On inverse limit sequence

The following arose out of an unsuccessful attempt to answer the question is there a map of the unit interval onto itself whose inverse limit is hereditarily indecomposable? This question naturally leads to the broader problem of determining what sort of continua may be obtained by taking the inverse limit of a single map on the unit interval. A very limited number of answers to this problem will be found in Chapter IV, chiefly dealing with how to obtain indecomposable continua. Chapter V gives some examples to show why Chapter IV contains very little in the way of theorems characterizing the inverse limits by means of reasonable properties of the map. Some examples are also given of continua which may be obtained. A complete answer is given in Chapter III to the question of what may be obtained as the inverse limit of a sequence of functions on the unit interval. The answer is complete since it is that every compact chainable continuum may be so obtained, and only such continua may be obtained. The question of which compact chainable continuum one will get with a given sequence of maps is not answered. The study of inverse limits has developed in two principal directions. The first direction is abstract homology theory, which is the source of the concept. This direction will not be considered. The second direction is apparently an outgrowth of the first. It consists of giving examples of unusual continua conveniently generated as inverse limits and the study of the properties used in generating the examples

Numerical modeling of buoyant plumes in a turbulent, stratified atmosphere

A widely applicable computational model of buoyant, bent-over plumes in realistic atmospheres is constructed. To do this, the two-dimensional, time-dependent fluid mechanics equations are numerically integrated, while a number of important physical approximations serve to keep the approach at a tractable level. A three-dimensional picture of a steady state plume is constructed from a se- quence of time-dependent, two-dimensional plume cross sec- tions--each cross section of the sequence is spaced pro- gressively further downwind as it is advected for a pro- gressively longer time by the prevailing wind. The dyna- mics of the plume simulations are quite general. The buoyancy sources in the plume include the sensible heat in the plume, the latent heat absorbed or released in plume moisture processes, and the heating of the plume by a radioactive pollutant in the plume. The atmospheric state in the simulations is also quite general. Atmospheric variables are allowed to be functions of height, and the ambient atmospheric turbulence (also a function of height) is included in the simulations. A demonstration of the ability of the model to repro- duce the solutions to problems that are known is under- taken. Comparisons to buoyant line-thermal laboratory experiments show that the model calculates the dynamics of the fluid motions to an acceptable accuracy. Comparisons to atmospheric plume rise and dispersion experiments show that the model can simulate individual plumes more accur- ately than existing correlations because it calculates the effect of the atmospheric turbulence and stratification from first-principles. The comparisons also show that improvements to the model are likely to be made by more accurately describing the anisotropic nature of atmospheric turbulence, and the production of turbulence by the sources of buoyancy.Sponsored by the Consolidated Edison Company of New York and Northeast Utilities Service Corporation

Quantum Entanglement and Order Parameter in a Paired Finite Fermi System

We study the pairing correlations in a finite Fermi system from quantum entanglement point of view. We investigate the relation between the order parameter, which has been introduced recently to describe both finite and infinite superconductors, and the concurrence. For a proper definition of the concurrence, we argue that a possible generalization of spin flip transformation is time reversal operation. While for a system with indefinite number of particles concurrence is a good measure of entanglement, for a finite system it does not distinguish between normal and superconducting states. We propose that the expectation value of the radial operator for the total pseudospin can be used to identify entanglement of pairing.Comment: submitted to Solid State Communications (the Festschrift in the honor of Prof. Salim Ciraci's 60th birthday

Secure quantum key distribution using squeezed states

We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor e^r=1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.Comment: 19 pages, 3 figures, RevTeX and epsf, new section on channel losse

The Mach-Zehnder and the Teleporter

We suggest a self-testing teleportation configuration for photon q-bits based on a Mach-Zehnder interferometer. That is, Bob can tell how well the input state has been teleported without knowing what that input state was. One could imagine building a "locked" teleporter based on this configuration. The analysis is performed for continuous variable teleportation but the arrangement could equally be applied to discrete manipulations.Comment: 4 pages, 5 figure

Interconvertibility of single-rail optical qubits

We show how to convert between partially coherent superpositions of a single photon with the vacuum using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input can improve the generalized efficiency.Comment: 3 pages, 2 figure

A Strategy for Nuclear Energy Research and Development

The United States is facing unprecedented challenges in climate change and energy security. President-elect Obama has called for a reduction of CO2 emissions to 1990 levels by 2020, with a further 80% reduction by 2050. Meeting these aggressive goals while gradually increasing the overall energy supply requires that all non-emitting technologies must be advanced. The development and deployment of nuclear energy can, in fact, help the United States meet several key challenges: 1) Increase the electricity generated by non-emitting sources to mitigate climate change, 2) Foster the safe and proliferation-resistant use of nuclear energy throughout the world, 3) Reduce the transportation sector’s dependence on imported fossil fuels, and 4) Reduce the demand on natural gas for process heat and hydrogen production. However, because of the scale, cost, and time horizons involved, increasing nuclear energy’s share will require a coordinated research effort—combining the efforts of industry and government, supported by innovation from the research community. This report outlines the significant nuclear energy research and development (R&D) necessary to create options that will allow government and industrial decision-makers to set policies and create nuclear energy initiatives that are decisive and sustainable. The nuclear energy R&D strategy described in this report adopts the following vision: Safe and economical nuclear energy in the United States will expand to address future electric and non-electric needs, significantly reduce greenhouse gas emissions and provide energy diversity, while providing leadership for safe, secure and responsible expansion of nuclear energy internationally

Quantum Cryptography without Switching

We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.Comment: 4 pages, 4 figures, Submitte

Quantum cryptography with a predetermined key, using continuous variable Einstein-Podolsky-Rosen correlations

Correlations of the type discussed by EPR in their original 1935 paradox for continuous variables exist for the quadrature phase amplitudes of two spatially separated fields. These correlations were experimentally reported in 1992. We propose to use such EPR beams in quantum cryptography, to transmit with high efficiency messages in such a way that the receiver and sender may later determine whether eavesdropping has occurred. The merit of the new proposal is in the possibility of transmitting a reasonably secure yet predetermined key. This would allow relay of a cryptographic key over long distances in the presence of lossy channels.Comment: 11 pages,3 figures, changes are important,presented at QELS(May,2000) San Francisc