Filtering bases and cohomology of nilpotent subalgebras of the Witt algebra and the algebra of loops in sl 2

We study the cohomology with trivial coefficients of the Lie algebras L k, k ≥ 1, of polynomial vector fields with zero k-jet on the circle and the cohomology of similar subalgebras ℒk of the algebra of polynomial loops with values in sl 2 The main result is a construction of special bases in the exterior complexes of these algebras. Using this construction, we obtain the following results. We calculate the cohomology of L k and ℒL. We obtain formulas in terms of Schur polynomials for cycles representing the homology of these algebras. We introduce "stable” filtrations of the exterior complexes of L k and ℒk, thus generalizing Goncharova's notion of stable cycles for L k, and give a polynomial description of these filtrations. We find the spectral resolutions of the Laplace operators for L 1 and ℒ

Lead telluride bonding and segmentation study Semiannual phase report, Aug. 1, 1967 - Jan. 31, 1968

Constitutional studies of SnTe and Si-Ge metal systems, segmented Si-Ge-PdTe thermocouple efficiencies, and pore migration in PbSnTe thermoelement

Quantum Fidelity Decay of Quasi-Integrable Systems

We show, via numerical simulations, that the fidelity decay behavior of quasi-integrable systems is strongly dependent on the location of the initial coherent state with respect to the underlying classical phase space. In parallel to classical fidelity, the quantum fidelity generally exhibits Gaussian decay when the perturbation affects the frequency of periodic phase space orbits and power-law decay when the perturbation changes the shape of the orbits. For both behaviors the decay rate also depends on initial state location. The spectrum of the initial states in the eigenbasis of the system reflects the different fidelity decay behaviors. In addition, states with initial Gaussian decay exhibit a stage of exponential decay for strong perturbations. This elicits a surprising phenomenon: a strong perturbation can induce a higher fidelity than a weak perturbation of the same type.Comment: 11 pages, 11 figures, to be published Phys. Rev.

Template-based Gravitational-Wave Echoes Search Using Bayesian Model Selection

The ringdown of the gravitational-wave signal from a merger of two black holes has been suggested as a probe of the structure of the remnant compact object, which may be more exotic than a black hole. It has been pointed out that there will be a train of echoes in the late-time ringdown stage for different types of exotic compact objects. In this paper, we present a template-based search methodology using Bayesian statistics to search for echoes of gravitational waves. Evidence for the presence or absence of echoes in gravitational-wave events can be established by performing Bayesian model selection. The Occam factor in Bayesian model selection will automatically penalize the more complicated model that echoes are present in gravitational-wave strain data because of its higher degree of freedom to fit the data. We find that the search methodology was able to identify gravitational-wave echoes with Abedi et al.'s echoes waveform model about 82.3% of the time in simulated Gaussian noise in the Advanced LIGO and Virgo network and about 61.1% of the time in real noise in the first observing run of Advanced LIGO with $\geq 5\sigma$ significance. Analyses using this method are performed on the data of Advanced LIGO's first observing run, and we find no statistical significant evidence for the detection of gravitational-wave echoes. In particular, we find $<1\sigma$ combined evidence of the three events in Advanced LIGO's first observing run. The analysis technique developed in this paper is independent of the waveform model used, and can be used with different parametrized echoes waveform models to provide more realistic evidence of the existence of echoes from exotic compact objects.Comment: 16 pages, 6 figure

Quarks, Gluons and Frustrated Antiferromagnets

The Contractor Renormalization Group method (CORE) is used to establish the equivalence of various Hamiltonian free fermion theories and a class of generalized frustrated antiferromagnets. In particular, after a detailed discussion of a simple example, it is argued that a generalized frustrated SU(3) antiferromagnet whose single-site states have the quantum numbers of mesons and baryons is equivalent to a theory of free massless quarks. Furthermore, it is argued that for slight modification of the couplings which define the frustrated antiferromagnet Hamiltonian, the theory becomes a theory of quarks interacting with color gauge-fields.Comment: 21 pages, Late

Fidelity Decay as an Efficient Indicator of Quantum Chaos

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For random eigenvector statistics the decay is exponential with a rate fixed precisely by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction and discussion

Thermionic research program, volume I Final report

Design, fabrication, calibration, instrumentation, and operation of test converter to generate parameters in thermionic converter operatio

Replace Hand Washing with Use of a Waterless Alcohol Hand Rub?

Hand hygiene is one of the basic components of any infection control program and is frequently considered synonymous with hand washing. However, health care workers frequently do not wash their hands, and compliance rarely exceeds 40%. Hand rubbing with a waterless, alcohol-based rub-in cleanser is commonly used in many European countries instead of hand washing. Scientific evidence and ease of use support employment of a hand rub for routine hand hygiene. It is microbiologically more effective in vitro and in vivo, it saves time, and preliminary data demonstrate better compliance than with hand washing. Therefore, a task force comprising experts from the Centers for Disease Control and Prevention and from professional societies is designing guidelines for the use of a hand rub in the United States. Today, most countries of Northern Europe recommend a hand rub for hand hygiene unless the hands are visibly soiled. Side effects are rare and are mainly related to dryness of the skin. This review evaluates the scientific and clinical evidence that support the use of alcohol-based hand rubs in health care facilities as a new option for hand hygien