Nonbipartite Dulmage-Mendelsohn Decomposition for Berge Duality

The Dulmage-Mendelsohn decomposition is a classical canonical decomposition in matching theory applicable for bipartite graphs, and is famous not only for its application in the field of matrix computation, but also for providing a prototypal structure in matroidal optimization theory. The Dulmage-Mendelsohn decomposition is stated and proved using the two color classes, and therefore generalizing this decomposition for nonbipartite graphs has been a difficult task. In this paper, we obtain a new canonical decomposition that is a generalization of the Dulmage-Mendelsohn decomposition for arbitrary graphs, using a recently introduced tool in matching theory, the basilica decomposition. Our result enables us to understand all known canonical decompositions in a unified way. Furthermore, we apply our result to derive a new theorem regarding barriers. The duality theorem for the maximum matching problem is the celebrated Berge formula, in which dual optimizers are known as barriers. Several results regarding maximal barriers have been derived by known canonical decompositions, however no characterization has been known for general graphs. In this paper, we provide a characterization of the family of maximal barriers in general graphs, in which the known results are developed and unified

Theory of Flux-Flow Resistivity near Hc2H_{c2} for s-wave Type-II Superconductors

This paper presents a microscopic calculation of the flux-flow resistivity $\rho_{f}$ for s-wave type-II superconductors with arbitrary impurity concentrations near the upper critical field $H_{c2}$. It is found that, as the mean free path $l$ becomes longer, $\rho_{f}$ increases gradually from the dirty-limit result of Thompson [Phys. Rev. B{\bf 1}, 327 (1970)] and Takayama and Ebisawa [Prog. Theor. Phys. {\bf 44}, 1450 (1970)]. The limiting behaviors suggest that $\rho_{f}(H)$ at low temperatures may change from convex downward to upward as $l$ increases, thus deviating substantially from the linear dependence $\rho_{f}\propto H/H_{c2}$ predicted by the Bardeen-Stephen theory [Phys. Rev. {\bf 140}, A1197 (1965)]

Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors

We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along extremal orbits is relevant for the magnitude of the extra damping, thereby providing a support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which gives a good fit to the numerical results.Comment: 5 pages, 1 figure, changes in Introductio

Oxygen-isotope and trace element constraints on the origins of silica-rich melts in the subarc mantle

Peridotitic xenoliths in basaltic andesites from Batan island in the Luzon arc contain silica-rich (broadly dacitic) hydrous melt inclusions that were likely trapped when these rocks were within the upper mantle wedge underlying the arc. These melt inclusions have been previously interpreted to be slab-derived melts. We tested this hypothesis by analyzing the oxygen isotope compositions of these inclusions with an ion microprobe. The melt inclusions from Batan xenoliths have δ 18OVSMOW values of 6.45 ± 0.51‰. These values are consistent with the melts having been in oxygen isotope exchange equilibrium with average mantle peridotite at temperatures of ≥875°C. We suggest the δ 18O values of Batan inclusions, as well as their major and trace element compositions, can be explained if they are low-degree melts (or differentiation products of such melts) of peridotites in the mantle wedge that had previously undergone extensive melt extraction followed by metasomatism by small amounts (several percent or less) of slab-derived components. A model based on the trace element contents of Batan inclusions suggests that this metasomatic agent was an aqueous fluid extracted from subducted basalts and had many characteristics similar to slab-derived components of the sources of arc-related basalts at Batan and elsewhere. Batan inclusions bear similarities to “adakites,” a class of arc-related lava widely considered to be slab-derived melts. Our results suggest the alternative interpretation that at least some adakite-like liquids might be generated from low-degree melting of metasomatized peridotites

Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate

We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from $\hat{G}$, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an "improper" structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.Comment: 9 pages, 6 gigure

Experimental and Atomistic Theoretical Study of Degree of Polarization from Multi-layer InAs/GaAs Quantum Dots

Recent experimental measurements, without any theoretical guidance, showed that isotropic polarization response can be achieved by increasing the number of QD layers in a QD stack. Here we analyse the polarization response of multi-layer quantum dot stacks containing up to nine quantum dot layers by linearly polarized PL measurements and by carrying out a systematic set of multi-million atom simulations. The atomistic modeling and simulations allow us to include correct symmetry properties in the calculations of the optical spectra: a factor critical to explain the experimental evidence. The values of the degree of polarization (DOP) calculated from our model follows the trends of the experimental data. We also present detailed physical insight by examining strain profiles, band edges diagrams and wave function plots. Multi-directional PL measurements and calculations of the DOP reveal a unique property of InAs quantum dot stacks that the TE response is anisotropic in the plane of the stacks. Therefore a single value of the DOP is not sufficient to fully characterize the polarization response. We explain this anisotropy of the TE-modes by orientation of hole wave functions along the [-110] direction. Our results provide a new insight that isotropic polarization response measured in the experimental PL spectra is due to two factors: (i) TM[001]-mode contributions increase due to enhanced intermixing of HH and LH bands, and (ii) TE[110]-mode contributions reduce significantly due to hole wave function alignment along the [-110] direction. We also present optical spectra for various geometry configurations of quantum dot stacks to provide a guide to experimentalists for the design of multi-layer QD stacks for optical devices. Our results predict that the QD stacks with identical layers will exhibit lower values of the DOP than the stacks with non-identical layers.Comment: 10 pages, 7 figures, and 1 tabl

Reactivity difference between protolytic forms of some macrocyclic chromium(III) complexes in ligand substitution and electron transfer processes

The review provides insight into the mechanism of ligand substitution and electron transfer (from chromium( III) to iron(III)) by comparison of the reactivity of some tetraazamacrocyclic chromium(III) complexes in the conjugate acid-base forms. Use of two geometrical isomers made possible to estimate the influence of geometry and protolytic reactions in trans and cis position towards the leaving group on the rate enhancement. Studies on the reaction rates in different media demonstrated the role played by outer sphere interactions in a monodentate ligand substitution

Abelian Chern-Simons Term in Superfluid 3He-A

We show in this paper that Abelian Chern-Simons term is induced in 2+1 and 3+1 dimensional rotating superfluid $^{3}$He-A and plays important roles in its dynamics. Because U(1) symmetry is spontaneously broken in $^{3}$He-A, Goldstone mode appears and contributes to induced Chern-Simons term. We found that the coefficient of Chern-Simons term, which is equivalent to Hall conductance, depends on an infra-red cut off of the Goldstone mode, and that the orbital angular momentum of $^{3}$He-A in a cylinder geometry is derived from Chern-Simons term.Comment: 16 pages, 2 figures, LaTeX, minor points are changed, references are added. Accepted for publication in Physics Letters

Self-Consistent Approximations for Superconductivity beyond the Bardeen-Cooper-Schrieffer Theory

We develop a concise self-consistent perturbation expansion for superconductivity where all the pair processes are naturally incorporated without drawing "anomalous" Feynman diagrams. This simplification results from introducing an interaction vertex that is symmetric in the particle-hole indices besides the ordinary space-spin coordinates. The formalism automatically satisfies conservation laws, includes the Luttinger-Ward theory as the normal-state limit, and reproduces the Bardeen-Cooper-Schrieffer theory as the lowest-order approximation. It enables us to study the thermodynamic, single-particle, two-particle, and dynamical properties of superconductors with competing fluctuations based on a single functional $\Phi[\hat{G}]$ of Green's function $\hat{G}$ in the Nambu space. Specifically, we derive closed equations in the FLEX-S approximation, i.e., the fluctuation exchange approximation for superconductivity with all the pair processes, which contains extra terms besides those in the standard FLEX approximation.Comment: 14 pages, 6 figure