34,215 research outputs found
Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation
As a continuum work of Bhaumik et al who derived the common eigenvector of
the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9
(1976) 1507) we search for the simultaneous eigenvector of Q and
(ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite
entangled state representation. The differential equation is then solved in
terms of the two-variable Hermite polynomials and the formal hypergeometric
functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by
Fan and Klauder, in which the common eigenkets of Q and pair creators are
discussed
Clustering Coefficients of Protein-Protein Interaction Networks
The properties of certain networks are determined by hidden variables that
are not explicitly measured. The conditional probability (propagator) that a
vertex with a given value of the hidden variable is connected to k of other
vertices determines all measurable properties. We study hidden variable models
and find an averaging approximation that enables us to obtain a general
analytical result for the propagator. Analytic results showing the validity of
the approximation are obtained. We apply hidden variable models to
protein-protein interaction networks (PINs) in which the hidden variable is the
association free-energy, determined by distributions that depend on
biochemistry and evolution. We compute degree distributions as well as
clustering coefficients of several PINs of different species; good agreement
with measured data is obtained. For the human interactome two different
parameter sets give the same degree distributions, but the computed clustering
coefficients differ by a factor of about two. This shows that degree
distributions are not sufficient to determine the properties of PINs.Comment: 16 pages, 3 figures, in Press PRE uses pdflate
Stabilization of the p-wave superfluid state in an optical lattice
It is hard to stabilize the p-wave superfluid state of cold atomic gas in
free space due to inelastic collisional losses. We consider the p-wave Feshbach
resonance in an optical lattice, and show that it is possible to have a stable
p-wave superfluid state where the multi-atom collisional loss is suppressed
through the quantum Zeno effect. We derive the effective Hamiltonian for this
system, and calculate its phase diagram in a one-dimensional optical lattice.
The results show rich phase transitions between the p-wave superfluid state and
different types of insulator states induced either by interaction or by
dissipation.Comment: 5 pages, 5 figure
Spectral Transition and Torque Reversal in X-ray Pulsar 4U 1626-67
The accretion-powered, X-ray pulsar 4U 1626-67 has recently shown an abrupt
torque reversal accompanied by a dramatic spectral transition and a relatively
small luminosity change. The time-averaged X-ray spectrum during spin-down is
considerably harder than during spin-up. The observed torque reversal can be
explained by an accretion flow transition triggered by a gradual change in the
mass accretion rate. The sudden transition to spin-down is caused by a change
in the accretion flow rotation from Keplerian to sub-Keplerian. 4U 1626-67 is
estimated to be near spin equilibrium with a mass accretion rate Mdot~2x10**16
g/s, Mdot decreasing at a rate ~6x10**14 g/s/yr, and a polar surface magnetic
field of ~2b_p**{-1/2} 10^**12G where b_p is the magnetic pitch. During
spin-up, the Keplerian flow remains geometrically thin and cool. During
spin-down, the sub-Keplerian flow becomes geometrically thick and hot. Soft
photons from near the stellar surface are Compton up-scattered by the hot
accretion flow during spin-down while during spin-up such scattering is
unlikely due to the small scale-height and low temperature of the flow. This
mechanism accounts for the observed spectral hardening and small luminosity
change. The scattering occurs in a hot radially falling column of material with
a scattering depth ~0.3 and a temperature ~10^9K. The X-ray luminosity at
energies >5keV could be a poor indicator of the mass accretion rate. We briefly
discuss the possible application of this mechanism to GX 1+4, although there
are indications that this system is significantly different from other
torque-reversal systems.Comment: 10 pages, 1 figure, ApJ
On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability
The Particle-In-Cell (PIC) method is widely used in relativistic particle
beam and laser plasma modeling. However, the PIC method exhibits numerical
instabilities that can render unphysical simulation results or even destroy the
simulation. For electromagnetic relativistic beam and plasma modeling, the most
relevant numerical instabilities are the finite grid instability and the
numerical Cherenkov instability. We review the numerical dispersion relation of
the electromagnetic PIC algorithm to analyze the origin of these instabilities.
