We study the persistence of Poincaré Treshchev tori on a resonant surface of a nearly integrable Hamiltonian system in which the unperturbed Hamiltonian needs not satisfy the Kolmogorov non-degenerate condition. The persistence of the majority of invariant tori associated to g-nondegenerate relative equilibria on the resonant surface will be shown under a Rüssmann like condition.

We experimentally demonstrate the first remote state preparation of arbitrary single-qubit states, encoded in the polarization of photons generated by spontaneous parametric down-conversion. Utilizing degenerate and nondegenerate wavelength entangled sources, we remotely prepare arbitrary states at two wavelengths. Further, we derive theoretical bounds on the states that may be remotely prepare...

— We perform the exact numerical diagonalization of the Hamiltonians that describe both degenerate and nondegenerate parametric amplifiers, by exploiting the conservation laws pertaining each device. We clarify the conditions under which the parametric approximation holds, showing that the most relevant requirement is the coherence of the pump after the interaction, rather than its undepletion.

The outermost layers of some neutron stars are likely to be dominated by hydrogen, as a result of fast gravitational settling of heavier elements. These layers directly mediate thermal radiation from the stars, and determine the characteristics of X-ray/EUV spectra. For a neutron star with surface temperature T <∼ 10 K and magnetic field B >∼ 10 G, various forms of hydrogen can be present in th...

In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of nondegenerate developable triangular patches are provided.

Abstract We explore the optical response of a multimode optomechanical system with quadratic coupling to weak probe field, where cavity is driven by strong control field and two movable membranes are, respectively, excited coherent mechanical driving fields. study cases that are degenerate nondegenerate. For case, it shown only one transparency window occurs transition between optomechanically ...

We study the solvability in Sobolev spaces of boundary value problems for elliptic and parabolic equations with variable coefficients presence an involution (involutive deviation) at higher derivatives, both nondegenerate degenerate cases. For under study, we prove existence theorems as well uniqueness regular solutions, i.e., those that have all weak derivatives equation.

This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress–energy tensor in its contravariant and mixed forms. We solve MC equations two cases: when energy–momentum is nondegenerate degenerate. For case a degenerate tensor, we employ direct integration technique to equations, which leads an infinite-dimensional Lie algebra. On other hand, form ...