3,936 research outputs found
On the periodicity of some Farhi arithmetical functions
Let . Let be any polynomial such that
and are coprime in . We call
a Farhi arithmetic function. In
this paper, we prove that is periodic. This generalizes the previous
results of Farhi and Kane, and Hong and Yang.Comment: 14 pag
The optical selection rules of a graphene quantum dot in external electric fields
We study theoretically the single-electron triangular zigzag graphene quantum
dot in three typical in-plane electric fields. The far-infrared absorption
spectra of the dot are calculated by the tight-binding method and then the
optical selection rules are identified by contrast with the corresponding
energy spectra. Our result shows that there exist the remarkable optical
selection rules due to the C3 symmetry of the dot. When the electric field
possesses also the C3 symmetry, there are only two absorption peaks in the
absorption spectra. As the C3 symmetry of the system is damaged by the electric
fields, both the intensity of the strongest peak and the number of the
forbidden transitions decrease gradually. Moreover, the polarization causes the
decrease of the peak intensities and even new forbidden transitions. Our
findings may be useful for the application of graphene quantum dots to
electronic and optoelectronic devices
Optomechanically-Based Probing of Spin-Charge Separation in Ultracold Gases
We propose a new approach to investigate the spin-charge separation in 1D
quantum liquids via the optomechanical coupled atom-cavity system. We show
that, one can realize an effective two-modes optomechanical model with the
spin/charge modes playing the role of mechanical resonators. By tuning the weak
probe laser under a pump field, the signal of spin-charge separation could be
probed explicitly in the sideband regime via cavity transmissions. Moreover,
the spin/charge modes can be addressed separately by designing the probe field
configurations, which may be beneficial for future studies of the atom-cavity
systems and quantum many-body physics.Comment: 4 pages, 5 figure
An oscillating Casimir potential between two impurities in a spin-orbit coupled Bose-Einstein condensate
We study the Casimir potential between two impurities immersed in a
spin-orbit coupled BoseEinstein condensate (BEC) with plane-wave order. We find
that, by exchanging the virtual phonons/excitations, a remarkable anisotropic
oscillating potential with both positive and negative parts can be induced
between the impurities, with the period of the oscillation depending on the
spin-orbit coupling strength. As a consequence, this would inevitably lead to a
non-central Casimir force, which can be tuned by varying the strength of
spin-orbit coupling . These results are elucidated for BECs with
one-dimensional Raman-induced and two-dimensional Rashba-type SOC.Comment: 6 pages, 3 figure
Storage of polarization-encoded cluster states in an atomic system
We present a scheme for entanglement macroscopic atomic ensembles which are
four spatially separate regions of an atomic cloud using cluster-correlated
beams. We show that the cluster-type polarization-encoded entanglement could be
mapped onto the long-lived collective ground state of the atomic ensembles, and
the stored entanglement could be retrieved based on the technique of
electromagnetically induced transparency. We also discuss the efficiency of,
the lifetime of, and some quantitative restrictions to the proposed quantum
memory.Comment: 7 pages, 4 figure
Electrically-induced polarization selection rules of a graphene quantum dot
We study theoretically the single-electron triangular zigzag graphene quantum
dot in uniform in-plane electric fields. The far-infrared absorption spectra of
the dot are calculated by the tight-binding method. The energy spectra and the
distribution of wave functions are also presented to analyse the far-infrared
spectra. The orthogonal zero-energy eigenstates are arranged along to the
direction of the external field. The remarkable result is that all intraband
transitions and some interband transitions are forbidden when the absorbed
light is polarized along the direction of the electric field. With x-direction
electric field, all intraband absorption is y polarized due to the
electric-field-direction-polarization selection rule. Moreover, with
y-direction electric field, all absorption is either x or y polarized due to
the parity selection rule as well as to the
electric-field-direction-polarization selection rule. Our calculation shows
that the formation of the FIR spectra is co-decided by the polarization
selection rules and the overlap between the eigenstates of the transition.Comment: arXiv admin note: text overlap with arXiv:1703.0423
Longitudinal polarization of hyperons in high jets in singly polarized pp collisions at high energies
We calculate the longitudinal polarizations of hyperons in high
jets in collisions in which one of the protons is longitudinally polarized
at RHIC energies using different models for the spin transfer in fragmentation
process. The results show that the measurements of these polarizations can be
used to study the spin transfer in high energy fragmentation processes in
general and to test the different models in particular. Our results show
especially that the magnitude of the polarization of is rather small
whereas that of is considerably larger in the large rapidity region.
