289,493 research outputs found
Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities
Since the kinetic and the potential energy term of the real time nonlinear
Schr\"odinger equation can each be solved exactly, the entire equation can be
solved to any order via splitting algorithms. We verified the fourth-order
convergence of some well known algorithms by solving the Gross-Pitaevskii
equation numerically. All such splitting algorithms suffer from a latent
numerical instability even when the total energy is very well conserved. A
detail error analysis reveals that the noise, or elementary excitations of the
nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is
due to the exponential growth of high wave number noises caused by the
splitting process. For a continuum wave function, this instability is
unavoidable no matter how small the time step. For a discrete wave function,
the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where
.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
Spin-Isospin Structure and Pion Condensation in Nucleon Matter
We report variational calculations of symmetric nuclear matter and pure
neutron matter, using the new Argonne v18 two-nucleon and Urbana IX
three-nucleon interactions. At the equilibrium density of 0.16 fm^-3 the
two-nucleon densities in symmetric nuclear matter are found to exhibit a
short-range spin-isospin structure similar to that found in light nuclei. We
also find that both symmetric nuclear matter and pure neutron matter undergo
transitions to phases with pion condensation at densities of 0.32 fm^-3 and 0.2
fm^-3, respectively. Neither transtion occurs with the Urbana v14 two-nucleon
interaction, while only the transition in neutron matter occurs with the
Argonne v14 two-nucleon interaction. The three-nucleon interaction is required
for the transition to occur in symmetric nuclear matter, whereas the the
transition in pure neutron matter occurs even in its absence. The behavior of
the isovector spin-longitudinal response and the pion excess in the vicinity of
the transition, and the model dependence of the transition are discussed.Comment: 44 pages RevTeX, 15 postscript figures. Minor modifications to
original postin
Chaos in an Exact Relativistic 3-body Self-Gravitating System
We consider the problem of three body motion for a relativistic
one-dimensional self-gravitating system. After describing the canonical
decomposition of the action, we find an exact expression for the 3-body
Hamiltonian, implicitly determined in terms of the four coordinate and momentum
degrees of freedom in the system. Non-relativistically these degrees of freedom
can be rewritten in terms of a single particle moving in a two-dimensional
hexagonal well. We find the exact relativistic generalization of this
potential, along with its post-Newtonian approximation. We then specialize to
the equal mass case and numerically solve the equations of motion that follow
from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining
orbits in both the hexagonal and 3-body representations of the system, and plot
the Poincare sections as a function of the relativistic energy parameter . We find two broad categories of periodic and quasi-periodic motions that we
refer to as the annulus and pretzel patterns, as well as a set of chaotic
motions that appear in the region of phase-space between these two types.
Despite the high degree of non-linearity in the relativistic system, we find
that the the global structure of its phase space remains qualitatively the same
as its non-relativisitic counterpart for all values of that we could
study. However the relativistic system has a weaker symmetry and so its
Poincare section develops an asymmetric distortion that increases with
increasing . For the post-Newtonian system we find that it experiences a
KAM breakdown for : above which the near integrable regions
degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon
reques
Solar Neutrinos from CNO Electron Capture
The neutrino flux from the sun is predicted to have a CNO-cycle contribution
as well as the known pp-chain component. Previously, only the fluxes from beta+
decays of 13N, 15O, and 17F have been calculated in detail. Another neutrino
component that has not been widely considered is electron capture on these
nuclei. We calculate the number of interactions in several solar neutrino
detectors due to neutrinos from electron capture on 13N, 15O, and 17F, within
the context of the Standard Solar Model. We also discuss possible non-standard
models where the CNO flux is increased.Comment: 4 pages, 1 figure, submitted to Phys. Rev. C; v2 has minor changes
including integration over solar volume and addition of missing reference to
previous continuum electron capture calculation; v3 has minor changes
including addition of references and the correction of a small (about 1%)
