2,710 research outputs found
Green function for hyperbolic media
We revisit the problem of the electromagnetic Green function for homogeneous
hyperbolic media, where longitudinal and transverse components of the
dielectric permittivity tensor have different signs. We analyze the dipole
emission patterns for both dipole orientations with respect to the symmetry
axis and for different signs of dielectric constants, and show that the
emission pattern is highly anisotropic and has a characteristic cross-like
shape: the waves are propagating within a certain cone and are evanescent
outside this cone. We demonstrate the coexistence of the cone-like pattern due
to emission of the extraordinary TM-polarized waves and elliptical pattern due
to emission of ordinary TE-polarized waves. We find a singular complex term in
the Green function, proportional to the function and governing the
photonic density of states and Purcell effect in hyperbolic media.Comment: 10 pages, 7 figure
Purcell effect in wire metamaterials
We study theoretically the enhancement of spontaneous emission in wire
metamaterials. We analyze the dependence of the Purcell factor dependence on
wire dielectric constant for both electric and magnetic dipole sources, and
find an optimal value of the dielectric constant for maximizing the Purcell
factor for the electric dipole. We obtain analytical expressions for the
Purcell factor and also provide estimates for the Purcell factor in realistic
structures operating in both microwave and optical spectral range.Comment: 15 pages, 7 figure
Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses
In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys.
A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassical
approximation the general theory of calculation of effective currents and
sources generating bremsstrahlung of an arbitrary number of soft quarks and
soft gluons at collision of a high-energy color-charged particle with thermal
partons in a hot quark-gluon plasma, is developed. For the case of one- and
two-scattering thermal partons with radiation of one or two soft excitations,
the effective currents and sources are calculated in an explicit form. In the
model case of `frozen' medium, approximate expressions for energy losses
induced by the most simple processes of bremsstrahlung of soft quark and soft
gluon, are derived. On the basis of a conception of the mutual cancellation of
singularities in the sum of so-called `diagonal' and `off-diagonal'
contributions to the energy losses, an effective method of determining color
factors in scattering probabilities, containing the initial values of Grassmann
color charges, is suggested. The dynamical equations for Grassmann color
charges of hard particle used by us early are proved to be insufficient for
investigation of the higher radiative processes. It is shown that for correct
description of these processes the given equations should be supplemented
successively with the higher-order terms in powers of the soft fermionic field.Comment: 93 pages, 20 figure
Subexponential estimations in Shirshov's height theorem (in English)
In 1993 E. I. Zelmanov asked the following question in Dniester Notebook:
"Suppose that F_{2, m} is a 2-generated associative ring with the identity
x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential
growth?" We show that the nilpotency degree of l-generated associative algebra
with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l
(nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by
this result. It is the consequence of one fact, which is based on combinatorics
of words. Let l, n and d>n be positive integers. Then all the words over
alphabet of cardinality l which length is greater than Psi(n,d,l) are either
n-divided or contain d-th power of subword, where a word W is n-divided, if it
can be represented in the following form W=W_0 W_1...W_n such that W_1 >'
W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov
proved that the set of non n-divided words over alphabet of cardinality l has
bounded height h over the set Y consisting of all the words of degree <n.
Original Shirshov's estimation was just recursive, in 1982 double exponent was
obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation.
We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our
proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link
arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55
Access to improve the muon mass and magnetic moment anomaly via the bound-muon factor
A theoretical description of the factor of a muon bound in a nuclear
potential is presented. One-loop self-energy and multi-loop vacuum polarization
corrections are calculated, taking into account the interaction with the
binding potential exactly. Nuclear effects on the bound-muon factor are
also evaluated. We put forward the measurement of the bound-muon factor via
the continuous Stern-Gerlach effect as an independent means to determine the
free muons magnetic moment anomaly and mass. The scheme presented enables to
increase the accuracy of the mass by more than an order of magnitude
Tailoring and enhancing spontaneous two-photon emission processes using resonant plasmonic nanostructures
The rate of spontaneous emission is known to depend on the environment of a
light source, and the enhancement of one-photon emission in a resonant cavity
is known as the Purcell effect. Here we develop a theory of spontaneous
two-photon emission for a general electromagnetic environment including
inhomogeneous dispersive and absorptive media. This theory is used to evaluate
the two-photon Purcell enhancement in the vicinity of metallic nanoparticles
and it is demonstrated that the surface plasmon resonances supported by these
particles can enhance the emission rate by more than two orders of magnitude.
The control over two-photon Purcell enhancement given by tailored
nanostructured environments could provide an emitter with any desired spectral
response and may serve as an ultimate route for designing light sources with
novel properties
Sub-wavelength imaging at optical frequencies using canalization regime
Imaging with sub-wavelength resolution using a lens formed by periodic
metal-dielectric layered structure is demonstrated. The lens operates in
canalization regime as a transmission device and it does not involve negative
refraction and amplification of evanescent modes. The thickness of the lens
have to be an integer number of half-wavelengths and can be made as large as
required for ceratin applications, in contrast to the other sub-wavelength
lenses formed by metallic slabs which have to be much smaller than the
wavelength. Resolution of at 600 nm wavelength is confirmed by
numerical simulation for a 300 nm thick structure formed by a periodic stack of
10 nm layers of glass with and 5 nm layers of metal-dielectric
composite with . Resolution of is predicted for a
structure with same thickness, period and operating frequency, but formed by
7.76 nm layers of silicon with and 7.24 nm layers of silver with
.Comment: 4 pages, 4 figures, submitted to PR
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