Quantum tunneling in a Kerr medium with parametric pumping

A quantum optical model with a classical phase space exhibiting nonlinear oscillations around two elliptic fixed points is investigated. The quantum system is found to display coherent tunneling between near coherent states of opposite phase centered at the classical fixed points

Double-slit interference pattern from single-slit screen and its gravitational analogues

The double slit experiment (DSE) is known as an important cornerstone in the foundations of physical theories such as Quantum Mechanics and Special Relativity. A large number of different variants of it were designed and performed over the years. We perform and discuss here a new verion with the somewhat unexpected results of obtaining interference pattern from single-slit screen. This outcome, which shows that the routes of the photons through the array were changed, leads one to discuss it, using the equivalence principle, in terms of geodesics mechanics. We show using either the Brill's version of the canonical formulation of general relativity or the linearized version of it that one may find corresponding and analogous situations in the framework of general relativity.Comment: 51 pages, 12 Figures five of them contain two subfigures and thus the number of figures is 17, 1 Table. Some minor changes introduced, especially, in the reference

Wavy stripes and squares in zero P number convection

A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher mode, may lead to a competition between the two sets of wavy rolls. The appearance of square patterns is due to the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late

Alfv\'en Reflection and Reverberation in the Solar Atmosphere

Magneto-atmospheres with Alfv\'en speed [a] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A common example involves uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfv\'en speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where a(x) is analytic and unbounded present no internal reflection of harmonic Alfv\'en waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as O(t-1) or O(t-1 ln t), depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfv\'en waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.Comment: Accepted by Solar Physic

A robust spectral method for solving Heston’s model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979)