numerical error in the table
Late-Time Optical and UV Spectra of SN 1979C and SN 1980K
A low-dispersion Keck I spectrum of SN 1980K taken in August 1995 (t = 14.8
yr after explosion) and a November 1997 MDM spectrum (t = 17.0 yr) show broad
5500 km s^{-1} emission lines of H\alpha, [O I] 6300,6364 A, and [O II]
7319,7330 A. Weaker but similarly broad lines detected include [Fe II] 7155 A,
[S II] 4068,4072 A, and a blend of [Fe II] lines at 5050--5400 A. The presence
of strong [S II] 4068,4072 A emission but a lack of [S II] 6716,6731 A emission
suggests electron densities of 10^{5-6} cm^{-3}. From the 1997 spectra, we
estimate an H\alpha flux of 1.3 \pm 0.2 \times 10^{-15} erg cm^{-2} s^{-1}
indicating a 25% decline from 1987--1992 levels during the period 1994 to 1997,
possibly related to a reported decrease in its nonthermal radio emission.Comment: 21 pages, 8 figures, submitted to the Astronomical Journa
Dynamic of a non homogeneously coarse grained system
To study materials phenomena simultaneously at various length scales,
descriptions in which matter can be coarse grained to arbitrary levels, are
necessary. Attempts to do this in the static regime (i.e. zero temperature)
have already been developed. In this letter, we present an approach that leads
to a dynamics for such coarse-grained models. This allows us to obtain
temperature-dependent and transport properties. Renormalization group theory is
used to create new local potentials model between nodes, within the
approximation of local thermodynamical equilibrium. Assuming that these
potentials give an averaged description of node dynamics, we calculate thermal
and mechanical properties. If this method can be sufficiently generalized it
may form the basis of a Molecular Dynamics method with time and spatial
coarse-graining.Comment: 4 pages, 4 figure
Effective Pure States for Bulk Quantum Computation
In bulk quantum computation one can manipulate a large number of
indistinguishable quantum computers by parallel unitary operations and measure
expectation values of certain observables with limited sensitivity. The initial
state of each computer in the ensemble is known but not pure. Methods for
obtaining effective pure input states by a series of manipulations have been
described by Gershenfeld and Chuang (logical labeling) and Cory et al. (spatial
averaging) for the case of quantum computation with nuclear magnetic resonance.
We give a different technique called temporal averaging. This method is based
on classical randomization, requires no ancilla qubits and can be implemented
in nuclear magnetic resonance without using gradient fields. We introduce
several temporal averaging algorithms suitable for both high temperature and
low temperature bulk quantum computing and analyze the signal to noise behavior
of each.Comment: 24 pages in LaTex, 14 figures, the paper is also avalaible at
http://qso.lanl.gov/qc
Fractional generalization of Fick's law: a microscopic approach
In the study of transport in inhomogeneous systems it is common to construct
transport equations invoking the inhomogeneous Fick law. The validity of this
approach requires that at least two ingredients be present in the system.
First, finite characteristic length and time scales associated to the dominant
transport process must exist. Secondly, the transport mechanism must satisfy a
microscopic symmetry: global reversibility. Global reversibility is often
satisfied in nature. However, many complex systems exhibit a lack of finite
characteristic scales. In this Letter we show how to construct a generalization
of the inhomogeneous Fick law that does not require the existence of
characteristic scales while still satisfying global reversibility.Comment: 4 pages. Published versio
BPS Saturated Vacua Interpolation along One Compact Dimension
A class of generalized Wess-Zumino models with distinct vacua is
investigated. These models allow for BPS saturated vacua interpolation along
one compact spatial dimension. The properties of these interpolations are
studied.Comment: 8 pages, 4 figure
Collinear Photon Emission from the Quark-Gluon Plasma: The Light-Cone Path Integral Formulation
We give a simple physical derivation of the photon emission rate from the
weakly coupled quark-gluon plasma connected with the collinear processes and . The analysis is based on the light-cone
path integral approach to the induced radiation. Our results agree with that by
Arnold, Moore and Yaffe obtained using the real-time thermal perturbation
theory. It is demonstrated that the solution of the AMY integral equation is
nothing but the time-integrated Green's function of the light-cone path
integral approach written in the momentum representation.Comment: 12 pages, 2 figure
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