1,773 research outputs found
Vortices on Hyperbolic Surfaces
It is shown that abelian Higgs vortices on a hyperbolic surface can be
constructed geometrically from holomorphic maps , where is also
a hyperbolic surface. The fields depend on and on the metrics of and
. The vortex centres are the ramification points, where the derivative of
vanishes. The magnitude of the Higgs field measures the extent to which
is locally an isometry.
Witten's construction of vortices on the hyperbolic plane is rederived, and
new examples of vortices on compact surfaces and on hyperbolic surfaces of
revolution are obtained. The interpretation of these solutions as
SO(3)-invariant, self-dual SU(2) Yang--Mills fields on is also given.Comment: Revised version: new section on four-dimensional interpretation of
hyperbolic vortices added
Polar type density of states in non-unitary odd-parity superconducting states of gap with point nodes
It is shown that the density of states (DOS) proportional to the excitation
energy, the so-called polar like DOS, can arise in the odd-parity states with
the superconducting gap vanishing at points even if the spin-orbit interaction
for Cooper pairing is strong enough. Such gap stuructures are realized in the
non-unitary states, F_{1u}(1,i,0), F_{1u}(1,varepsilon,varepsilon^{2}), and
F_{2u}(1,i,0), classified by Volovik and Gorkov, Sov. Phys.-JETP Vol.61 (1985)
843. This is due to the fact that the gap vanishes in quadratic manner around
the point on the Fermi surface. It is also shown that the region of quadratic
energy dependence of DOS, in the state F_{2u}(1,varepsilon,varepsilon^{2}), is
restricted in very small energy region making it difficult to distinguish from
the polar-like DOS.Comment: 5 pages, 3 figures, submitted to J. Phys.: Condens. Matter Lette
Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems
In this paper we show that, if an integrable Hamiltonian system admits a
nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov
condegeneracy condition near that singularity (under a mild additional
condition, which is trivial if the singularity contains a fixed point)Comment: revised version, 11p, accepted for publication in a sepecial volume
in Regular and Chaotic Dynamics in honor of Richard Cushma
Measurement of miniband parameters of a doped superlattice by photoluminescence in high magnetic fields
We have studied a 50/50\AA superlattice of GaAs/AlGaAs
composition, modulation-doped with Si, to produce
cm electrons per superlattice period. The modulation-doping was tailored
to avoid the formation of Tamm states, and photoluminescence due to interband
transitions from extended superlattice states was detected. By studying the
effects of a quantizing magnetic field on the superlattice photoluminescence,
the miniband energy width, the reduced effective mass of the electron-hole
pair, and the band gap renormalization could be deduced.Comment: minor typing errors (minus sign in eq. (5)
Research on Effective Teaching in Elementary School Physical Education
The perspective of this article is that the purpose of the elementary physical education program is the development of a physically active lifestyle. We discuss the relative contribution of the development of motor skills, fitness, content related to encouraging participation, and the affective goals of the program to the development of a physically active lifestyle. Teaching must be effective if children are to acquire the skills to lead a physically active lifestyle. We explore the research base identifying effective teaching in an elementary school physical education setting in terms of academic learning time and management roles and communication and content-development skills of the teacher. Similarities and differences between teaching in a gymnasium and in a classroom are identified
A Cantor set of tori with monodromy near a focus-focus singularity
We write down an asymptotic expression for action coordinates in an
integrable Hamiltonian system with a focus-focus equilibrium. From the
singularity in the actions we deduce that the Arnol'd determinant grows
infinitely large near the pinched torus. Moreover, we prove that it is possible
to globally parametrise the Liouville tori by their frequencies. If one
perturbs this integrable system, then the KAM tori form a Whitney smooth
family: they can be smoothly interpolated by a torus bundle that is
diffeomorphic to the bundle of Liouville tori of the unperturbed integrable
system. As is well-known, this bundle of Liouville tori is not trivial. Our
result implies that the KAM tori have monodromy. In semi-classical quantum
mechanics, quantisation rules select sequences of KAM tori that correspond to
quantum levels. Hence a global labeling of quantum levels by two quantum
numbers is not possible.Comment: 11 pages, 2 figure
Many-body theory of pump-probe spectra for highly excited semiconductors
We present a unified theory for pump-probe spectra in highly excited
semiconductors, which is applicable throughout the whole density regime
including the high-density electron-hole BCS state and the low-density
excitonic Bose-Einstein condensate (BEC). The analysis is based on the BCS-like
pairing theory combined with the Bethe-Salpeter (BS) equation, which first
enables us to incorporate the state-filling effect, the band-gap
renormalization and the strong/weak electron-hole pair correlations in a
unified manner. We show that the electron-hole BCS state is distinctly
stabilized by the intense pump-light, and this result strongly suggests that
the macroscopic quantum state can be observed under the strong photoexcitation.
The calculated spectra considerably deviate from results given by the BCS-like
mean field theory and the simple BS equation without electron-hole pair
correlation especially in the intermediate density states between the
electron-hole BCS state and the excitonic BEC state. In particular, we find the
sharp stimulated emission and absorption lines which originate from the optical
transition accompanied by the collective phase fluctuation mode in the
electron-hole BCS state. From the pump-probe spectral viewpoint, we show that
this fluctuation mode changes to the exciton mode with decreasing carrier
densityComment: RevTeX 11 pages, 10 figures. To appear in Phys.Rev.B1
Ultrafast Coulomb-induced dynamics of 2D magnetoexcitons
We study theoretically the ultrafast nonlinear optical response of quantum
well excitons in a perpendicular magnetic field. We show that for
magnetoexcitons confined to the lowest Landau levels, the third-order
four-wave-mixing (FWM) polarization is dominated by the exciton-exciton
interaction effects. For repulsive interactions, we identify two regimes in the
time-evolution of the optical polarization characterized by exponential and
{\em power law} decay of the FWM signal. We describe these regimes by deriving
an analytical solution for the memory kernel of the two-exciton wave-function
in strong magnetic field. For strong exciton-exciton interactions, the decay of
the FWM signal is governed by an antibound resonance with an
interaction-dependent decay rate. For weak interactions, the continuum of
exciton-exciton scattering states leads to a long tail of the time-integrated
FWM signal for negative time delays, which is described by the product of a
power law and a logarithmic factor. By combining this analytic solution with
numerical calculations, we study the crossover between the exponential and
non-exponential regimes as a function of magnetic field. For attractive
exciton-exciton interaction, we show that the time-evolution of the FWM signal
is dominated by the biexcitonic effects.Comment: 41 pages with 11 fig
Vanishing Twist near Focus-Focus Points
We show that near a focus-focus point in a Liouville integrable Hamiltonian
system with two degrees of freedom lines of locally constant rotation number in
the image of the energy-momentum map are spirals determined by the eigenvalue
of the equilibrium. From this representation of the rotation number we derive
that the twist condition for the isoenergetic KAM condition vanishes on a curve
in the image of the energy-momentum map that is transversal to the line of
constant energy. In contrast to this we also show that the frequency map is
non-degenerate for every point in a neighborhood of a focus-focus point.Comment: 13 page
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