Airy functions over local fields

Airy integrals are very classical but in recent years they have been generalized to higher dimensions and these generalizations have proved to be very useful in studying the topology of the moduli spaces of curves. We study a natural generalization of these integrals when the ground field is a non-archimedean local field such as the field of p-adic numbers. We prove that the p-adic Airy integrals are locally constant functions of moderate growth and present evidence that the Airy integrals associated to compact p-adic Lie groups also have these properties.Comment: Minor change

Anomalous conductance oscillations and half-metallicity in atomic Ag-O chains

Using spin density functional theory we study the electronic and magnetic properties of atomically thin, suspended chains containing silver and oxygen atoms in an alternating sequence. Chains longer than 4 atoms develop a half-metallic ground state implying fully spin polarized charge carriers. The conductances of the chains exhibit weak even-odd oscillations around an anomalously low value of 0.1G_0 (G_0 = 2e^2h) which coincide with the averaged experimental conductance in the long chain limit. The unusual conductance properties are explained in terms of a resonating-chain model which takes the reflection probability and phase-shift of a single bulk-chain interface as the only input. The model also explains the conductance oscillations for other metallic chains.Comment: 5 pages, 4 figure

Effect of spatial resolution on the estimates of the coherence length of excitons in quantum wells

We evaluate the effect of diffraction-limited resolution of the optical system on the estimates of the coherence length of 2D excitons deduced from the interferometric study of the exciton emission. The results are applied for refining our earlier estimates of the coherence length of a cold gas of indirect excitons in coupled quantum wells [S. Yang et al., Phys. Rev. Lett. 97, 187402(2006)]. We show that the apparent coherence length is well approximated by the quadratic sum of the actual exciton coherence length and the diffraction correction given by the conventional Abbe limit divided by 3.14. In practice, accounting for diffraction is necessary only when the coherence length is smaller than about one wavelength. The earlier conclusions regarding the strong enhancement of the exciton coherence length at low temperatures remain intact.Comment: 6 pages, 5 figure

Arago (1810): the first experimental result against the ether

95 years before Special Relativity was born, Arago attempted to detect the absolute motion of the Earth by measuring the deflection of starlight passing through a prism fixed to the Earth. The null result of this experiment gave rise to the Fresnel's hypothesis of an ether partly dragged by a moving substance. In the context of Einstein's Relativity, the sole frame which is privileged in Arago's experiment is the proper frame of the prism, and the null result only says that Snell's law is valid in that frame. We revisit the history of this premature first evidence against the ether theory and calculate the Fresnel's dragging coefficient by applying the Huygens' construction in the frame of the prism. We expose the dissimilar treatment received by the ray and the wave front as an unavoidable consequence of the classical notions of space and time.Comment: 16 pages. To appear in European Journal of Physic

Rainbow scattering in the gravitational field of a compact object

We study the elastic scattering of a planar wave in the curved spacetime of a compact object such as a neutron star, via a heuristic model: a scalar field impinging upon a spherically symmetric uniform density star of radius R and mass M. For R<rc, there is a divergence in the deflection function at the light-ring radius rc ¼ 3GM=c2, which leads to spiral scattering (orbiting) and a backward glory; whereas for R>rc, there instead arises a stationary point in the deflection function which creates a caustic and rainbow scattering. As in nuclear rainbow scattering, there is an Airy-type oscillation on a Rutherford-like cross section, followed by a shadow zone. We show that, for R ∼ 3.5GM=c2, the rainbow angle lies close to 180°, and thus there arises enhanced backscattering and glory. We explore possible implications for gravitational wave astronomy and dark matter models

An investigation of uniform expansions of large order Bessel functions in Gravitational Wave Signals from Pulsars

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be valid in the entire range of the argument

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are suggested. Using the algorithm, the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases discussed, the hybrid model is more than 10 times faster than just using the ESBI method, and it is also much faster than other methods reported in the literature