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On a Z(3)-graded generalization of the Witten index
No full textWe construct a realization of the algebra of the Z(3)-graded topological symmetry of type (1, 1, 1) in terms of a pair of operators D-1 : H-1 --> H-2, D-2 : H-2 --> H-3 satisfying [D1D1dagger, (D2D2)-D-dagger] = 0. We show that the sequence of the restriction of these operators to the zero-energy subspace forms a complex and establish the equality of the corresponding topological invariants with the analytic indices of these operators. (C) 2002 Published by Elsevier Science B.V
Differential realization of pseudo-Hermiticity: a quantum mechanical analog of Einstein's field equation
No full textFor a given pseudo-Hermitian Hamiltonian of the standard form: H=p(2)/2m+v(x), we reduce the problem of finding the most general (pseudo-)metric operator eta satisfying H(dagger)=eta H eta(-1) to the solution of a differential equation. If the configuration space is R, this is a Klein-Gordon equation with a nonconstant mass term. We obtain a general series solution of this equation that involves a pair of arbitrary functions. These characterize the arbitrariness in the choice of eta. We apply our general results to calculate eta for the PT-symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials. For the first two systems, our method reproduces the known results in a straightforward and extremely efficient manner. For all these systems we obtain the most general eta up to second-order terms in the coupling constants
Quantum mechanics of Proca fields
No full textWe construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries
Base-rate information in consumer attributions of product-harm crises
No full textConsumers spontaneously construct attributions for negative events such as product-harm crises. Base-rate information influences these attributions. The research findings suggest that for brands with positive prior beliefs, a high (vs. low) base rate of product-harm crises leads to less blame if the crisis is said to be similar to others in the industry (referred to as the "discounting effect"). However, in the absence of similarity information, a low (vs. high) base rate of crises leads to less blame toward the brand (referred to as the "subtyping effect"). For brands with negative prior beliefs, the extent of blame attributed to the brand is unaffected by the base-rate and similarity information. Importantly, the same base-rate information may have a different effect on the attribution of a subsequent crisis depending on whether discounting or subtyping occurred in the attribution of the first crisis. Consumers who discount a first crisis also tend to discount a second crisis for the same brand, whereas consumers who subtype a first crisis are unlikely to subtype again
D-region ionosphere response to the total solar eclipse of 22 July 2009 deduced from ELF-VLF tweek observations in the Indian sector
No full textObservations of tweeks with higher harmonics (n > 1) at low latitude stations Allahabad and Nainital, in the Indian sector, during the total solar eclipse on 22 July 2009, are presented. Allahabad and Nainital stations were in 100% and 85% of the totality paths. Observations suggest that about 30-40% obscuration of solar disc can lead to the tweeks occurrence which otherwise occur only in nighttime. A total of 148 tweeks at Allahabad and 20 tweeks at Nainital were recorded with some of them up to 3rd harmonics. The World Wide Lightning Location Network data indicated that tweeks observed were generated by lightning's located in the partial eclipse area of Asia-Oceania region. The changes in D-region ionospheric VLF reflection height and electron density (similar to 22-23 cm(-3)) during eclipse have been estimated from the first cut-off frequency of the tweeks. The reflection height increased from similar to 89 km from the first occurrence of tweek to about 91-92 km at the totality and then decreased to similar to 87 km at the end of the eclipse, suggesting a change of about 5 km in the reflection height during eclipse. The reflection heights are lower by 2-3 km as compared to normal nighttime tweek reflection heights. The above increase in the reflection height indicate that the partial nighttime condition is created during eclipse, as the main D-region ionizing radiation Lyman alpha is blocked but solar soft X-ray and EUV radiations originating from the limb solar corona are not totally blocked which produce some of ionization in the D-region
Sensitivity enhancement of bimaterial MOEMS thermal imaging sensor array using 2-lambda readout