The differences between the results from different pictures for
polarizations is also much larger. Hence, the measurement of
polarization should be more effective to distinguish between different models
especially the SU(6) or the DIS picture for spin transfer in fragmentation
processes.Comment: 26 pages, 11 figures; to appear in Phys. Rev.
Direct CP Violation in Charmless Three-body Decays of Mesons
Direct CP violation in charmless three-body hadronic decays of mesons is
studied within the framework of a simple model based on the factorization
approach. Three-body decays of heavy mesons receive both resonant and
nonresonant contributions. Dominant nonresonant contributions to tree-dominated
and penguin-dominated three-body decays arise from the tree transition
and penguin transition, respectively. The former can be evaluated in
the framework of heavy meson chiral perturbation theory with some modification,
while the latter is governed by the matrix element of the scalar density
. Strong phases in this work reside in
effective Wilson coefficients, propagators of resonances and the matrix element
of scalar density. In order to accommodate the branching fraction and CP
asymmetries observed in , the matrix element should have an additional strong phase, which might
arise from some sort of power corrections such as final-state interactions. We
calculate inclusive and regional CP asymmetries and find that nonresonant CP
violation is usually much larger than the resonant one and that the
interference effect is generally quite significant. If nonresonant
contributions are turned off in the mode, the predicted CP
asymmetries due to resonances will be wrong in sign when confronted with
experiment. In our study of , we find that should be positive in order to account for CP
asymmetries observed in this decay. However, all theories predict a large and
negative CP violation in . Measurements of CP-asymmetry
Dalitz distributions put very stringent constraints on the theoretical models.
We check the magnitude and the sign of violation in some (large) invariant mass
regions to test our model.Comment: 32 pages, 3 figure
Riemannian Inexact Newton Method for Structured Inverse Eigenvalue and Singular Value Problems
Inverse eigenvalue and singular value problems have been widely discussed for
decades. The well-known result is the Weyl-Horn condition, which presents the
relations between the eigenvalues and singular values of an arbitrary matrix.
This result by Weyl-Horn then leads to an interesting inverse problem, i.e.,
how to construct a matrix with desired eigenvalues and singular values. In this
work, we do that and more. We propose an eclectic mix of techniques from
differential geometry and the inexact Newton method for solving inverse
eigenvalue and singular value problems as well as additional desired
characteristics such as nonnegative entries, prescribed diagonal entries, and
even predetermined entries. We show theoretically that our method converges
globally and quadratically, and we provide numerical examples to demonstrate
the robustness and accuracy of our proposed method. {Having theoretical
interest, we provide in the appendix a necessary and sufficient condition for
the existence of a real matrix, or even a nonnegative matrix, with
prescribed eigenvalues, singular values, and main diagonal entries
Darboux Transformation and Variable Separation Approach: the Nizhnik-Novikov-Veselov equation
Darboux transformation is developed to systematically find variable
separation solutions for the Nizhnik-Novikov-Veselov equation. Starting from a
seed solution with some arbitrary functions, the once Darboux transformation
yields the variable separable solutions which can be obtained from the
truncated Painlev\'e analysis and the twice Darboux transformation leads to
some new variable separable solutions which are the generalization of the known
results obtained by using a guess ansatz to solve the generalized trilinear
equation.Comment: 12 pages, 6 figure
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