Matching Conditions on Capillary Ripples: Polarization

The matching conditions at the interface between two non-mixed fluids at rest are obtained directly using the equation of movement of the whole media. This is a non-usual point of view in hydrodynamics courses and our aim is to fix ideas about the intrinsic information contained in the matching conditions, on fluids in this case. Afterward, it is analyzed the polarization of the normal modes at the interface and it is shown that this information can be achieved through a physical analysis and reinforced later by the matching conditions. A detailed analysis of the matching conditions is given to understand the role that plays the continuity of the stress tensor through the interface on the physics of the surface particle movement. The main importance of the viscosity of each medium is deduced.Comment: 5 pages, two columns, 1 .ps figure. Submitted to Rev. Mex. Fisic

Heisenberg uniqueness pairs and the Klein-Gordon equation

The notion of a Heisenberg Uniqueness Pair (HUP) is introduced. This amounts to asking which collections of exponentials are weak-star fundamental in $L^\infty$ on a planar curve. In the case when the curve is a hyperbola, we can give a complete answer if the frequencies are restricted to equally spaced points on a lattice-cross. As a consequence, we solve a problem on the density of algebras generated by two inner functions raised by Matheson and Stessin.Comment: 16 page

The ionization equilibrium of iron in H II regions

We study the ionization equilibrium of Fe using photoionization models that incorporate improved values for the ionization and recombination cross-sections and the charge-exchange rates for the Fe ions. The previously available photoionization models predict concentrations of Fe3+ which are a factor of 3-8 higher than the values inferred from emission lines of [Fe III] and [Fe IV]. Our new models reduce these discrepancies to factors of 2-5. We discuss the possible reasons behind the remaining discrepancies and present an updated ionization correction factor for obtaining the Fe abundance from the Fe++ abundance.Comment: 4 pages, 1 figure, extended version of the paper to be published in "Recycling intergalactic and interstellar matter", IAU Symposium Series, Vol. 217, 2004, P.-A. Duc, J. Braine and E. Brinks, ed

The photon magnetic moment has not a perpendicular component and is fully paramagnetic

Our paper Phys. Rev. D \textbf{79}, 093002 (2009), in which it was shown the paramagnetic behavior of photons propagating in magnetized vacuum, is criticized in Phys. Rev. D \textbf{81}, 105019, (2010) and even claimed that the photon has a diamagnetic component. Here it is shown that such criticism is inadequate and that the alleged "perpendicular component" is due to a mistake in differentiating a vanishing term with regard to the magnetic field $B$, or either by mistaking the derivative of a scalar product as that of a dyadic product. A discussion on the physical side of the problem is also made

Is the photon paramagnetic?

A photon exhibits a tiny anomalous magnetic moment $\mu_{\gamma}$ due to its interaction with an external constant magnetic field in vacuum through the virtual electron-positron background. It is paramagnetic ($\mu_{\gamma}>0$) in the whole region of transparency, i.e. below the first threshold energy for pair creation and has a maximum near this threshold. The photon magnetic moment is different for eigenmodes polarized along and perpendicular to the magnetic field. Explicit expressions are given for $\mu_{\gamma}$ for the cases of photon energies smaller and closer to the first pair creation threshold. The region beyond the first threshold is briefly discussed

Vacuum pressures and energy in a strong magnetic field

We study vacuum in a strong magnetic field. It shows a nonlinear response, as a ferromagnetic medium. Anisotropic pressures arise, and a negative pressure is exerted in the direction perpendicular to the field. The analogy of this effect with the Casimir effect is analyzed. The vacuum transverse pressure is found to be of the same order of the statistical pressure for $B\sim10^{15}G$ and $N\sim10^{33}electrons/cm^{3}$. Vacuum interaction with the field is studied also for $B\sim10^{16}G$ and larger, including the electron anomalous magnetic moment. We estimate quark contribution to vacuum behavior.Comment: Presented in the International Workshop on Strong Magnetic Fields and Neutron Stars, Havana, Cuba, April 200

Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment

We start from the analytical expression of the eigenvalues $\kappa^{(i)}$ of the photon self-energy tensor in an external constant magnetic field $B$ calculated by Batalin Shabad in the Furry representation, and in the one-loop approximation. We expand in power series of the external field and in terms of the squared photon transverse momentum $z_2$ and (minus) transverse energy $z_1=k^2-z_2$, in terms of which are expressed $\kappa^{(i)}$. A general expression is given for the photon anomalous magnetic moment $\mu_{\gamma}>0$ in the region of transparency, below the first threshold for pair creation, and it is shown that it is positive, i.e. paramagnetic. The results of the numerical calculation for $\mu_{\gamma}>0$ are displayed in a region close to the threshold

Magnetic Fields in Quantum Degenerate Systems and in Vacuum

We consider self-magnetization of charged and neutral vector bosons bearing a magnetic moment in a gas and in vacuum. For charged vector bosons (W bosons) a divergence of the magnetization in both the medium and the electroweak vacuum occurs for the critical field B=B_{wc}=m_{w}^{2}/e. For B>B_{wc} the system is unstable. This behavior suggests the occurrence of a phase transition at B=B_{c}, where the field is self-consistently maintained. This mechanism actually prevents $B$ from reaching the critical value B_{c}. For virtual neutral vector bosons bearing an anomalous magnetic moment, the ground state has a similar behavior for B=B_{nbc}=m_{nb}^{2}/q . The magnetization in the medium is associated to a Bose-Einstein condensate and we conjecture a similar condensate occurs also in the case of vacuum. The model is applied to virtual electron-positron pairs bosonization in a magnetic field B \sim B_{pc}\lesssim 2m_{e}^{2}/e, where m_e is the electron mass. This would lead also to vacuum self-magnetization in QED, where in both cases the symmetry breaking is due to a condensate of quasi-massless particles

Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the fermion-antifermion gas is studied. The connection between Faraday Effect and Quantum Hall Effect (QHE) is discussed. The Faraday Effect is also investigated for a massless relativistic (2D+1)-dimensional fermion system which is derived by using the compactification along the dimension parallel to the magnetic field. The Faraday angle shows a quantized behavior as Hall conductivity in two and three dimensions.Comment: 15 pages, 5 figure

Quantum Walks with Gremlin

A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the sampling of the probability distribution generated from the quantum wavefunction. Simple quantum walks are studied analytically, but for large graph structures with complex topologies, numerical solutions are typically required. For the quantum theorist, the Gremlin graph traversal machine and language can be used for the numerical analysis of quantum walks on such structures. Additionally, for the graph theorist, the adoption of quantum walk principles can transform what are currently side-effect laden traversals into pure, stateless functional flows. This is true even when the constraints of quantum mechanics are not fully respected (e.g. reversible and unitary evolution). In sum, Gremlin allows both types of theorist to leverage each other's constructs for the advancement of their respective disciplines.Comment: GraphDay '16, 1(1), pages 1-16, Austin Texas, January 201