interaction,
motivated by a scenario of radiative anomalous generation of masses for the
right-handed sterile neutrinos. The model, involving either a pseudo-scalar or
a scalar, is consistent both at the classical and quantum levels, and
particular attention is given to its properties under improper Lorentz
transformations. The path integral is consistently defined with a Euclidean
signature, and we discuss the energetics of the model, which show that no
dynamical mass generation can occur, unless extra interactions are considered.Comment: 7 pages, comments adde
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