2,778 research outputs found
Self consistent determination of plasmonic resonances in ternary nanocomposites
We have developed a self consistent technique to predict the behavior of
plasmon resonances in multi-component systems as a function of wavelength. This
approach, based on the tight lower bounds of the Bergman-Milton formulation, is
able to predict experimental optical data, including the positions, shifts and
shapes of plasmonic peaks in ternary nanocomposites without using any ftting
parameters. Our approach is based on viewing the mixing of 3 components as the
mixing of 2 binary mixtures, each in the same host. We obtained excellent
predictions of the experimental optical behavior for mixtures of Ag:Cu:SiO2 and
alloys of Au-Cu:SiO2 and Ag-Au:H2 O, suggesting that the essential physics of
plasmonic behavior is captured by this approach.Comment: 7 pages and 4 figure
Entanglement of macroscopic test masses and the Standard Quantum Limit in laser interferometry
We show that the generation of entanglement of two heavily macroscopic
mirrors with masses of up to several kilograms are feasible with state of the
art techniques of high-precision laser interferometry. The basis of such a
demonstration would be a Michelson interferometer with suspended mirrors and
simultaneous homodyne detections at both interferometer output ports. We
present the connection between the generation of entanglement and the Standard
Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in
operating interferometers for gravitational-wave detection and provides a
measure of when macroscopic entanglement can be observed in the presence of
realistic decoherence processes
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
Relativistic diffusion processes and random walk models
The nonrelativistic standard model for a continuous, one-parameter diffusion
process in position space is the Wiener process. As well-known, the Gaussian
transition probability density function (PDF) of this process is in conflict
with special relativity, as it permits particles to propagate faster than the
speed of light. A frequently considered alternative is provided by the
telegraph equation, whose solutions avoid superluminal propagation speeds but
suffer from singular (non-continuous) diffusion fronts on the light cone, which
are unlikely to exist for massive particles. It is therefore advisable to
explore other alternatives as well. In this paper, a generalized Wiener process
is proposed that is continuous, avoids superluminal propagation, and reduces to
the standard Wiener process in the non-relativistic limit. The corresponding
relativistic diffusion propagator is obtained directly from the nonrelativistic
Wiener propagator, by rewriting the latter in terms of an integral over
actions. The resulting relativistic process is non-Markovian, in accordance
with the known fact that nontrivial continuous, relativistic Markov processes
in position space cannot exist. Hence, the proposed process defines a
consistent relativistic diffusion model for massive particles and provides a
viable alternative to the solutions of the telegraph equation.Comment: v3: final, shortened version to appear in Phys. Rev.
Granger causality and transfer entropy are equivalent for Gaussian variables
Granger causality is a statistical notion of causal influence based on
prediction via vector autoregression. Developed originally in the field of
econometrics, it has since found application in a broader arena, particularly
in neuroscience. More recently transfer entropy, an information-theoretic
measure of time-directed information transfer between jointly dependent
processes, has gained traction in a similarly wide field. While it has been
recognized that the two concepts must be related, the exact relationship has
until now not been formally described. Here we show that for Gaussian
variables, Granger causality and transfer entropy are entirely equivalent, thus
bridging autoregressive and information-theoretic approaches to data-driven
causal inference.Comment: In review, Phys. Rev. Lett., Nov. 200
Time-Domain Measurement of Broadband Coherent Cherenkov Radiation
We report on further analysis of coherent microwave Cherenkov impulses
emitted via the Askaryan mechanism from high-energy electromagnetic showers
produced at the Stanford Linear Accelerator Center (SLAC). In this report, the
time-domain based analysis of the measurements made with a broadband (nominally
1-18 GHz) log periodic dipole array antenna is described. The theory of a
transmit-receive antenna system based on time-dependent effective height
operator is summarized and applied to fully characterize the measurement
antenna system and to reconstruct the electric field induced via the Askaryan
process. The observed radiation intensity and phase as functions of frequency
were found to agree with expectations from 0.75-11.5 GHz within experimental
errors on the normalized electric field magnitude and the relative phase; 0.039
microV/MHz/TeV and 17 deg, respectively. This is the first time this agreement
has been observed over such a broad bandwidth, and the first measurement of the
relative phase variation of an Askaryan pulse. The importance of validation of
the Askaryan mechanism is significant since it is viewed as the most promising
way to detect cosmogenic neutrino fluxes at E > 10^15 eV.Comment: 10 pages, 9 figures, accepted by Phys. Rev.
Warren McCulloch and the British cyberneticians
Warren McCulloch was a significant influence on a number of British cyberneticians, as some British pioneers in this area were on him. He interacted regularly with most of the main figures on the British cybernetics scene, forming close friendships and collaborations with several, as well as mentoring others. Many of these interactions stemmed from a 1949 visit to London during which he gave the opening talk at the inaugural meeting of the Ratio Club, a gathering of brilliant, mainly young, British scientists working in areas related to cybernetics. This paper traces some of these relationships and interaction
Distribution of roots of random real generalized polynomials
The average density of zeros for monic generalized polynomials,
, with real holomorphic and
real Gaussian coefficients is expressed in terms of correlation functions of
the values of the polynomial and its derivative. We obtain compact expressions
for both the regular component (generated by the complex roots) and the
singular one (real roots) of the average density of roots. The density of the
regular component goes to zero in the vicinity of the real axis like
. We present the low and high disorder asymptotic
behaviors. Then we particularize to the large limit of the average density
of complex roots of monic algebraic polynomials of the form with real independent, identically distributed
Gaussian coefficients having zero mean and dispersion . The average density tends to a simple, {\em universal}
function of and in the domain where nearly all the roots are located for
large .Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed
tarfile (.66MB) containing 8 Postscript figures is available by e-mail from
[email protected]
Fractional Quantum Mechanics
A path integral approach to quantum physics has been developed. Fractional
path integrals over the paths of the L\'evy flights are defined. It is shown
that if the fractality of the Brownian trajectories leads to standard quantum
and statistical mechanics, then the fractality of the L\'evy paths leads to
fractional quantum mechanics and fractional statistical mechanics. The
fractional quantum and statistical mechanics have been developed via our
fractional path integral approach. A fractional generalization of the
Schr\"odinger equation has been found. A relationship between the energy and
the momentum of the nonrelativistic quantum-mechanical particle has been
established. The equation for the fractional plane wave function has been
obtained. We have derived a free particle quantum-mechanical kernel using Fox's
H function. A fractional generalization of the Heisenberg uncertainty relation
has been established. Fractional statistical mechanics has been developed via
the path integral approach. A fractional generalization of the motion equation
for the density matrix has been found. The density matrix of a free particle
has been expressed in terms of the Fox's H function. We also discuss the
relationships between fractional and the well-known Feynman path integral
approaches to quantum and statistical mechanics.Comment: 27 page
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