3,953 research outputs found
Diagrammatic approach in the variational coupled-cluster method
Recently, as demonstrated by an antiferromagnetic spin-lattice application,
we have successfully extended the coupled-cluster method (CCM) to a variational
formalism in which two sets of distribution functions are introduced to
evaluate Hamiltonian expectation. We calculated these distribution functions by
employing an algebraic scheme. Here we present an alternative calculation based
on a diagrammatic technique. Similar to the method of correlated-basis
functionals (CBF), a generating functional is introduced and calculated by a
linked-cluster expansion in terms of diagrams which are categorized and
constructed according to a few simple rules and using correlation coefficients
and Pauli exclusion principle (or Pauli line) as basic elements. Infinite
resummations of diagrams can then be done in a straightforward manner. One such
resummation, which includes all so-called ring diagrams and ignores Pauli
exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond
SWT are also given. Interestingly, one such approximation including all
so-called super-ring diagrams by a resummation of infinite Pauli lines in
additional to resummations of ring diagrams produces a convergent, precise
number for the order-parameter of the one-dimensional isotropic model, contrast
to the well-known divergence of SWT. We also discuss the direct relation
between our variational CCM and CBF and discuss a possible unification of the
two theories.Comment: 18 pages, 9 figure
Longitudinal excitations in quantum antiferromagnets
By extending our recently proposed magnon-density-waves to low dimensions, we
investigate, using a microscopic many-body approach, the longitudinal
excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg
antiferromagnetic systems on a bipartite lattice with a general spin quantum
number. We obtain the full energy spectrum of the longitudinal mode as a
function of the coupling constants in the original lattice Hamiltonian and find
that it always has a non-zero energy gap if the ground state has a long-range
order and becomes gapless for the pure isotropic 1d model. The numerical value
of the minimum gap in our approximation agrees with that of a longitudinal mode
observed in the quasi-1d antiferromagnetic compound KCuF at low
temperature. It will be interesting to compare values of the energy spectrum at
other momenta if their experimental results are available.Comment: 19 pages, 4 figure
Excited states of quantum many-body interacting systems: A variational coupled-cluster description
We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin . In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.Comment: 17 pages, 4 figure
The reaction at low energies in a chiral quark model
A chiral quark-model approach is extended to the study of the
scattering at low energies. The process of at
MeV/c (i.e. the center mass energy GeV) is
investigated. This approach is successful in describing the differential cross
sections and total cross section with the roles of the low-lying
resonances in shells clarified. The dominates the
reactions over the energy region considered here. Around MeV/c,
the is responsible for a strong resonant peak in the
cross section. The has obvious contributions around
MeV/c, while the contribution of is less
important in this energy region. The non-resonant background contributions,
i.e. -channel and -channel, also play important roles in the explanation
of the angular distributions due to amplitude interferences.Comment: 18 pages and 7 figure
Two-dimensional Poisson Trees converge to the Brownian web
The Brownian web can be roughly described as a family of coalescing
one-dimensional Brownian motions starting at all times in and at all
points of . It was introduced by Arratia; a variant was then studied by
Toth and Werner; another variant was analyzed recently by Fontes, Isopi, Newman
and Ravishankar. The two-dimensional \emph{Poisson tree} is a family of
continuous time one-dimensional random walks with uniform jumps in a bounded
interval. The walks start at the space-time points of a homogeneous Poisson
process in and are in fact constructed as a function of the point
process. This tree was introduced by Ferrari, Landim and Thorisson. By
verifying criteria derived by Fontes, Isopi, Newman and Ravishankar, we show
that, when properly rescaled, and under the topology introduced by those
authors, Poisson trees converge weakly to the Brownian web.Comment: 22 pages, 1 figure. This version corrects an error in the previous
proof. The results are the sam
Ballistic Thermal Rectification in Asymmetric Three-Terminal Mesoscopic Dielectric Systems
By coupling the asymmetric three-terminal mesoscopic dielectric system with a
temperature probe, at low temperature, the ballistic heat flux flow through the
other two asymmetric terminals in the nonlinear response regime is studied
based on the Landauer formulation of transport theory. The thermal
rectification is attained at the quantum regime. It is a purely quantum effect
and is determined by the dependence of the ratio
on , the phonon's frequency.
Where and are respectively the
transmission coefficients from two asymmetric terminals to the temperature
probe, which are determined by the inelastic scattering of ballistic phonons in
the temperature probe. Our results are confirmed by extensive numerical
simulations.Comment: 10 pages, 4 figure
On a property of random-oriented percolation in a quadrant
Grimmett's random-orientation percolation is formulated as follows. The
square lattice is used to generate an oriented graph such that each edge is
oriented rightwards (resp. upwards) with probability and leftwards (resp.
downwards) otherwise. We consider a variation of Grimmett's model proposed by
Hegarty, in which edges are oriented away from the origin with probability ,
and towards it with probability , which implies rotational instead of
translational symmetry. We show that both models could be considered as special
cases of random-oriented percolation in the NE-quadrant, provided that the
critical value for the latter is 1/2. As a corollary, we unconditionally obtain
a non-trivial lower bound for the critical value of Hegarty's
random-orientation model. The second part of the paper is devoted to higher
dimensions and we show that the Grimmett model percolates in any slab of height
at least 3 in .Comment: The abstract has been updated, discussion has been added to the end
of the articl
Translating Tolerogenic Therapies to the Clinic – Where Do We Stand and What are the Barriers?
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