No full textDiffraction gratings integrated with MEMS sensors offer sensitive displacement measurements. However, the sensitivity of the interferometric readout may drop significantly based on the sensor position. A two wavelength readout method was developed and tested previously in order to maintain the sensitivity of the readout > %50 maximum sensitivity over a broad range (i.e. several um's for visible wavelengths). This work demonstrates the sensitivity enhancement of a MEMS thermal imaging sensor array. Measurement of the target scene was performed using two lasers at different wavelengths (633, 650 nm). The diffracted 1(st) order light from the array was imaged onto a single CCD camera for both sources. The target scene was reconstructed by observing the change in the 1(st) diffracted order diffraction intensity for both wavelengths. Merging of the data, acquired with two different sources, is performed by assigning each pixel in the final image with the higher sensitivity pixel among two measurements. > 30% increase in the average sensitivity was demonstrated for the sensor array
Microlens array-based exit pupil expander for full color display applications
No full textRetinal Scanning Display (RSD) is a near-to-eye scanned beam display technology. An exit pupil expander (EPE) or numerical aperture (NA) expander is used in RSDs to create a large display exit pupil. A novel EPE approach that uses two microlens arrays (MLA) is presented in this paper. The approach is based on cascading two identical microlens arrays spaced precisely at one focal length distance with sub-micron registration tolerances relative to each other. We demonstrated a dual MLA based EPE that: produced excellent exit pupil uniformity and better than 90% diffraction efficiency for all three wavelengths in a color display system. Registration was performed with sub-micron precision using farfield alignment techniques. Both numerical and experimental results are presented, and three fabrication technologies: grayscale lithography, photoresist reflow, and isotropic etching, are compared
Zero-phonon-line emission of single molecules for applications in quantum information processing
No full textA single photon source which generates transform limited single photons is highly desirable for applications in quantum optics. Transform limited emission guarantees the indistinguishability of the emitted single photons. This, in turn brings groundbreaking applications in linear optics quantum information processing within an experimental reach. Recently, self-assembled InAs quantum dots and trapped atoms have successfully been demonstrated as such sources for highly indistinguishable single photons. Here, we demonstrate that nearly transform limited zero-phonon-line (ZPL) emission from single molecules can be obtained by using vibronic excitation. Furthermore we report the results of coincidence detection experiments at the output of a Michelson-type interferometer. These experiments reveal Hong-Ou-Mandel correlations as a proof of the indistinguishability of the single photons emitted consecutively from a single molecule. Therefore, single molecules constitute an attractive alternative to single InAs quantum dots and trapped atoms for applications in linear optics quantum information processing. Experiments were performed with a home-built confocal microscope keeping the sample in a superfluid liquid Helium bath at 1.4K. We investigated terrylenediimide (TDI) molecules highly diluted in hexadecane (Shpol'skii matrix). A continuous wave single mode dye laser was used for excitation of vibronic transitions of individual molecules. From the integral fluorescence, the ZPL of single molecules was selected with a spectrally narrow interference filter. The ZPL emission was then sent to a scanning Fabry-Perot interferometer for linewidth measurements or a Michelson-type interferometer for coincidence detection
Coherence lifetimes of excitations in an atomic condensate due to the thin spectrum
No full textWe study the quantum coherence properties of a finite sized atomic condensate using a toy model and the thin spectrum model formalism. The decoherence time for a condensate in the ground state, nominally taken as a variational symmetry breaking state, is investigated for both zero and finite temperatures. We also consider the lifetimes for Bogoliubov quasiparticle excitations, and contrast them to the observable window determined by the ground-state coherence time. The lifetimes are shown to exhibit a general characteristic dependence on the temperature, determined by the thin spectrum accompanying the spontaneous symmetry breaking ground state
Decoherence in two-dimensional quantum random walks with traps
No full textQuantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical transition is examined as a function of the density of the traps. It is shown that traps act as a serious and additional source of quantum decoherence. Furthermore, nontrivial temporal dependence of the standard deviation of the probability distribution of the walker is found when the trapping imperfections are introduced