45,163 research outputs found
On the solvable multi-species reaction-diffusion processes
A family of one-dimensional multi-species reaction-diffusion processes on a
lattice is introduced. It is shown that these processes are exactly solvable,
provided a nonspectral matrix equation is satisfied. Some general remarks on
the solutions to this equation, and some special solutions are given. The
large-time behavior of the conditional probabilities of such systems are also
investigated.Comment: 13 pages, LaTeX2
Generating a Quadratic Forms from a Given Genus
Given a non-empty genus in dimensions with determinant , we give a
randomized algorithm that outputs a quadratic form from this genus. The time
complexity of the algorithm is poly; assuming Generalized Riemann
Hypothesis (GRH).Comment: arXiv admin note: text overlap with arXiv:1409.619
Paramagnetic Meissner Effect and Finite Spin Susceptibility in an Asymmetric Superconductor
A general analysis of Meissner effect and spin susceptibility of a uniform
superconductor in an asymmetric two-component fermion system is presented in
nonrelativistic field theory approach. We found that, the pairing mechanism
dominates the magnetization property of superconductivity, and the asymmetry
enhances the paramagnetism of the system. At the turning point from BCS to
breached pairing superconductivity, the Meissner mass squared and spin
susceptibility are divergent at zero temperature. In the breached pairing state
induced by chemical potential difference and mass difference between the two
kinds of fermions, the system goes from paramagnetism to diamagnetism, when the
mass ratio of the two species increases.Comment: 17pages, 2 figures, published in Physical Review
How to Understand LMMSE Transceiver Design for MIMO Systems From Quadratic Matrix Programming
In this paper, a unified linear minimum mean-square-error (LMMSE) transceiver
design framework is investigated, which is suitable for a wide range of
wireless systems. The unified design is based on an elegant and powerful
mathematical programming technology termed as quadratic matrix programming
(QMP). Based on QMP it can be observed that for different wireless systems,
there are certain common characteristics which can be exploited to design LMMSE
transceivers e.g., the quadratic forms. It is also discovered that evolving
from a point-to-point MIMO system to various advanced wireless systems such as
multi-cell coordinated systems, multi-user MIMO systems, MIMO cognitive radio
systems, amplify-and-forward MIMO relaying systems and so on, the quadratic
nature is always kept and the LMMSE transceiver designs can always be carried
out via iteratively solving a number of QMP problems. A comprehensive framework
on how to solve QMP problems is also given. The work presented in this paper is
likely to be the first shoot for the transceiver design for the future
ever-changing wireless systems.Comment: 31 pages, 4 figures, Accepted by IET Communication
An effective singular oscillator for Duffin-Kemmer-Petiau particles with a nonminimal vector coupling: a two-fold degeneracy
Scalar and vector bosons in the background of one-dimensional nonminimal
vector linear plus inversely linear potentials are explored in a unified way in
the context of the Duffin-Kemmer-Petiau theory. The problem is mapped into a
Sturm-Liouville problem with an effective singular oscillator. With boundary
conditions emerging from the problem, exact bound-state solutions in the spin-0
sector are found in closed form and it is shown that the spectrum exhibits
degeneracy. It is shown that, depending on the potential parameters, there may
or may not exist bound-state solutions in the spin-1 sector.Comment: 1 figure. arXiv admin note: substantial text overlap with
arXiv:1009.159
Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
After a summary of the TQFT wire model formalism we bridge the gap from
Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for
systems of triangular cells on fusion graphs that describe modules associated
with the fusion category of SU(3) at level k. We show how to solve these
equations in a number of examples.Comment: 44 figure
Classification of flat bands according to the band-crossing singularity of Bloch wave functions
We show that flat bands can be categorized into two distinct classes, that
is, singular and nonsingular flat bands, by exploiting the singular behavior of
their Bloch wave functions in momentum space. In the case of a singular flat
band, its Bloch wave function possesses immovable discontinuities generated by
the band-crossing with other bands, and thus the vector bundle associated with
the flat band cannot be defined. This singularity precludes the compact
localized states from forming a complete set spanning the flat band. Once the
degeneracy at the band crossing point is lifted, the singular flat band becomes
dispersive and can acquire a finite Chern number in general, suggesting a new
route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave
function of a nonsingular flat band has no singularity, and thus forms a vector
bundle. A nonsingular flat band can be completely isolated from other bands
while preserving the perfect flatness. All one-dimensional flat bands belong to
the nonsingular class. We show that a singular flat band displays a novel
bulk-boundary correspondence such that the presence of the robust boundary mode
is guaranteed by the singularity of the Bloch wave function. Moreover, we
develop a general scheme to construct a flat band model Hamiltonian in which
one can freely design its singular or nonsingular nature. Finally, we propose a
general formula for the compact localized state spanning the flat band, which
can be easily implemented in numerics and offer a basis set useful in analyzing
correlation effects in flat bands.Comment: 23 pages, 13 figure
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