370 research outputs found
Asymptotic Behavior of the Wave Packet Propagation through a Barrier: the Green's Function Approach Revisited
To model the decay of a quasibound state we use the modified two-potential
approach introduced by Gurvitz and Kalbermann. This method has proved itself
useful in the past for calculating the decay width and the energy shift of an
isolated quasistationary state. We follow the same approach in order to
propagate the wave-packet in time with the ultimate goal of extracting the
momentum-distribution of emitted particles. The advantage of the method is that
it provides the time-dependent wave function in a simple semi-analytic form. We
intend to apply this method to the modeling of metastable states for which no
direct integration of the time-dependent Schroedinger equation is available
today.Comment: 7 page
Dynamics of broken symmetry lambda phi^4 field theory
We study the domain of validity of a Schwinger-Dyson (SD) approach to
non-equilibrium dynamics when there is broken symmetry. We perform exact
numerical simulations of the one- and two-point functions of lambda phi^4 field
theory in 1+1 dimensions in the classical domain for initial conditions where <
phi(x) > not equal to 0. We compare these results to two self-consistent
truncations of the SD equations which ignore three-point vertex function
corrections. The first approximation, which sets the three-point function to
one (the bare vertex approximation (BVA)) gives an excellent description for <
phi(x) > = phi(t). The second approximation which ignores higher in 1/N
corrections to the 2-PI generating functional (2PI -1/N expansion) is not as
accurate for phi(t). Both approximations have serious deficiencies in
describing the two-point function when phi(0) > .4.Comment: 10 pages, 6 figure
Ghost contributions to charmonium production in polarized high-energy collisions
In a previous paper [Phys. Rev. D 68, 034017 (2003)], we investigated the
inclusive production of prompt J/psi mesons in polarized hadron-hadron,
photon-hadron, and photon-photon collisions in the factorization formalism of
nonrelativistic quantum chromodynamics providing compact analytic results for
the double longitudinal-spin asymmetry A_{LL}. For convenience, we adopted a
simplified expression for the tensor product of the gluon polarization
four-vector with its charge conjugate, at the expense of allowing for ghost and
anti-ghosts to appear as external particles. While such ghost contributions
cancel in the cross section asymmetry A_{LL} and thus were not listed in our
previous paper, they do contribute to the absolute cross sections. For
completeness and the reader's convenience, they are provided in this addendum.Comment: 5 page
On the properties of compacton-anticompacton collisions
We study the properties of compacton-anticompacton collision processes. We
compare and con- trast results for the case of compacton-anticompacton
solutions of the K(l, p) Rosenau-Hyman (RH) equation for l = p = 2, with
compacton-anticompacton solutions of the L(l,p) Cooper-Shepard- Sodano (CSS)
equation for p = 1 and l = 3. This study is performed using a Pad\'e
discretization of the RH and CSS equations. We find a significant difference in
the behavior of compacton- anticompacton scattering. For the CSS equation, the
scattering can be interpreted as "annihila- tion" as the wake left behind
dissolves over time. In the RH equation, the numerical evidence is that
multiple shocks form after the collision which eventually lead to "blowup" of
the resulting waveform.Comment: 8 pages, 7 figure
Coupled-cluster theory of a gas of strongly-interacting fermions in the dilute limit
We study the ground-state properties of a dilute gas of strongly-interacting
fermions in the framework of the coupled-cluster expansion (CCE). We
demonstrate that properties such as universality, opening of a gap in the
excitation spectrum and applicability of s-wave approximations appear naturally
in the CCE approach. In the zero-density limit, we show that the ground-state
energy density depends on only one parameter which in turn may depend at most
on the spatial dimensionality of the system.Comment: 7 figure
Electron-phonon coupling in semimetals in a high magnetic field
We consider the effect of electron-phonon coupling in semimetals in high
magnetic fields, with regard to elastic modes that can lead to a redistribution
of carriers between pockets. We show that in a clean three dimensional system,
at each Landau level crossing, this leads to a discontinuity in the
magnetostriction, and a divergent contribution to the elastic modulus. We
estimate the magnitude of this effect in the group V semimetal Bismuth.Comment: 2 figure
Stability and dynamical properties of Rosenau-Hyman compactons using Pade approximants
We present a systematic approach for calculating higher-order derivatives of
smooth functions on a uniform grid using Pad\'e approximants. We illustrate our
findings by deriving higher-order approximations using traditional second-order
finite-differences formulas as our starting point. We employ these schemes to
study the stability and dynamical properties of K(2,2) Rosenau-Hyman (RH)
compactons including the collision of two compactons and resultant shock
formation. Our approach uses a differencing scheme involving only nearest and
next-to-nearest neighbors on a uniform spatial grid. The partial differential
equation for the compactons involves first, second and third partial
derivatives in the spatial coordinate and we concentrate on four different
fourth-order methods which differ in the possibility of increasing the degree
of accuracy (or not) of one of the spatial derivatives to sixth order. A method
designed to reduce roundoff errors was found to be the most accurate
approximation in stability studies of single solitary waves, even though all
derivates are accurate only to fourth order. Simulating compacton scattering
requires the addition of fourth derivatives related to artificial viscosity.
For those problems the different choices lead to different amounts of
"spurious" radiation and we compare the virtues of the different choices.Comment: 12 figure
Acoustic attenuation rate in the Fermi-Bose model with a finite-range fermion-fermion interaction
We study the acoustic attenuation rate in the Fermi-Bose model describing a
mixtures of bosonic and fermionic atom gases. We demonstrate the dramatic
change of the acoustic attenuation rate as the fermionic component is evolved
through the BEC-BCS crossover, in the context of a mean-field model applied to
a finite-range fermion-fermion interaction at zero temperature, such as
discussed previously by M.M. Parish et al. [Phys. Rev. B 71, 064513 (2005)] and
B. Mihaila et al. [Phys. Rev. Lett. 95, 090402 (2005)]. The shape of the
acoustic attenuation rate as a function of the boson energy represents a
signature for superfluidity in the fermionic component
Parallel algorithm with spectral convergence for nonlinear integro-differential equations
We discuss a numerical algorithm for solving nonlinear integro-differential
equations, and illustrate our findings for the particular case of Volterra type
equations. The algorithm combines a perturbation approach meant to render a
linearized version of the problem and a spectral method where unknown functions
are expanded in terms of Chebyshev polynomials (El-gendi's method). This
approach is shown to be suitable for the calculation of two-point Green
functions required in next to leading order studies of time-dependent quantum
field theory.Comment: 15 pages, 9 figure
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