Geometric phases, gauge symmetries and ray representation

The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood as defining generalized rays in the Hilbert space is not generally consistent with the superposition principle in interference and polarization phenomena. The hidden local gauge symmetry, which arises from the arbitrariness of the choice of coordinates in the functional space, is then proposed as a basic gauge symmetry in the non-adiabatic phase. This re-formulation reproduces all the successful aspects of the non-adiabatic phase in a manner manifestly consistent with the conventional notion of rays and the superposition principle. The hidden local symmetry is thus identified as the natural origin of the gauge symmetry in both of the adiabatic and non-adiabatic phases in the absence of gauge fields, and it allows a unified treatment of all the geometric phases. The non-adiabatic phase may well be regarded as a special case of the adiabatic phase in this re-formulation, contrary to the customary understanding of the adiabatic phase as a special case of the non-adiabatic phase. Some explicit examples of geometric phases are discussed to illustrate this re-formulation.Comment: 30 pages. Some clarifying sentences have been added in abstract and in the body of the paper. A new additional reference and some typos have been corrected. To appear in Int. J. Mod. Phys.

Guest editorial: Special issue on matching under preferences

No abstract available

Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U < 0 using the density matrix renormalization group method as well as a perturbation theory. We find that the ground state is a charge density wave state with a long range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap which is the same as the four-particle excitation gap is a non-monotonic function of U, while the spin gap and others increase with increasing |U| and have linear asymptotic behaviors.Comment: 4 pages, 3 figures, submitte

Scanning SQUID microscopy of vortex clusters in multiband superconductors

In type-1.5 superconductors, vortices emerge in clusters, which grow in size with increasing magnetic field. These novel vortex clusters and their field dependence are directly visualized by scanning SQUID microscopy at very low vortex densities in MgB2 single crystals. Our observations are elucidated by simulations based on a two-gap Ginzburg-Landau theory in the type-1.5 regime.Comment: 4 pages, 5 figures, to be published in Physical Review

Hard variants of stable marriage

The Stable Marriage Problem and its many variants have been widely studied in the literature (Gusfield and Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, Cambridge, MA, 1989; Roth and Sotomayor, Two-sided matching: a study in game-theoretic modeling and analysis, Econometric Society Monographs, vol. 18, Cambridge University Press, Cambridge, 1990; Knuth, Stable Marriage and its Relation to Other Combinatorial Problems, CRM Proceedings and Lecture Notes, vol. 10, American Mathematical Society, Providence, RI, 1997), partly because of the inherent appeal of the problem, partly because of the elegance of the associated structures and algorithms, and partly because of important practical applications, such as the National Resident Matching Program (Roth, J. Political Economy 92(6) (1984) 991) and similar large-scale matching schemes. Here, we present the first comprehensive study of variants of the problem in which the preference lists of the participants are not necessarily complete and not necessarily totally ordered. We show that, under surprisingly restrictive assumptions, a number of these variants are hard, and hard to approximate. The key observation is that, in contrast to the case where preference lists are complete or strictly ordered (or both), a given problem instance may admit stable matchings of different sizes. In this setting, examples of problems that are hard are: finding a stable matching of maximum or minimum size, determining whether a given pair is stable––even if the indifference takes the form of ties on one side only, the ties are at the tails of lists, there is at most one tie per list, and each tie is of length 2; and finding, or approximating, both an `egalitarian' and a `minimum regret' stable matching. However, we give a 2-approximation algorithm for the problems of finding a stable matching of maximum or minimum size. We also discuss the significant implications of our results for practical matching schemes

Effects of small Hsp genes on developmental stability and microenvironmental canalization

