1,785 research outputs found
Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
Goldstone's theorem states that there is a massless mode for each broken
symmetry generator. It has been known for a long time that the naive
generalization of this counting fails to give the correct number of massless
modes for spontaneously broken spacetime symmetries. We explain how to get the
right count of massless modes in the general case, and discuss examples
involving spontaneously broken Poincare and conformal invariance.Comment: 4 pages; 1 figure; v2: minor corrections. version to appear on PR
Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass
A Fermion in 2+1 dimensions, with a mass function which depends on one
spatial coordinate and passes through a zero ( a domain wall mass), is
considered. In this model, originally proposed by Callan and Harvey, the gauge
variation of the effective gauge action mainly consists of two terms. One comes
from the induced Chern-Simons term and the other from the chiral fermions,
bound to the 1+1 dimensional wall, and they are expected to cancel each other.
Though there exist arguments in favour of this, based on the possible forms of
the effective action valid far from the wall and some facts about theories of
chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this
paper we present an explicit calculation of this cancellation at one loop valid
even close to the wall. We show that, integrating out the ``massive'' modes of
the theory does produce the Chern-Simons term, as appreciated previously. In
addition we show that it generates a term that softens the high energy
behaviour of the 1+1 dimensional effective chiral theory thereby resolving an
ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61
Pseudospin SU(2) Symmetry Breaking, Charge Density Wave and Superconductivity in the Hubbard Model
In this paper, we discuss physical consequences of pseudospin SU(2) symmetry
breaking in the negative-U Hubbard model at half-filling. If pseudospin
symmetry is spontaneously broken while its unique subgroup U(1) remains
invariant, it will lead to the charge density wave (CDW) ground state.
Furthermore, if the U(1) symmetry is also broken, the ground state will have
the off-diagonal long range order (ODLRO), signaling a superconductor. In this
case, CDW and superconductivity coexist to form a supersolid. Finally, we show
that CDW suppresses, but does not destroy superconductivity.Comment: 7 page
Inclusion of non-spherical components of the Pauli blocking operator in (p,p') reactions
We present the first calculations of proton elastic and inelastic scattering
in which the Pauli blocking operator contains the leading non-spherical
components as well as the usual spherical (angle-averaged) part. We develop a
formalism for including the contributions to the effective nucleon-nucleon
interaction from the resulting new G-matrix elements that extend the usual
two-nucleon spin structure and may not conserve angular momentum. We explore
the consequences of parity conservation, time reversal invariance, and
nucleon-nucleon antisymmetrization for the new effective interaction. Changes
to the calculated cross section and spin observables are small in the energy
range from 100 to 200 MeV.Comment: 24 pages, 4 figures, to be published in Physical Review
Damping of Tensor Modes in Cosmology
An analytic formula is given for the traceless transverse part of the
anisotropic stress tensor due to free streaming neutrinos, and used to derive
an integro-differential equation for the propagation of cosmological
gravitational waves. The solution shows that anisotropic stress reduces the
squared amplitude by 35.6 % for wavelengths that enter the horizon during the
radiation-dominated phase, independent of any cosmological parameters. This
decreases the tensor temperature and polarization correlation functions for
these wavelengths by the same amount. The effect is less for wavelengths that
enter the horizon at later times. At the longest wavelengths the decrease in
the tensor correlation functions due to neutrino free streaming ranges from
10.7% for to 9.0% for . An Appendix gives a
general proof that tensor as well as scalar modes satisfy a conservation law
for perturbations outside the horizon, even when the anisotropic stress tensor
is not negligible.Comment: 14 pages. The original version of this paper has been expanded to
deal with perturbations of any wavelength. While for wavelengths short enough
to enter the horizon during radiation dominance, temperature and polarization
correlations are damped by 35.6%, at the longest wavelengths the damping is
from 9.0% to 11%. An added Appendix gives a general proof that tensor as well
as scalar modes satisfy a conservation law outside the horizon, even during
neutrino decoupling. Some references are also adde
Field theoretic description of the abelian and non-abelian Josephson effect
We formulate the Josephson effect in a field theoretic language which affords
a straightforward generalization to the non-abelian case. Our formalism
interprets Josephson tunneling as the excitation of pseudo-Goldstone bosons. We
demonstrate the formalism through the consideration of a single junction
separating two regions with a purely non-abelian order parameter and a sandwich
of three regions where the central region is in a distinct phase. Applications
to various non-abelian symmetry breaking systems in particle and condensed
matter physics are given.Comment: 10 pages no figure
Emergence of a confined state in a weakly bent wire
In this paper we use a simple straightforward technique to investigate the
emergence of a bound state in a weakly bent wire. We show that the bend behaves
like an infinitely shallow potential well, and in the limit of small bending
angle and low energy the bend can be presented by a simple 1D delta function
potential.Comment: 4 pages, 3 Postscript figures (uses Revtex); added references and
rewritte
Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate
We theoretically study the properties of Nambu-Goldstone bosons in an
interacting single-component Bose-Einstein condensate (BEC). We first point out
that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf
127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas
the first proof deals with the poles of the single-particle Green's function
, the second one concerns those of the two-particle Green's function.
Thus, there may be multiple Nambu-Goldstone bosons even in the single-component
BEC with broken U(1) symmetry. The second mode turns out to have an infinite
lifetime in the long-wavelength limit in agreement with the conventional
viewpoint. In contrast, the first mode from , i.e., the Bogoliubov
mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating
temporally out of and back into the condensate. The substantial lifetime
originates from an "improper" structure of the self-energy inherent in the BEC,
which has been overlooked so far and will be elucidated here, and removes
various infrared divergences pointed out previously.Comment: 9 pages, 6 gigure
Polymers in Curved Boxes
We apply results derived in other contexts for the spectrum of the Laplace
operator in curved geometries to the study of an ideal polymer chain confined
to a spherical annulus in arbitrary space dimension D and conclude that the
free energy compared to its value for an uncurved box of the same thickness and
volume, is lower when , stays the same when , and is higher when
\mbox{}. Thus confining an ideal polymer chain to a cylindrical shell,
lowers the effective bending elasticity of the walls, and might induce
spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned
results show that {\em {any}} shell in induces this effect, except for
a spherical shell). We compute the contribution of this effect to the bending
rigidities in the Helfrich free energy expression.Comment: 20 pages RevTeX, epsf; 4 figures; submitted to Macromoledule
Topological Excitations of One-Dimensional Correlated Electron Systems
Properties of low-energy excitations in one-dimensional superconductors and
density-wave systems are examined by the bosonization technique. In addition to
the usual spin and charge quantum numbers, a new, independently measurable
attribute is introduced to describe elementary, low-energy excitations. It can
be defined as a number w which determines, in multiple of , how many times
the phase of the order parameter winds as an excitation is transposed from far
left to far right. The winding number is zero for electrons and holes with
conventional quantum numbers, but it acquires a nontrivial value w=1 for
neutral spin-1/2 excitations and for spinless excitations with a unit electron
charge. It may even be irrational, if the charge is irrational. Thus, these
excitations are topological, and they can be viewed as composite particles made
of spin or charge degrees of freedom and dressed by kinks in the order
parameter.Comment: 5 pages. And we are not only splitting point
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