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

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

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

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