295 research outputs found
Classification of resonance Regge trajectories and a modified Mulholland formula
We employ a simple potential model to analyse the effects which a Regge
trajectory, correlating with a bound or a metastable state at zero angular
momentum, has on an integral cross section. A straightforward modification of
the Mulholland formula of Macek et al is proposed for more efficient separation
of the resonance contribution.Comment: 4 pages, 5 figure
Large time behavior for vortex evolution in the half-plane
In this article we study the long-time behavior of incompressible ideal flow
in a half plane from the point of view of vortex scattering. Our main result is
that certain asymptotic states for half-plane vortex dynamics decompose
naturally into a nonlinear superposition of soliton-like states. Our approach
is to combine techniques developed in the study of vortex confinement with weak
convergence tools in order to study the asymptotic behavior of a self-similar
rescaling of a solution of the incompressible 2D Euler equations on a half
plane with compactly supported, nonnegative initial vorticity.Comment: 30 pages, no figure
The absolute position of a resonance peak
It is common practice in scattering theory to correlate between the position
of a resonance peak in the cross section and the real part of a complex energy
of a pole of the scattering amplitude. In this work we show that the resonance
peak position appears at the absolute value of the pole's complex energy rather
than its real part. We further demonstrate that a local theory of resonances
can still be used even in cases previously thought impossible
Kramers-Kronig, Bode, and the meaning of zero
The implications of causality, as captured by the Kramers-Kronig relations
between the real and imaginary parts of a linear response function, are
familiar parts of the physics curriculum. In 1937, Bode derived a similar
relation between the magnitude (response gain) and phase. Although the
Kramers-Kronig relations are an equality, Bode's relation is effectively an
inequality. This perhaps-surprising difference is explained using elementary
examples and ultimately traces back to delays in the flow of information within
the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea
Demonstration of superluminal effects in an absorptionless, non-reflective system
We present an experimental and theoretical study of a simple, passive system
consisting of a birefringent, two-dimensional photonic crystal and a polarizer
in series, and show that superluminal dispersive effects can arise even though
no incident radiation is absorbed or reflected. We demonstrate that a vector
formulation of the Kramers-Kronig dispersion relations facilitates an
understanding of these counter-intuitive effects.Comment: 6 pages, 3 figures, accepted on Physical Review Letter
Non-reciprocal phase shift induced by an effective magnetic flux for light
Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials
Two-Pion Exchange in Proton-Proton Scattering
The contribution of the box and crossed two-pion-exchange diagrams to
proton-proton scattering at 90 is calculated in the laboratory
momentum range up to 12 GeV/c. Relativistic form factors related to the nucleon
and pion size and representing the pion source distribution based on the quark
structure of the hadronic core are included at each vertex of the pion-nucleon
interaction. These form factors depend on the four-momenta of the exchanged
pions and scattering nucleons. Feynman-diagram amplitudes calculated without
form factors are checked against those derived from dispersion relations. In
this comparison, one notices that a very short-range part of the crossed
diagram, neglected in dispersion-relation calculations of the two-pion-exchange
nucleon-nucleon potential, gives a sizable contribution. In the Feynman-diagram
calculation with form factors the agreement with measured spin-separated cross
sections, as well as amplitudes in the lower part of the energy range
considered, is much better for pion-nucleon pseudo-vector vis \`a vis
pseudo-scalar coupling. While strengths of the box and crossed diagrams are
comparable for laboratory momenta below 2 GeV/c, the crossed diagram dominates
for larger momenta, largely due to the kinematics of the crossed diagram
allowing a smaller momentum transfer in the nucleon center of mass. An
important contribution arises from the principal-value part of the integrals
which is non-zero when form factors are included. It seems that the importance
of the exchange of color singlets may extend higher in energy than expected
On the electromagnetic properties of active media
Several results concerning active media or metamaterials are proved and
discussed. In particular, we consider the permittivity, permeability, wave
vector, and refractive index, and discuss stability, refraction, gain, and
fundamental limitations resulting from causality
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