348 research outputs found

    Studies of Breakup Mechanisms in the Reaction of E/A = 25 MeV 6-Li Ions with 232-U

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    This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

    Exploring the multi-humped fission barrier of 238U via sub-barrier photofission

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    The photofission cross-section of 238U was measured at sub-barrier energies as a function of the gamma-ray energy using, for the first time, a monochromatic, high-brilliance, Compton-backscattered gamma-ray beam. The experiment was performed at the High Intensity gamma-ray Source (HIgS) facility at beam energies between E=4.7 MeV and 6.0 MeV and with ~3% energy resolution. Indications of transmission resonances have been observed at gamma-ray beam energies of E=5.1 MeV and 5.6 MeV with moderate amplitudes. The triple-humped fission barrier parameters of 238U have been determined by fitting EMPIRE-3.1 nuclear reaction code calculations to the experimental photofission cross section.Comment: 5 pages, 3 figure

    Multiplicity of Gamma-Ray Transitions Observed in Lithium-Induced Reactions

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    This work was supported by National Science Foundation Grant PHY 76-84033 and Indiana Universit

    Bellman equations for optimal feedback control of qubit states

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    Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.Comment: 10 pages, no figures, replaced the simpler model in section

    Probabilistic programming interfaces for random graphs: Markov categories, graphons, and nominal sets

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    We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, and conversely, every graphon arises in this way. We provide three constructions for showing that every graphon arises from an equational theory. The first is an abstract construction, using Markov categories and monoidal indeterminates. The second and third are more concrete. The second is in terms of traditional measure theoretic probability, which covers ‘black-and-white’ graphons. The third is in terms of probability monads on the nominal sets of Gabbay and Pitts. Specifically, we use a variation of nominal sets induced by the theory of graphs, which covers Erdős-Rényi graphons. In this way, we build new models of graph probabilistic programming from graphons

    Spectra of soft ring graphs

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    We discuss of a ring-shaped soft quantum wire modeled by δ\delta interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the dependence of eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is investigated also in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.Comment: LaTeX 2e, 17 pages, with 10 ps figure

    Boundary Conditions for Singular Perturbations of Self-Adjoint Operators

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    Let A:D(A)\subseteq\H\to\H be an injective self-adjoint operator and let \tau:D(A)\to\X, X a Banach space, be a surjective linear map such that \|\tau\phi\|_\X\le c \|A\phi\|_\H. Supposing that \text{\rm Range} (\tau')\cap\H' =\{0\}, we define a family AΘτA^\tau_\Theta of self-adjoint operators which are extensions of the symmetric operator A∣{τ=0}.A_{|\{\tau=0\}.}. Any ϕ\phi in the operator domain D(AΘτ)D(A^\tau_\Theta) is characterized by a sort of boundary conditions on its univocally defined regular component \phireg, which belongs to the completion of D(A) w.r.t. the norm \|A\phi\|_\H. These boundary conditions are written in terms of the map τ\tau, playing the role of a trace (restriction) operator, as \tau\phireg=\Theta Q_\phi, the extension parameter Θ\Theta being a self-adjoint operator from X' to X. The self-adjoint extension is then simply defined by A^\tau_\Theta\phi:=A \phireg. The case in which Aϕ=T∗ϕA\phi=T*\phi is a convolution operator on LD, T a distribution with compact support, is studied in detail.Comment: Revised version. To appear in Operator Theory: Advances and Applications, vol. 13
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