The Schrodinger-like Equation for a Nonrelativistic Electron in a Photon Field of Arbitrary Intensity

The ordinary Schrodinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrodinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The "eigenvalue" in the new equation is an operator in a Cartan subalgebra. An approximation consistent with the nonrelativistic energy level derived from its relativistic value replaces the "eigenvalue" operator by an ordinary number, recovering the ordinary Schrodinger eigenvalue equation used in the formal scattering formalism. The Schrodinger-like equation for the multimode case is also presented.Comment: Tex file, 13 pages, no figur

Microscopic Approach to Shear Viscosities in Superfluid Gases: From BCS to BEC

We compute the shear viscosity, $\eta$, at general temperatures $T$, in a BCS-BEC crossover scheme which is demonstrably consistent with conservation laws. The study of $\eta$ is important because it constrains microscopic theories by revealing the excitation spectra. The onset of a normal state pairing gap and the contribution from pair degrees of freedom imply that $\eta$ at low $T$ becomes small, rather than exhibiting the upturn predicted by most others. Using the local density approximation, we find quite reasonable agreement with just-published experiments.Comment: 4 pages, 2 figure

The Euler-Lagrange Cohomology and General Volume-Preserving Systems

We briefly introduce the conception on Euler-Lagrange cohomology groups on a symplectic manifold $(\mathcal{M}^{2n}, \omega)$ and systematically present the general form of volume-preserving equations on the manifold from the cohomological point of view. It is shown that for every volume-preserving flow generated by these equations there is an important 2-form that plays the analog role with the Hamiltonian in the Hamilton mechanics. In addition, the ordinary canonical equations with Hamiltonian $H$ are included as a special case with the 2-form $\frac{1}{n-1} H \omega$. It is studied the other volume preserving systems on $({\cal M}^{2n}, \omega)$. It is also explored the relations between our approach and Feng-Shang's volume-preserving systems as well as the Nambu mechanics.Comment: Plain LaTeX, use packages amssymb and amscd, 15 pages, no figure

Almost Perfect Privacy for Additive Gaussian Privacy Filters

We study the maximal mutual information about a random variable $Y$ (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only $\epsilon$ bits of information is leaked about a random variable $X$ (representing private information) that is correlated with $Y$. Denoting this quantity by $g_\epsilon(X,Y)$, we show that for perfect privacy, i.e., $\epsilon=0$, one has $g_0(X,Y)=0$ for any pair of absolutely continuous random variables $(X,Y)$ and then derive a second-order approximation for $g_\epsilon(X,Y)$ for small $\epsilon$. This approximation is shown to be related to the strong data processing inequality for mutual information under suitable conditions on the joint distribution $P_{XY}$. Next, motivated by an operational interpretation of data privacy, we formulate the privacy-utility tradeoff in the same setup using estimation-theoretic quantities and obtain explicit bounds for this tradeoff when $\epsilon$ is sufficiently small using the approximation formula derived for $g_\epsilon(X,Y)$.Comment: 20 pages. To appear in Springer-Verla

An optical diode made from a `flying' photonic crystal

Optical diodes controlling the flow of light are of principal significance for optical information processing 1. They transmit light from an input to an output, but not in reverse direction. This breaking of time reversal symmetry is typically achieved via non-linear 2,3 or magnetic effects 4, which imposes limits to all-optical control 5-7, on-chip integration 7-11, or single-photon operation 12. Here, we propose an optical diode which requires neither magnetic fields nor strong input fields. It is based on a flying photonic crystal. Due to the Doppler effect, the crystal has a band gap with frequency depending on the light propagation direction relative to the crystal motion. Counter-intuitively, our setup does not involve the movement of any material parts. Rather, the flying photonic crystal is realized by optically inducing a spatially periodic but moving modulation of the optical properties of a near-resonant medium. The flying crystal not only opens perspectives for optical diodes operating at low light levels or integrated in small solid state devices, but also enables novel photonic devices such as optically tunable mirrors and cavities.Comment: 13 pages, 4 figures, presented in PQE 201

Topological Analysis of Emerging Bipole Clusters Producing Violent Solar Events

During the rising phase of Solar Cycle 24 tremendous activity occurred on the Sun with fast and compact emergence of magnetic flux leading to bursts of flares (C to M and even X-class). We investigate the violent events occurring in the cluster of two active regions (ARs), NOAA numbers 11121 and 11123, observed in November 2010 with instruments onboard the {\it Solar Dynamics Observatory} and from Earth. Within one day the total magnetic flux increased by $70\%$ with the emergence of new groups of bipoles in AR 11123. From all the events on 11 November, we study, in particular, the ones starting at around 07:16 UT in GOES soft X-ray data and the brightenings preceding them. A magnetic-field topological analysis indicates the presence of null points, associated separatrices and quasi-separatrix layers (QSLs) where magnetic reconnection is prone to occur. The presence of null points is confirmed by a linear and a non-linear force-free magnetic-field model. Their locations and general characteristics are similar in both modelling approaches, which supports their robustness. However, in order to explain the full extension of the analysed event brightenings, which are not restricted to the photospheric traces of the null separatrices, we compute the locations of QSLs. Based on this more complete topological analysis, we propose a scenario to explain the origin of a low-energy event preceding a filament eruption, which is accompanied by a two-ribbon flare, and a consecutive confined flare in AR 11123. The results of our topology computation can also explain the locations of flare ribbons in two other events, one preceding and one following the ones at 07:16 UT. Finally, this study provides further examples where flare-ribbon locations can be explained when compared to QSLs and only, partially, when using separatrices.Comment: 42 pages, 15 figure