Volume 56, Issue 5, May 2015
Index of content:
- Partial Differential Equations
56(2015); http://dx.doi.org/10.1063/1.4919670View Description Hide Description
In this paper, we establish an existence result for a quasilinear Kirchhoff equation, via a sub- and supersolution approach, by using the Minty-Browder’s Theorem for pseudomonotone operators theory.
56(2015); http://dx.doi.org/10.1063/1.4917284View Description Hide Description
We consider a spatially inhomogeneous sine-Gordon equation with a double-well potential, describing long Josephson junctions with phase-shifts. We discuss the interactions of symmetric and antisymmetric bound states in the system. Using a multiple scale expansion, we show that the modes decay algebraically in time due to the energy transfer from the discrete to the continuous spectrum. In particular, exciting the two modes at the same time yields an increased decay rate. An external time-periodic drive is shown to sustain symmetric state, while it damps the antisymmetric one.
- Quantum Mechanics
Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories56(2015); http://dx.doi.org/10.1063/1.4919546View Description Hide Description
Steering is one of the most counter intuitive non-classical features of bipartite quantum system, first noticed by Schrödinger at the early days of quantum theory. On the other hand, measurement incompatibility is another non-classical feature of quantum theory, initially pointed out by Bohr. Recently, Quintino et al. [Phys. Rev. Lett. 113, 160402 (2014)] and Uola et al. [Phys. Rev. Lett. 113, 160403 (2014)] have investigated the relation between these two distinct non-classical features. They have shown that a set of measurements is not jointly measurable (i.e., incompatible) if and only if they can be used for demonstrating Schrödinger-Einstein-Podolsky-Rosen steering. The concept of steering has been generalized for more general abstract tensor product theories rather than just Hilbert space quantum mechanics. In this article, we discuss that the notion of measurement incompatibility can be extended for general probability theories. Further, we show that the connection between steering and measurement incompatibility holds in a border class of tensor product theories rather than just quantum theory.
56(2015); http://dx.doi.org/10.1063/1.4919674View Description Hide Description
Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.
- Statistical Physics
Emergence of q-statistical functions in a generalized binomial distribution with strong correlations56(2015); http://dx.doi.org/10.1063/1.4919678View Description Hide Description
We study a symmetric generalization of the binomial distribution recently introduced by Bergeron et al., where η ∈ [0, 1] denotes the win probability and α is a positive parameter. This generalization is based on q-exponential generating functions where qgen = 1 + 1/α. The numerical calculation of the probability distribution function of the number of wins k, related to the number of realizations N, strongly approaches a discrete qdisc -Gaussian distribution, for win-loss equiprobability (i.e., η = 1/2) and all values of α. Asymptotic N → ∞ distribution is in fact a qatt -Gaussian , where qatt = 1 − 2/(α − 2) and β = (2α − 4). The behavior of the scaled quantity k/N γ is discussed as well. For γ < 1, a large-deviation-like property showing a qldl -exponential decay is found, where qldl = 1 + 1/(ηα). For η = 1/2, qldl and qatt are related through 1/(qldl − 1) + 1/(qatt − 1) = 1, ∀α. For γ = 1, the law of large numbers is violated, and we consistently study the large-deviations with respect to the probability of the N → ∞ limit distribution, yielding a power law, although not exactly a qLD -exponential decay. All q-statistical parameters which emerge are univocally defined by (η, α). Finally, we discuss the analytical connection with the Pólya urn problem.
- Methods of Mathematical Physics
56(2015); http://dx.doi.org/10.1063/1.4919544View Description Hide Description
We construct coherent states through special superpositions of eigenstates of the relativistic isotonic oscillator. In each superposition, the coefficients are chosen to be L 2-eigenfunctions of a σ-weight Maass Laplacian on the Poincaré disk, which are associated with the eigenvalue , . For each nonzero m, the associated coherent states transform constitutes the m-true-polyanalytic extension of a relativistic version of the second Bargmann transform, whose integral kernel is expressed in terms of a special Appel-Kampé de Fériet’s hypergeometric function. The obtained results could be used to extend the known semi-classical analysis of quantum dynamics of the relativistic isotonic oscillator.