1,720,970 research outputs found
Quadratic forms for the fermionic unitary gas model
No full textWe consider a quantum system in dimension three composed by a group of N identical fermions, with mass 1/2, interacting via zero-range interaction with a group of M identical fermions of a different type, with mass m/2. Exploiting a renormalization procedure, we construct the corresponding quadratic form and define the so-called Skornyakov-Ter-Martirosyan extension H α, which is the natural candidate as a possible Hamiltonian of the system. It is shown that if the form is unbounded from below then H α is not a self-adjoint and bounded from below operator, and this in particular suggests that the so-called Thomas effect could occur. In the special case N = 2, M = 1 we prove that this is in fact the case when a suitable condition on the parameter m is satisfied. © 2012 Polish Scientific Publishers
Asymptotic expansion for the wave function in a one-dimensional model of inelastic interaction
No full textWe consider a two-body quantum system in dimension one composed by a test particle interacting with a harmonic oscillator placed at the position a > 0. At time zero the test particle is concentrated around the position R(0) with average velocity+/-v(0) while the oscillator is in its ground state. In a suitable scaling limit, corresponding for the test particle to a semiclassical regime with small energy exchange with the oscillator, we give a complete asymptotic expansion of the wave function of the system in both cases R(0) a. (C) 2011 American Institute of Physics. [doi:10.1063/1.3549587
Singularly perturbed hamiltonians of a quantum Rayleigh gas defined as quadratic forms
No full textWe consider a class of singular, zero-range perturbations of the quantum Hamiltonian of a system consisting of a test particle and N harmonic oscillators (Rayleigh gas). Using the theory of quadratic forms we construct the self-adjoint and bounded from below perturbed Hamiltonian and we give representation formulas for the resolvent and the unitary group. The one-dimensional, two-dimensional and three-dimensional cases are discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
On the structure of critical energy levels for the cubic focusing NLS on star graphs
No full textWe provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with the cubic focusing Schrödinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant L2-norm. We moreover show that the only stationary state with prescribed L2-norm is indeed a saddle point
Constrained energy minimization and orbital stability for the NLS equation on a star graph
Full text linkOn a star graph script G, we consider a nonlinear Schrödinger equation with focusing nonlinearity of power type and an attractive Dirac's delta potential located at the vertex. The equation can be formally written as i∂tψ(t)= -Δψ(t) - |ψ(t)|2μψ(t) + αδ0ψ(t), where the strength α of the vertex interaction is negative and the wave function ψ is supposed to be continuous at the vertex. The values of the mass and energy functionals are conserved by the flow. We show that for 0 < μ ≤ 2 the energy at fixed mass is bounded from below and that for every mass m below a critical mass m∗ it attains its minimum value at a certain ψm ∈H1(script G). Moreover, the set of minimizers has the structure script M = {eiθψm, θ ∈ double-struck R}. Correspondingly, for every m < m∗ there exists a unique ω = ω(m) such that the standing wave ψωeiωt is orbitally stable. To prove the above results we adapt the concentration-compactness method to the case of a star graph. This is nontrivial due to the lack of translational symmetry of the set supporting the dynamics, i.e. the graph. This affects in an essential way the proof and the statement of concentration-compactness lemma and its application to minimization of constrained energy. The existence of a mass threshold comes from the instability of the system in the free (or Kirchhoff's) case, that in our setting corresponds to α =
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Variational properties and orbital stability of standing waves for NLS equation on a star graph
No full textWe study standing waves for a nonlinear Schrödinger equation on a star graph G, i.e. N halflines joined at a vertex. At the vertex an interaction occurs described by a boundary condition of delta type with strength α≤0. The nonlinearity is of focusing power type. The dynamics is given by an equation of the form iddtΨt=HΨt-|Ψt|2μΨt, where H is the Hamiltonian operator which generates the linear Schrödinger dynamics. We show the existence of several families of standing waves for every sign of the coupling at the vertex for every ω>α2N2. Furthermore, we determine the ground states, as minimizers of the action on the Nehari manifold, and order the various families. Finally, we show that the ground states are orbitally stable for every allowed ω if the nonlinearity is subcritical or critical, and for ω<ω* otherwise
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