On Geometric Phase from Pure Projections

The geometric phase is usually treated as a quantity modulo 2\pi, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question the usefulness of such a definition of the geometric phase in that it throws away useful and measurable information about the system, for example strengths of singularities giving rise to the geometric phase. Such singularities have been directly demonstrated by phase-shift measurement in interference experiments. In this paper, two recent polarization experiments (Hariharan et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43 (1996)p.165) are analysed and compared with previous experiments and potentially detectible singularities in these experiments pointed out.Comment: Latex, 15 pages, 6 figures; ([email protected]

Observable Dirac-type singularities in Berry's phase and the monopole

The physical reality and observability of 2n\pi Berry phases, as opposed to the usually considered modulo 2\pi topological phases is demonstrated with the help of computer simulation of a model adiabatic evolution whose parameters are varied along a closed loop in the parameter space. Using the analogy of Berry's phase with the Dirac monopole, it is concluded that an interferometer loop taken around a magnetic monopole of strength n/2 yields an observable 2n\pi phase shift, where n is an integer. An experiment to observe the effect is proposed.Comment: 12 pages Latex, 3 postscript figures; submitted to Physical Review Letters 15 September 2000; revised 19 November 200

The physiological effects of Transcranial Electrical Stimulation do not apply to parameters commonly used in studies of Cognitive Neuromodulation

Transcranial direct current stimulation (tDCS) and transcranial random noise stimulation (tRNS) have been claimed to produce many remarkable enhancements in perception, cognition, learning and numerous clinical conditions. The physiological basis of the claims for tDCS rests on the finding that 1 mA of unilateral anodal stimulation increases cortical excitation and 1 mA of cathodal produces inhibition. Here we show that these classic excitatory and inhibitory effects do not hold for the bilateral stimulation or 2 mA intensity conditions favoured in cognitive enhancement experiments. This is important because many, including some of the most salient claims are based on experiments using 2 mA bilateral stimulation. The claims for tRNS are also based on unilateral stimulation. Here we show that, again the classic excitatory effects of unilateral tRNS do not extend to the bilateral stimulation preferred in enhancement experiments. Further, we show that the effects of unilateral tRNS do not hold when one merely doubles the stimulation duration. We are forced to two conclusions: (i) that even if all the data on TES enhancements are true, the physiological explanations on which the claims are based are at best not established but at worst false, and (ii) that we cannot explain, scientifically at least, how so many experiments can have obtained data consistent with physiological effects that may not exist

Topological properties of Berry's phase

By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval $T$. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born-Oppenheimer approximation, where a large but finite ratio of two time scales is involved.Comment: 9 pages. A new reference was added, and the abstract and the presentation in the body of the paper have been expanded and made more precis

The physiological effects of transcranial electrical stimulation do not apply to parameters commonly used in studies of cognitive neuromodulation

Transcranial direct current stimulation (tDCS) and transcranial random noise stimulation (tRNS) have been claimed to produce many remarkable enhancements in perception, cognition, learning and numerous clinical conditions. The physiological basis of the claims for tDCS rests on the finding that 1 mA of unilateral anodal stimulation increases cortical excitation and 1 mA of cathodal produces inhibition. Here we show that these classic excitatory and inhibitory effects do not hold for the bilateral stimulation or 2 mA intensity conditions favoured in cognitive enhancement experiments. This is important because many, including some of the most salient claims are based on experiments using 2 mA bilateral stimulation. The claims for tRNS are also based on unilateral stimulation. Here we show that, again the classic excitatory effects of unilateral tRNS do not extend to the bilateral stimulation preferred in enhancement experiments. Further, we show that the effects of unilateral tRNS do not hold when one merely doubles the stimulation duration. We are forced to two conclusions: (i) that even if all the data on TES enhancements are true, the physiological explanations on which the claims are based are at best not established but at worst false, and (ii) that we cannot explain, scientifically at least, how so many experiments can have obtained data consistent with physiological effects that may not exist

The Geometric Phase and Ray Space Isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy

Tackling 3D ToF Artifacts Through Learning and the FLAT Dataset

Scene motion, multiple reflections, and sensor noise introduce artifacts in the depth reconstruction performed by time-of-flight cameras. We propose a two-stage, deep-learning approach to address all of these sources of artifacts simultaneously. We also introduce FLAT, a synthetic dataset of 2000 ToF measurements that capture all of these nonidealities, and allows to simulate different camera hardware. Using the Kinect 2 camera as a baseline, we show improved reconstruction errors over state-of-the-art methods, on both simulated and real data.Comment: ECCV 201

Cosmogenic effects in Mbale chondrite

This article does not have an abstract

Geometric Phases and Multiple Degeneracies in Harmonic Resonators

In a recent experiment Lauber et al. have deformed cyclically a microwave resonator and have measured the adiabatic normal-mode wavefunctions for each shape along the path of deformation. The nontrivial observed cyclic phases around a 3-fold degeneracy were accounted for by Manolopoulos and Child within an approximate theory. However, open-path geometrical phases disagree with experiment. By solving exactly the problem, we find unsuspected extra degeneracies around the multiple one that account for the measured phase changes throughout the path. It turns out that proliferation of additional degeneracies around a multiple one is a common feature of quantum mechanics.Comment: 4 pages, 4 figures. Accepted in Phys. Rev. Let

The first interferometric detections of Fast Radio Bursts

We present the first interferometric detections of Fast Radio Bursts (FRBs), an enigmatic new class of astrophysical transient. In a 180-day survey of the Southern sky we discovered 3 FRBs at 843 MHz with the UTMOST array, as part of commissioning science during a major ongoing upgrade. The wide field of view of UTMOST ($\approx 9$ deg$^{2}$) is well suited to FRB searches. The primary beam is covered by 352 partially overlapping fan-beams, each of which is searched for FRBs in real time with pulse widths in the range 0.655 to 42 ms, and dispersion measures $\leq$2000 pc cm$^{-3}$. Detections of FRBs with the UTMOST array places a lower limit on their distances of $\approx 10^4$ km (limit of the telescope near-field) supporting the case for an astronomical origin. Repeating FRBs at UTMOST or an FRB detected simultaneously with the Parkes radio telescope and UTMOST, would allow a few arcsec localisation, thereby providing an excellent means of identifying FRB host galaxies, if present. Up to 100 hours of follow-up for each FRB has been carried out with the UTMOST, with no repeating bursts seen. From the detected position, we present 3$\sigma$ error ellipses of 15 arcsec x 8.4 deg on the sky for the point of origin for the FRBs. We estimate an all-sky FRB rate at 843 MHz above a fluence $\cal F_\mathrm{lim}$ of 11 Jy ms of $\sim 78$ events sky$^{-1}$ d$^{-1}$ at the 95 percent confidence level. The measured rate of FRBs at 843 MHz is of order two times higher than we had expected, scaling from the FRB rate at the Parkes radio telescope, assuming that FRBs have a flat spectral index and a uniform distribution in Euclidean space. We examine how this can be explained by FRBs having a steeper spectral index and/or a flatter log$N$-log$\mathcal{F}$ distribution than expected for a Euclidean Universe.Comment: 13 pages, 8 figures, 2 table