Background: Progression of development has to be insulated from the damaging impacts of environmental and genetic perturbations to produce highly predictable phenotypes. Molecular chaperones, such as the heat shock proteins (HSPs), are known to buffer various environmental stresses, and are deeply involved in protein homeostasis. These characteristics of HSPs imply that they might affect developmental buffering and canalization. Results: We examined the role of nine Hsp genes using the GAL4/UAS-RNAi system on phenotypic variation of various morphological traits in Drosophila melanogaster. The stability of bristle number, wing size and wing shape was characterized through fluctuating asymmetry (FA) and the coefficient of variation (CV), or among-individual variation. Progeny of the GAL4/Hsp-RNAi crosses tended to have reduced trait means for both wing size and wing shape. Transcriptional knockdown of Hsp67Bc and Hsp22 significantly increased FA of bristle number, while knockdown of Hsp67Ba significantly increased FA and among-individual variation of wing shape but only in males. Suppression of Hsp67Bb expression significantly increased among-individual variation of bristle number. The knockdown of gene expression was confirmed for Hsp67Ba, Hsp67Bc, Hsp22, and Hsp67Bb. Correlation between FA and CV or among-individual variation of each trait is weak and not significant except for the case of male wing shape. Conclusion: Four small Hsp genes (Hsp22, Hsp67Ba, Hsp67Bb and Hsp67Bc) showed involvement in the processes of morphogenesis and developmental stability. Due to possible different functions in terms of developmental buffering of these small Hsps, phenotypic stability of an organism is probably maintained by multiple mechanisms triggered by different environmental and genetic stresses on different traits. This novel finding may lead to a better understanding of non-Hsp90 molecular mechanisms controlling variability in morphological traits

X-ray Measurements of the Gravitational Potential Profile in the Central Region of the Abell 1060 Cluster of Galaxies

X-ray spectral and imaging data from ASCA and ROSAT were used to measure the total mass profile in the central region of Abell 1060, a nearby and relatively poor cluster of galaxies. The ASCA X-ray spectra, after correcting for the spatial response of the X-ray telescope, show an isothermal distribution of the intra-cluster medium (ICM) within at least $\sim$ 12' (or $160h_{70}^{-1}$ kpc; $H_0 = 70 h_{70}$ km s$^{-1}$Mpc$^{-1}$) in radius of the cluster center. The azimuthally averaged surface brightness profile from the ROSAT PSPC exhibits a central excess above an isothermal $\beta$ model. The ring-sorted ASCA GIS spectra and the radial surface brightness distribution from the ROSAT PSPC were simultaneously utilized to constrain the gravitational potential profile. Some analytic models of the total mass density profile were examined. The ICM density profile was also specified by analytic forms. The ICM temperature distribution was constrained to satisfy the hydrostatic equilibrium, and to be consistent with the data. Then, the total mass distribution was found to be described better by the universal dark halo profile proposed by Navarro, Frenk, and White (1996;1997) than by a King-type model with a flat density core. A profile with a central cusp together with a logarithmic radial slope of $\sim 1.5$ was also consistent with the data. Discussions are made concerning the estimated dark matter distribution around the cluster center.Comment: 32 pages. Accepted: ApJ 2000, 35 pages, Title was correcte

Simultaneous ground and satellite observations of an isolated proton arc at subauroral latitudes

We observed an isolated proton arc at the Athabasca station MLAT: 62◦N) in Canada on 5 September, 2005, using a ground-based allsky imager at wavelengths of 557.7 nm, 630.0 nm, and 486.1 nm (Hβ). This arc is similar to the detached proton arc observed recently by the IMAGE satellite [Immel et al., 2002]. The arc appeared at 0500-0700 UT (2100-2300 MLT) coincident with strong Pc 1 geomagnetic pulsations in the frequency range of the electromagnetic ion cyclotron (EMIC) wave. A small substorm took place at 0550 UT, while the isolated arc did not change its structure and intensity before and after the substorm onset. From particle data obtained by the NOAA 17 satellite, we found that the isolated arc was located in the localized (L ∼4) enhancement of ion precipitation fluxes at an energy range of 30-80 keV. Trapped ion flux enhancements (ring current ions) were also observed at two latitudinally separated regions. The localized ion precipitation was located at the outer boundary of the inner ring current ions. The DMSP F13 satellite observed signatures of ionospheric plasma trough near the conjugate point of the arc in the southern hemisphere. The trough is considered to be connected to the plasmapause. These results indicate that the source region of the isolated arc was located near the plasmapause and in the ring current. We conclude that the observed isolated proton arc at subauroral latitudes were driven by the EMIC waves, which were generated near the plasmapause and scattered the ring current protons resonantly into the loss cone

Geometric phases and hidden local gauge symmetry

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published in Phys. Rev.