11,383 research outputs found
Solution of Some Integrable One-Dimensional Quantum Systems
In this paper, we investigate a family of one-dimensional multi-component
quantum many-body systems. The interaction is an exchange interaction based on
the familiar family of integrable systems which includes the inverse square
potential. We show these systems to be integrable, and exploit this
integrability to completely determine the spectrum including degeneracy, and
thus the thermodynamics. The periodic inverse square case is worked out
explicitly. Next, we show that in the limit of strong interaction the "spin"
degrees of freedom decouple. Taking this limit for our example, we obtain a
complete solution to a lattice system introduced recently by Shastry, and
Haldane; our solution reproduces the numerical results. Finally, we emphasize
the simple explanation for the high multiplicities found in this model
Spectral flow in the supersymmetric - model with a interaction
The spectral flow in the supersymmetric {\it t-J} model with
interaction is studied by analyzing the exact spectrum with twisted boundary
conditions. The spectral flows for the charge and spin sectors are shown to
nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although
fractional exclusion statistics for the spin sector clearly shows up in the
period of the spectral flow at half filling, such a property is generally
hidden once any number of holes are doped, because the commensurability
condition in the motif is not met in the metallic phase.Comment: 8 pages, revtex, Phys. Rev. B54 (1996) August 15, in pres
The Numerical Simulation of Radiative Shocks I: The elimination of numerical shock instabilities using a localized oscillation filter
We address a numerical instability that arises in the directionally split
computation of hydrodynamic flows when shock fronts are parallel to a grid
plane. Transverse oscillations in pressure, density and temperature are
produced that are exacerbated by thermal instability when cooling is present,
forming post--shock `stripes'. These are orthogonal to the classic post--shock
'ringing' fluctuations. The resulting post--shock `striping' substantially
modifies the flow. We discuss three different methods to resolve this problem.
These include (1) a method based on artificial viscosity; (2) grid--jittering
and (3) a new localized oscillation filter that acts on specific grid cells in
the shock front. These methods are tested using a radiative wall shock problem
with an embedded shear layer. The artificial viscosity method is unsatisfactory
since, while it does reduce post--shock ringing, it does not eliminate the
stripes and the excessive shock broadening renders the calculation of cooling
inaccurate, resulting in an incorrect shock location. Grid--jittering
effectively counteracts striping. However, elsewhere on the grid, the shear
layer is unphysically diffused and this is highlighted in an extreme case. The
oscillation filter method removes stripes and permits other high velocity
gradient regions of the flow to evolve in a physically acceptable manner. It
also has the advantage of only acting on a small fraction of the cells in a two
or three dimensional simulation and does not significantly impair performance.Comment: 20 pages, 6 figures, revised version submitted to ApJ Supplement
Serie
Partially Solvable Anisotropic t-J Model with Long-Range Interactions
A new anisotropic t-J model in one dimension is proposed which has long-range
hopping and exchange. This t-J model is only partially solvable in contrast to
known integrable models with long-range interaction. In the high-density limit
the model reduces to the XXZ chain with the long-range exchange. Some exact
eigenfunctions are shown to be of Jastrow-type if certain conditions for an
anisotropy parameter are satisfied. The ground state as well as the excitation
spectrum for various cases of the anisotropy parameter and filling are derived
numerically. It is found that the Jastrow-type wave function is an excellent
trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure
Exact Results of the 1D Supersymmetric t-J Model without Translational Invariance
In this work, we continue the study of the supersymmetric t-J model with
1/r^2 hopping and exchange without translational invariance. A set of Jastrow
wavefunctions are obtained for the system, with eigenenergies explicitly
calculated. The ground state of the t-J model is included in this set of
wavefunctions. The spectrum of this t-J model consists of equal-distant energy
levels which are highly degenerate.Comment: 14 pages, Late
Solutions to the Multi-Component 1/R Hubbard Model
In this work we introduce one dimensional multi-component Hubbard model of
1/r hopping and U on-site energy. The wavefunctions, the spectrum and the
thermodynamics are studied for this model in the strong interaction limit
. In this limit, the system is a special example of Luttinger
liquids, exhibiting spin-charge separation in the full Hilbert space.
Speculations on the physical properties of the model at finite on-site energy
are also discussed.Comment: 9 pages, revtex, Princeton-May1
Controlling integrability in a quasi-1D atom-dimer mixture
We analytically study the atom-dimer scattering problem in the
near-integrable limit when the oscillator length l_0 of the transverse
confinement is smaller than the dimer size, ~l_0^2/|a|, where a<0 is the
interatomic scattering length. The leading contributions to the atom-diatom
reflection and break-up probabilities are proportional to a^6 in the bosonic
case and to a^8 for the up-(up-down) scattering in a two-component fermionic
mixture. We show that by tuning a and l_0 one can control the "degree of
integrability" in a quasi-1D atom-dimer mixture in an extremely wide range
leaving thermodynamic quantities unchanged. We find that the relaxation to
deeply bound states in the fermionic (bosonic) case is slower (faster) than
transitions between different Bethe ansatz states. We propose a realistic
experiment for detailed studies of the crossover from integrable to
nonintegrable dynamics.Comment: 12 pages, 1 figur
Exact solution and spectral flow for twisted Haldane-Shastry model
The exact solution of the spin chain model with exchange is found for
twisted boundary conditions. The spectrum thus obtained can be reproduced by
the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined
exactly as a function of the twist angle. We find that the period for
the ground state nicely fits in with the notion of fractional exclusion
statistics.Comment: 4 pages, revtex, 1 figure available on request, to appear in PR
Dynamical Mass Measurements of Contaminated Galaxy Clusters Using Machine Learning
We study dynamical mass measurements of galaxy clusters contaminated by
interlopers and show that a modern machine learning (ML) algorithm can predict
masses by better than a factor of two compared to a standard scaling relation
approach. We create two mock catalogs from Multidark's publicly available
-body MDPL1 simulation, one with perfect galaxy cluster membership
information and the other where a simple cylindrical cut around the cluster
center allows interlopers to contaminate the clusters. In the standard
approach, we use a power-law scaling relation to infer cluster mass from galaxy
line-of-sight (LOS) velocity dispersion. Assuming perfect membership knowledge,
this unrealistic case produces a wide fractional mass error distribution, with
a width of . Interlopers introduce additional
scatter, significantly widening the error distribution further
(). We employ the support distribution machine (SDM)
class of algorithms to learn from distributions of data to predict single
values. Applied to distributions of galaxy observables such as LOS velocity and
projected distance from the cluster center, SDM yields better than a
factor-of-two improvement () for the contaminated
case. Remarkably, SDM applied to contaminated clusters is better able to
recover masses than even the scaling relation approach applied to
uncontaminated clusters. We show that the SDM method more accurately reproduces
the cluster mass function, making it a valuable tool for employing cluster
observations to evaluate cosmological models.Comment: 18 pages, 12 figures, accepted for publication at Ap
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