15,382 research outputs found
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
By numerical calculation, the Planck spectrum with zero-point radiation is
shown to satisfy a natural maximum-entropy principle whereas alternative
choices of spectra do not. Specifically, if we consider a set of
conducting-walled boxes, each with a partition placed at a different location
in the box, so that across the collection of boxes the partitions are uniformly
spaced across the volume, then the Planck spectrum correspond to that spectrum
of random radiation (having constant energy kT per normal mode at low
frequencies and zero-point energy (1/2)hw per normal mode at high frequencies)
which gives maximum uniformity across the collection of boxes for the radiation
energy per box. The analysis involves Casimir energies and zero-point radiation
which do not usually appear in thermodynamic analyses. For simplicity, the
analysis is presented for waves in one space dimension.Comment: 11 page
Grover's quantum searching algorithm is optimal
I improve the tight bound on quantum searching by Boyer et al.
(quant-ph/9605034) to a matching bound, thus showing that for any probability
of success Grovers quantum searching algorithm is optimal. E.g. for near
certain success we have to query the oracle pi/4 sqrt{N} times, where N is the
size of the search space. I also show that unfortunately quantum searching
cannot be parallelized better than by assigning different parts of the search
space to independent quantum computers. Earlier results left open the
possibility of a more efficient parallelization.Comment: 13 pages, LaTeX, essentially published versio
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
Squeezed Light and Entangled Images from Four-Wave-Mixing in Hot Rubidium Vapor
Entangled multi-spatial-mode fields have interesting applications in quantum
information, such as parallel quantum information protocols, quantum computing,
and quantum imaging. We study the use of a nondegenerate four-wave mixing
process in rubidium vapor at 795 nm to demonstrate generation of
quantum-entangled images. Owing to the lack of an optical resonator cavity, the
four-wave mixing scheme generates inherently multi-spatial-mode output fields.
We have verified the presence of entanglement between the multi-mode beams by
analyzing the amplitude difference and the phase sum noise using a dual
homodyne detection scheme, measuring more than 4 dB of squeezing in both cases.
This paper will discuss the quantum properties of amplifiers based on
four-wave-mixing, along with the multi mode properties of such devices.Comment: 11 pages, 8 figures. SPIE Optics and Photonics 2008 proceeding (San
Diego, CA
Study of basic bio-electrochemistry Sixth monthly progress report, 1-31 Aug. 1963
Contribution of hydrogen peroxide to electrode reaction in electrochemical cell by considering effect of catalyst on cell curren
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
The quantum query complexity of Boolean matrix multiplication is typically
studied as a function of the matrix dimension, n, as well as the number of 1s
in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values
of \ell. This is an improvement over previous algorithms for all values of
\ell. On the other hand, we show that for any \eps < 1 and any \ell <= \eps
n^2, there is an \Omega(n\sqrt{\ell}) lower bound for this problem, showing
that our algorithm is essentially tight.
We first reduce Boolean matrix multiplication to several instances of graph
collision. We then provide an algorithm that takes advantage of the fact that
the underlying graph in all of our instances is very dense to find all graph
collisions efficiently
Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts
The classical electromagnetic interaction of a point charge and a magnet is
discussed by first calculating the interaction of point charge with a simple
model magnetic moment and then suggesting a multiparticle limit. The Darwin
Lagrangian is used to analyze the electromagnetic behavior of the model
magnetic moment (composed of two oppositely charged particles of different mass
in an initially circular orbit) interacting with a passing point charge. The
changing mangetic moment is found to put a force back on a passing charge; this
force is of order 1/c^2 and depends upon the magnitude of the magnetic moment.
It is suggested that in the limit of a multiparticle magnetic toroid, the
electric fields of the passing charge are screened out of the body of the
magnet while the magnetic fields penetrate into the magnet. This is consistent
with our understanding of the penetration of electromagnetic velocity fields
into ohmic conductors. Conservation laws are discussed. The work corresponds to
a classical electromagnetic analysis of the interaction which is basic to
understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase
shifts and represents a refutation of the suggestions of Aharonov, Pearle, and
Vaidman.Comment: 33 page
Gravitational Chern-Simons and the adiabatic limit
We compute the gravitational Chern-Simons term explicitly for an adiabatic
family of metrics using standard methods in general relativity. We use the fact
that our base three-manifold is a quasi-regular K-contact manifold heavily in
this computation. Our key observation is that this geometric assumption
corresponds exactly to a Kaluza-Klein Ansatz for the metric tensor on our three
manifold, which allows us to translate our problem into the language of general
relativity. Similar computations have been performed in a paper of Guralnik,
Iorio, Jackiw and Pi (2003), although not in the adiabatic context.Comment: 17 page
Strong low-frequency quantum correlations from a four-wave mixing amplifier
We show that a simple scheme based on nondegenerate four-wave mixing in a hot
atomic vapor behaves like a near-perfect phase-insensitive optical amplifier,
which can generate bright twin beams with a measured quantum noise reduction in
the intensity difference of more than 8 dB, close to the best optical
parametric amplifiers and oscillators. The absence of a cavity makes the system
immune to external perturbations, and the strong quantum noise reduction is
observed over a large frequency range.Comment: 4 pages, 4 figures. Major rewrite of the previous version. New
experimental results and further analysi
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
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