We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm,
and then specialize to the Yee FDTD scheme. In particular, we account for the
manner in which the PIC algorithm updates and samples the fields and
distribution function. Temporal and spatial phase factors from solving
Maxwell's equations on the Yee grid with the leapfrog scheme are also
explicitly accounted for. Numerical solutions to the electrostatic-like modes
in the 1D dispersion relation for a cold drifting plasma are obtained for
parameters of interest. In the succeeding analysis, we investigate how the
finite grid instability arises from the interaction of the numerical 1D modes
admitted in the system and their aliases. The most significant interaction is
due critically to the correct represenation of the operators in the dispersion
relation. We obtain a simple analytic expression for the peak growth rate due
to this interaction.Comment: 25 pages, 6 figure
Modelling the multi-wavelength emissions from PSR B1259-63/LS 2883: the effects of the stellar disc on shock radiations
PSR B1259-63/LS 2883 is an elliptical pulsar/Be star binary and emits
broadband emissions from radio to TeV -rays. The massive star possesses
an equatorial disc, which is inclined with the orbital plane of the pulsar. The
non-thermal emission from the system is believed to be produced by the pulsar
wind shock and the double-peak profiles in the X-ray and TeV -ray light
curves are related to the phases of the pulsar passing through the disc region
of the star. In this paper, we investigate the interactions between the pulsar
wind and stellar outflows, especially with the presence of the disc, and
present a multi-wavelength modelling of the emission from this system. We show
that the double-peak profiles of X-ray and TeV -ray light curves are
caused by the enhancements of the magnetic field and the soft photons at the
shock during the disc passages. As the pulsar is passing through the equatorial
disc, the additional pressure of the disc pushes the shock surface closer to
the pulsar, which causes the enhancement of magnetic field in the shock, and
thus increases the synchrotron luminosity. The TeV -rays due to the
inverse-Compton (IC) scattering of shocked electrons with seed photons from the
star is expected to peak around periastron which is inconsistent with
observations. However, the shock heating of the stellar disc could provide
additional seed photons for IC scattering during the disc passages, and thus
produces the double-peak profiles as observed in the TeV -ray light
curve. Our model can possibly be examined and applied to other similar
gamma-ray binaries, such as PSR J2032+4127/MT91 213, HESS J0632+057, and LS
I+61303.Comment: 14 pages, 6 figure
Aharonov-Anandan Effect Induced by Spin-Orbit Interaction and Charge-Density-Waves in Mesoscopic Rings
We study the spin-dependent geometric phase effect in mesoscopic rings of
charge-density-wave(CDW) materials. When electron spin is explicitly taken into
account, we show that the spin-dependent Aharonov-Casher phase can have a
pronounced frustration effects on such CDW materials with appropriate electron
filling. We show that this frustration has observable consequences for
transport experiment. We identify a phase transition from a Peierls insulator
to metal, which is induced by spin-dependent phase interference effects.
Mesoscopic CDW materials and spin-dependent geometric phase effects, and their
interplay, are becoming attractive opportunities for exploitation with the
rapid development of modern fabrication technology.Comment: 5 pages, 6 figures, to appear in Phys.Rev.B(Aug.15, 1998
Integral Human Pose Regression
State-of-the-art human pose estimation methods are based on heat map
representation. In spite of the good performance, the representation has a few
issues in nature, such as not differentiable and quantization error. This work
shows that a simple integral operation relates and unifies the heat map
representation and joint regression, thus avoiding the above issues. It is
differentiable, efficient, and compatible with any heat map based methods. Its
effectiveness is convincingly validated via comprehensive ablation experiments
under various settings, specifically on 3D pose estimation, for the first time
Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schr\"{o}dinger equations
Weak interactions of solitary waves in the generalized nonlinear
Schr\"{o}dinger equations are studied. It is first shown that these
interactions exhibit similar fractal dependence on initial conditions for
different nonlinearities. Then by using the Karpman-Solov'ev method, a
universal system of dynamical equations is derived for the velocities,
amplitudes, positions and phases of interacting solitary waves. These dynamical
equations contain a single parameter, which accounts for the different forms of
nonlinearity. When this parameter is zero, these dynamical equations are
integrable, and the exact analytical solutions are derived. When this parameter
is non-zero, the dynamical equations exhibit fractal structures which match
those in the original wave equations both qualitatively and quantitatively.
Thus the universal nature of fractal structures in the weak interaction of
solitary waves is analytically established. The origin of these fractal
structures is also explored. It is shown that these structures bifurcate from
the initial conditions where the solutions of the integrable dynamical
equations develop finite-time singularities. Based on this observation, an
analytical criterion for the existence and locations of fractal structures is
obtained. Lastly, these analytical results are applied to the generalized
nonlinear Schr\"{o}dinger equations with various nonlinearities such as the
saturable nonlinearity, and predictions on their weak interactions of solitary
waves are made.Comment: 22pages, 15 figure
Quantum mechanical photon-count formula derived by entangled state representation
By introducing the thermo entangled state representation, we derived four new
photocount distribution formulas for a given density operator of light field.
It is shown that these new formulas, which is convenient to calculate the
photocount, can be expressed as such integrations over Laguree-Gaussian
function with characteristic function, Wigner function, Q-function, and
P-function, respectively.Comment: 5 pages, no figur
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