31,526 research outputs found

    Generalized Swanson models and their solutions

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    We analyze a class of non-Hermitian quadratic Hamiltonians, which are of the form H=AA+αA2+βA2 H = {\cal{A}}^{\dagger} {\cal{A}} + \alpha {\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} , where α,β \alpha, \beta are real constants, with αβ \alpha \neq \beta , and A{\cal{A}}^{\dagger} and A{\cal{A}} are generalized creation and annihilation operators. Thus these Hamiltonians may be classified as generalized Swanson models. It is shown that the eigenenergies are real for a certain range of values of the parameters. A similarity transformation ρ\rho, mapping the non-Hermitian Hamiltonian HH to a Hermitian one hh, is also obtained. It is shown that HH and hh share identical energies. As explicit examples, the solutions of a couple of models based on the trigonometric Rosen-Morse I and the hyperbolic Rosen-Morse II type potentials are obtained. We also study the case when the non-Hermitian Hamiltonian is PT{\cal{PT}} symmetric.Comment: 17 page

    Three-dimensional flow instability in a lid-driven isosceles triangular cavity

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    Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed

    Trap Loss in a Dual-Species Rb-Ar* Magneto-Optical Trap

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    We have investigated trap loss in a dual-species magneto-optical trap (MOT) comprised of 85Rb and metastable 40Ar. We measure the trap loss rate coefficients for each species due to the presence of the other as a function of trap light intensity. We clearly identify both Penning ionization of Rb by Ar* and associative ionization to form the molecular ion RbAr+ as two of the trap loss channels. We have also measured the trap loss rate coefficient for the Ar* MOT alone and observe production of Ar+ and Ar2+ ions

    Physical Aspects of Pseudo-Hermitian and PTPT-Symmetric Quantum Mechanics

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    For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables O of the quantum mechanics based on H. In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian quantization scheme that relates the latter to the ordinary classical position and momentum observables. These allow us to address the problem of determining the conserved probability density and the underlying classical system for pseudo-Hermitian and in particular PT-symmetric quantum systems. As a concrete example we construct the Hermitian Hamiltonian h, the physical observables O, the localized states, and the conserved probability density for the non-Hermitian PT-symmetric square well. We achieve this by employing an appropriate perturbation scheme. For this system, we conduct a comprehensive study of both the kinematical and dynamical effects of the non-Hermiticity of the Hamiltonian on various physical quantities. In particular, we show that these effects are quantum mechanical in nature and diminish in the classical limit. Our results provide an objective assessment of the physical aspects of PT-symmetric quantum mechanics and clarify its relationship with both the conventional quantum mechanics and the classical mechanics.Comment: 45 pages, 13 figures, 2 table

    Choosing more mathematics : happiness through work?

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    This paper examines how A-level students construct relationships between work and happiness in their accounts of choosing mathematics and further mathematics A-level. I develop a theoretical framework that positions work and happiness as opposed, managed and working on the self and use this to examine students' dual engagement with individual practices of the self and institutional practices of school mathematics. Interviews with students acknowledge four imperatives that they use as discursive resources to position themselves as successful/unsuccessful students: you have to work, you have to not work, you have to be happy, you have to work at being happy. Tensions in these positions lead students to rework their identities or drop further mathematics. I then identify the practices of mathematics teaching that students use to explain un/happiness in work, and show how dependable mathematics and working together are constructed as 'happy objects' for students, who develop strategies for claiming control over these shapers of happiness. © 2010 British Society for Research into Learning Mathematics

    Investigation of contact edge effects in the channel of planar Gunn diodes

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    The effect of the edge of the channel on the operation of Planar Gunn diodes has been examined using Monte Carlo simulations. High fields at the corner of the anode contact are known to cause impact ionization and consequent electroluminescence, but our simulations show that the Gunn domains are attracted to these corners, perturbing the formation of the domains which can lead to chaotic dynamics within the rest of the channel leading to uneven heating and reduced RF output power. We show how novel shaping of the electrical contacts at the ends of the channel reduces the attraction and restores the domain wave-fronts for good device operation
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