Shielding and localization in presence of long range hopping

We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited states can be induced, which is mathematically equivalent to the superconducting gap. In the gapped regime, the dynamics within the excited states subspace is shielded from long range hopping, namely it occurs as if long range hopping would be absent. This is a cooperative phenomenon since shielding is effective over a time scale which diverges with the system size. We named this effect {\it Cooperative Shielding}. We also discuss the consequences of our findings on Anderson localization. Long range hopping is usually thought to destroy localization due to the fact that it induces an infinite number of resonances. Contrary to this common lore we show that the excited states display strong localized features when shielding is effective even in the regime of strong long range coupling. A brief discussion on the extension of our results to generic power-law decaying long range hopping is also given. Our preliminary results confirms that the effects found for the infinite range case are generic.Comment: 7 pages, 9 figur

Multimodal imaging of human brain activity: rational, biophysical aspects and modes of integration

Until relatively recently the vast majority of imaging and electrophysiological studies of human brain activity have relied on single-modality measurements usually correlated with readily observable or experimentally modified behavioural or brain state patterns. Multi-modal imaging is the concept of bringing together observations or measurements from different instruments. We discuss the aims of multi-modal imaging and the ways in which it can be accomplished using representative applications. Given the importance of haemodynamic and electrophysiological signals in current multi-modal imaging applications, we also review some of the basic physiology relevant to understanding their relationship

Electromagnetic inertia, reactive energy, and energy flow velocity

In a recent paper titled "Coherent electromagnetic wavelets and their twisting null congruences," I defined the local inertia density (I), reactive energy density (R), and energy flow velocity (v) of an electromagnetic field. These are the field equivalents of the mass, rest energy, and velocity of a relativistic particle. Thus R and I are Lorentz-invariant and |v|<=c, with equality if and only if R=0. The exceptional fields with |v|=c were called "coherent" because their energy moves in complete harmony with the field, leaving no inertia or reactive energy behind. Generic electromagnetic fields become coherent only in the far zone. Elsewhere, their energy flows at speeds |v|<c. The purpose of this paper is to confirm and clarify this statement by studying the local energy flow in several common systems: a time-harmonic electric dipole field, a time-dependent electric dipole field, and a standing plane wave. For these fields, the energy current (Poynting vector) is too weak to carry away all of the energy, thus leaving reactive energy in its wake. For the time-dependent dipole field, we find that the energy can flow both transversally and inwards, back to the source. Neither of these phenomena show up in the usual computation of the energy transport velocity which considers only averages over one period in the time-harmonic case.Comment: 20 pages, 7 figure

Helicity, polarization, and Riemann-Silberstein vortices

Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime where the complex form of a free electromagnetic field given by F=E+iB is null (F.F=0), and they can indeed be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of "C-lines" associated with a monochromatic electric or magnetic field, which are curves in space where the polarization ellipses degenerate to circles. However, it was noted that RS vortices of monochromatic fields generally oscillate at optical frequencies and are therefore unobservable while electric and magnetic C-lines are steady. Here I show that under the additional assumption of having definite helicity, RS vortices are not only steady but they coincide with both sets of C-lines, electric and magnetic. The two concepts therefore become one for waves of definite frequency and helicity. Since the definition of RS vortices is relativistically invariant while that of C-lines is not, it may be useful to regard the vortices as a wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on Singular Optics; minor changes from v.

Radiative corrections to neutral pion-pair production

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $\pi^-\gamma \to \pi^-\pi^0\pi^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral $\pi^+\pi^-\to\pi^0\pi^0$ contact-vertex depends only on the final-state invariant-mass it factors out of all photon-loop diagrams. We give analytical expressions for the multiplicative correction factor $R\sim \alpha/2\pi$ arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. The radiative corrections to the total cross section vary between $+2\%$ and $-2\%$ for center-of-mass energies from threshold up to $7m_\pi$. The finite part of the electromagnetic counterterm gives an additional constant contribution of about $1\%$, however with a large uncertainty.Comment: 10 pages, 6 figures, submitted to Eur. Phys. J.

Optical pattern formation with a 2-level nonlinearity

We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retro-reflected laser beam passing through a cloud of cold Rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a 2-level atom, which realizes the paradigmatic situation considered in many theoretical studies of optical pattern formation. In particular, we are able to observe the disappearance of the patterns at high intensity due to the intrinsic saturable character of 2-level atomic transitions.Comment: 5 pages, 4 figure

Magnetic Field Tomography

Neutral atoms may be trapped via the interaction of their magnetic dipole moment with magnetic field gradients. One of the possible schemes is the cloverleaf trap. It is often desirable to have at hand a fast and precise technique for measuring the magnetic field distribution. We introduce a novel diagnostic tool for instantaneous imaging the equipotential lines of a magnetic field within a region of space (the vacuum recipient) that is not accessible to massive probes. Our technique is based on spatially resolved observation of the fluorescence emitted by a hot beam of sodium atoms crossing a thin slice of resonant laser light within the magnetic field region to be investigated. The inhomogeneous magnetic field spatially modulates the resonance condition between the Zeeman-shifted hyperfine sublevels and the laser light and therefore the amount of scattered photons. We demonstrate this technique by mapping the field of our cloverleaf trap in three dimensions under various conditions.Comment: 8 pages, 8 figure

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.Comment: 32 pages, 18 figure