12,715 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
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
Conservation laws in the continuum systems
We study the conservation laws of both the classical and the quantum
mechanical continuum type systems. For the classical case, we introduce
new integrals of motion along the recent ideas of Shastry and Sutherland (SS),
supplementing the usual integrals of motion constructed much earlier by Moser.
We show by explicit construction that one set of integrals can be related
algebraically to the other. The difference of these two sets of integrals then
gives rise to yet another complete set of integrals of motion. For the quantum
case, we first need to resum the integrals proposed by Calogero, Marchioro and
Ragnisco. We give a diagrammatic construction scheme for these new integrals,
which are the quantum analogues of the classical traces. Again we show that
there is a relationship between these new integrals and the quantum integrals
of SS by explicit construction.Comment: 19 RevTeX 3.0 pages with 2 PS-figures include
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
Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
We calculate the exact dynamical magnetic structure factor S(Q,E) in the
ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2
spinon excitations, the Haldane-Shastry model with inverse-square exchange,
which is in the same low-energy universality class as Bethe's nearest-neighbor
exchange model. Only two-spinon excited states contribute, and S(Q,E) is found
to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903
Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions
We present an investigation of the sinh-cosh (SC) interaction model with
twisted boundary conditions. We argue that, when unlike particles repel, the SC
model may be usefully viewed as a Heisenberg-Ising fluid with moving
Heisenberg-Ising spins. We derive the Luttinger liquid relation for the
stiffness and the susceptibility, both from conformal arguments, and directly
from the integral equations. Finally, we investigate the opening and closing of
the ground state gaps for both SC and Heisenberg-Ising models, as the
interaction strength is varied.Comment: 10 REVTeX pages + 4 uuencoded figures, UoU-002029
The development of low temperature curing adhesives
An approach for the development of a practical low temperature (293 K-311 K/68 F-100 F) curing adhesive system based on a family of amide/ester resins was studied and demonstrated. The work was conducted on resin optimization and adhesive compounding studies. An improved preparative method was demonstrated which involved the reaction of an amine-alcohol precursor, in a DMF solution with acid chloride. Experimental studies indicated that an adhesive formulation containing aluminum powder provided the best performance when used in conjunction with a commercial primer
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