832 research outputs found
Conservation of connectivity of model-space effective interactions under a class of similarity transformation
Effective interaction operators usually act on a restricted model space and
give the same energies (for Hamiltonian) and matrix elements (for transition
operators etc.) as those of the original operators between the corresponding
true eigenstates. Various types of effective operators are possible. Those well
defined effective operators have been shown being related to each other by
similarity transformation. Some of the effective operators have been shown to
have connected-diagram expansions. It is shown in this paper that under a class
of very general similarity transformations, the connectivity is conserved. The
similarity transformation between hermitian and non-hermitian
Rayleigh-Schr\"{o}dinger perturbative effective operators is one of such
transformation and hence the connectivity can be deducted from each other.Comment: 12 preprint page
Ground state properties and excitation spectra of non-Galilean invariant interacting Bose systems
We study the ground state properties and the excitation spectrum of bosons
which, in addition to a short-range repulsive two body potential, interact
through the exchange of some dispersionless bosonic modes. The latter induces a
time dependent (retarded) boson-boson interaction which is attractive in the
static limit. Moreover the coupling with dispersionless modes introduces a
reference frame for the moving boson system and hence breaks the Galilean
invariance of this system. The ground state of such a system is depleted {\it
linearly} in the boson density due to the zero point fluctuations driven by the
retarded part of the interaction. Both quasiparticle (microscopic) and
compressional (macroscopic) sound velocities of the system are studied. The
microscopic sound velocity is calculated up the second order in the effective
two body interaction in a perturbative treatment, similar to that of Beliaev
for the dilute weakly interacting Bose gas. The hydrodynamic equations are used
to obtain the macroscopic sound velocity. We show that these velocities are
identical within our perturbative approach. We present analytical results for
them in terms of two dimensional parameters -- an effective interaction
strength and an adiabaticity parameter -- which characterize the system. We
find that due the presence of several competing effects, which determine the
speed of the sound of the system, three qualitatively different regimes can be
in principle realized in the parameter space and discuss them on physical
grounds.Comment: 6 pages, 2 figures, to appear in Phys. Rev.
Effect of the bound nucleon form factors on charged-current neutrino-nucleus scattering
We study the effect of bound nucleon form factors on charged-current
neutrino-nucleus scattering. The bound nucleon form factors of the vector and
axial-vector currents are calculated in the quark-meson coupling model. We
compute the inclusive C() cross sections using a
relativistic Fermi gas model with the calculated bound nucleon form factors.
The effect of the bound nucleon form factors for this reaction is a reduction
of 8% for the total cross section, relative to that calculated with the
free nucleon form factors.Comment: Latex, 11 pages, 3 figures, version to appear in Phys. Rev. C (Brief
Report
Superfluidity of bosons on a deformable lattice
We study the superfluid properties of a system of interacting bosons on a
lattice which, moreover, are coupled to the vibrational modes of this lattice,
treated here in terms of Einstein phonon model. The ground state corresponds to
two correlated condensates: that of the bosons and that of the phonons. Two
competing effects determine the common collective soundwave-like mode with
sound velocity , arising from gauge symmetry breaking: i) The sound velocity
(corresponding to a weakly interacting Bose system on a rigid lattice) in
the lowest order approximation is reduced due to reduction of the repulsive
boson-boson interaction, arising from the attractive part of phonon mediated
interaction in the static limit. ii) the second order correction to the sound
velocity is enhanced as compared to the one of bosons on a rigid lattice when
the the boson-phonon interaction is switched on due to the retarded nature of
phonon mediated interaction. The overall effect is that the sound velocity is
practically unaffected by the coupling with phonons, indicating the robustness
of the superfluid state. The induction of a coherent state in the phonon
system, driven by the condensation of the bosons could be of experimental
significance, permitting spectroscopic detections of superfluid properties of
the bosons. Our results are based on an extension of the Beliaev - Popov
formalism for a weakly interacting Bose gas on a rigid lattice to that on a
deformable lattice with which it interacts.Comment: 12 pages, 14 figures, to appear in Phys. Rev.
Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates
We formulate a conserving gapless mean-field theory for Bose-Einstein
condensates on the basis of a Luttinger-Ward thermodynamic functional. It is
applied to a weakly interacting uniform gas with density and s-wave
scattering length to clarify its fundamental thermodynamic properties. It
is found that the condensation here occurs as a first-order transition. The
shift of the transition temperature from the ideal-gas result
is positive and given to the leading order by , in agreement with a couple of previous estimates. The theory is
expected to form a new theoretical basis for trapped Bose-Einstein condensates
at finite temperatures.Comment: Minor errors remove
Infrared Behavior of Interacting Bosons at Zero Temperature
We exploit the symmetries associated with the stability of the superfluid
phase to solve the long-standing problem of interacting bosons in the presence
of a condensate at zero temperature. Implementation of these symmetries poses
strong conditions on the renormalizations that heal the singularities of
perturbation theory. The renormalized theory gives: For d>3 the Bogoliubov
quasiparticles as an exact result; for 1<d<=3 a nontrivial solution with the
exact exponent for the singular longitudinal correlation function, with phonons
again as low-lying excitations.Comment: Minor Changes. 4 pages, RevTeX, no figures, uses multicol.sty e-mail:
[email protected]
Bose-Einstein Condensation in a Confined Geometry with and without a Vortex
Various widely-used mean-field type theories for a dilute Bose gas are
critically examined in the light of the recent discovery of Bose-Einstein
condensation of atomic gases in a confined geometry. By numerically solving the
mean-field equations within the framework of the Bogoliubov approximation both
stationary non-uniform case and the vortex case under rotation in a
cylindrically symmetric vessel are investigated. We obtain spatial structures
of condensate, non-condensate, anomalous correlation. The low lying excitation
spectra, the local density of states and the circulating current density in a
vortex corresponding to various levels of mean-field theories are predicted.Comment: 16 pages, LaTeX with jpsj.sty, 13 eps figures. Figures improve
Infrared behavior of interacting bosons at zero temperature
We review the infrared behavior of interacting bosons at zero temperature.
After a brief discussion of the Bogoliubov approximation and the breakdown of
perturbation theory due to infrared divergences, we present two approaches that
are free of infrared divergences -- Popov's hydrodynamic theory and the
non-perturbative renormalization group -- and allow us to obtain the exact
infrared behavior of the correlation functions. We also point out the
connection between the infrared behavior in the superfluid phase and the
critical behavior at the superfluid--Mott-insulator transition in the
Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser
Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010
Localization via Automorphisms of the CARs. Local gauge invariance
The classical matter fields are sections of a vector bundle E with base
manifold M. The space L^2(E) of square integrable matter fields w.r.t. a
locally Lebesgue measure on M, has an important module action of C_b^\infty(M)
on it. This module action defines restriction maps and encodes the local
structure of the classical fields. For the quantum context, we show that this
module action defines an automorphism group on the algebra A, of the canonical
anticommutation relations on L^2(E), with which we can perform the analogous
localization. That is, the net structure of the CAR, A, w.r.t. appropriate
subsets of M can be obtained simply from the invariance algebras of appropriate
subgroups. We also identify the quantum analogues of restriction maps. As a
corollary, we prove a well-known "folk theorem," that the algebra A contains
only trivial gauge invariant observables w.r.t. a local gauge group acting on
E.Comment: 15 page
Ground State Energy of the Low Density Bose Gas
Now that the properties of low temperature Bose gases at low density, ,
can be examined experimentally it is appropriate to revisit some of the
formulas deduced by many authors 4-5 decades ago. One of these is that the
leading term in the energy/particle is , where is
the scattering length. Owing to the delicate and peculiar nature of bosonic
correlations, four decades of research have failed to establish this plausible
formula rigorously. The only known lower bound for the energy was found by
Dyson in 1957, but it was 14 times too small. The correct bound is proved here.Comment: 4 pages, Revtex, reference 12 change
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