19,351 research outputs found
Electromagnetic Vacuum of Complex Media: Dipole Emission vs. Light Propagation, Vacuum Energy, and Local Field Factors
We offer a unified approach to several phenomena related to the
electromagnetic vacuum of a complex medium made of point electric dipoles. To
this aim, we apply the linear response theory to the computation of the
polarization field propagator and study the spectrum of vacuum fluctuations.
The physical distinction among the local density of states which enter the
spectra of light propagation, total dipole emission, coherent emission, total
vacuum energy and Schwinger-bulk energy is made clear. Analytical expressions
for the spectrum of dipole emission and for the vacuum energy are derived.
Their respective relations with the spectrum of external light and with the
Schwinger-bulk energy are found. The light spectrum and the Schwinger-bulk
energy are determined by the Dyson propagator. The emission spectrum and the
total vacuum energy are determined by the polarization propagator. An exact
relationship of proportionality between both propagators is found in terms of
local field factors. A study of the nature of stimulated emission from a single
dipole is carried out. Regarding coherent emission, it contains two components.
A direct one which is transferred radiatively and directly from the emitter
into the medium and whose spectrum is that of external light. And an indirect
one which is radiated by induced dipoles. The induction is mediated by one (and
only one) local field factor. Regarding the vacuum energy, we find that in
addition to the Schwinger-bulk energy the vacuum energy of an effective medium
contains local field contributions proportional to the resonant frequency and
to the spectral line-width.Comment: Typos fixed, journal ref. adde
Public goods and decay in networks
We propose a simple behavioral model to analyze situations where (1) a group of agents repeatedly plays a public goods game within a network structure and (2) each agent only observes the past behavior of her neighbors, but is affected by the decisions of the whole group. The model assumes that agents are imperfect conditional cooperators, that they infer unobserved contributions assuming imperfect conditional cooperation by others, and that they have some degree of bounded rationality. We show that our model approximates quite accurately regularities derived from public goods game experiments
Cloaking dielectric spherical objects by a shell of metallic nanoparticles
We show that dielectric spheres can be cloaked by a shell of amorphously
arranged metallic nanoparticles. The shell represents an artificial medium with
tunable effective properties that can be adjusted such that the scattered
signals of shell and sphere almost cancel each other. We provide an analytical
model for the cloak design and prove numerically that the cloak operates as
desired. We show that more than 70% of the scattered signal of the sphere can
be suppressed at the design wavelength. Advantages and disadvantages of such a
cloak when compared to other implementations are disclosed.Comment: 14 pages, 6 figure
The interpretive approach to religious education : challenging Thompson's interpretation
In a recent book chapter, Matthew Thompson makes some criticisms of my work, including the interpretive approach to religious education and the research and activity of Warwick Religions and Education Research Unit. Against the background of a discussion of religious education in the public sphere, my response challenges Thompson’s account, commenting on his own position in relation to dialogical approaches to religious education. The article rehearses my long held view that the ideal form of religious education in fully state funded schools of a liberal democracy should be ‘secular’ but not ‘secularist’; there should be no implication of an axiomatic secular humanist interpretation of religions
Quadrupole collective modes in trapped finite-temperature Bose-Einstein condensates
Finite temperature simulations are used to study quadrupole excitations of a
trapped Bose-Einstein condensate. We focus specifically on the m=0 mode, where
a long-standing theoretical problem has been to account for an anomalous
variation of the mode frequency with temperature. We explain this behavior in
terms of the excitation of two separate modes, corresponding to coupled motion
of the condensate and thermal cloud. The relative amplitudes of the modes
depends sensitively on the temperature and on the frequency of the harmonic
drive used to excite them. Good agreement with experiment is found for
appropriate drive frequencies.Comment: 4 pages, 3 figure
Possible potentials responsible for stable circular relativistic orbits
Bertrand's theorem in classical mechanics of the central force fields
attracts us because of its predictive power. It categorically proves that there
can only be two types of forces which can produce stable, circular orbits. In
the present article an attempt has been made to generalize Bertrand's theorem
to the central force problem of relativistic systems. The stability criterion
for potentials which can produce stable, circular orbits in the relativistic
central force problem has been deduced and a general solution of it is
presented in the article. It is seen that the inverse square law passes the
relativistic test but the kind of force required for simple harmonic motion
does not. Special relativistic effects do not allow stable, circular orbits in
presence of a force which is proportional to the negative of the displacement
of the particle from the potential center.Comment: 11 pages, Latex fil
Quantum levitation by left-handed metamaterials
Left-handed metamaterials make perfect lenses that image classical
electromagnetic fields with significantly higher resolution than the
diffraction limit. Here we consider the quantum physics of such devices. We
show that the Casimir force of two conducting plates may turn from attraction
to repulsion if a perfect lens is sandwiched between them. For optical
left-handed metamaterials this repulsive force of the quantum vacuum may
levitate ultra-thin mirrors
Operator identities in q-deformed Clifford analysis
In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied
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