A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.Comment: 1 figure, LaTeX, 18 page

Binary Cosmic Strings

The properties of cosmic strings have been investigated in detail for their implications in early-universe cosmology. Although many variations of the basic structure have been discovered, with implications for both the microscopic and macroscopic properties of cosmic strings, the cylindrical symmetry of the short-distance structure of the string is generally unaffected. In this paper we describe some mechanisms leading to an asymmetric structure of the string core, giving the defects a quasi-two-dimensional character. We also begin to investigate the consequences of this internal structure for the microscopic and macroscopic physics.Comment: 19 pages; uses harvmac (not included

Alternative Mathematical Technique to Determine LS Spectral Terms

We presented an alternative computational method for determining the permitted LS spectral terms arising from $l^N$ electronic configurations. This method makes the direct calculation of LS terms possible. Using only basic algebra, we derived our theory from LS-coupling scheme and Pauli exclusion principle. As an application, we have performed the most complete set of calculations to date of the spectral terms arising from $l^N$ electronic configurations, and the representative results were shown. As another application on deducing LS-coupling rules, for two equivalent electrons, we deduced the famous Even Rule; for three equivalent electrons, we derived a new simple rule.Comment: Submitted to Phys. Rev.

The exact Darwin Lagrangian

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c)^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.Comment: 2.5 pages, no figure

Three flavour Quark matter in chiral colour dielectric model

We investigate the properties of quark matter at finite density and temperature using the nonlinear chiral extension of Colour Dielectric Model (CCM). Assuming that the square of the meson fields devlop non- zero vacuum expectation value, the thermodynamic potential for interacting three flavour matter has been calculated. It is found that $$and$$ remain zero in the medium whereas $$ changes in the medium. As a result, $u$ and $d$ quark masses decrease monotonically as the temperature and density of the quark matter is increased.In the present model, the deconfinement density and temperature is found to be lower compared to lattice results. We also study the behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.

Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice

The square root of the positive definite hermitian operator $D_w^{\dagger} D_w$ in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula $Y_{k+1} = {1/2} (Y_k + D_w^{\dagger} D_w Y_k^{-1})$ with Y_0 = \Id, where $Y_k^2$ converges to $D_w^{\dagger} D_w$ quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investigated. For smooth background gauge fields with non-zero topological charge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the Index Theorem is satisfied exactly. The fermionic determinants are also computed and they are in good agreement with the continuum exact solution.Comment: 18 pages (LaTeX), 2 figures (EPS

Theory of Crystalline Electric Field and Kondo Effect in Pr Skutterudites

Possible Kondo effect in Pr skutterudite is studied with attention to characteristic features of low-lying crystalline electric field (CEF) levels and the conduction band. A mechanism for the small CEF splitting between a singlet and a triplet is proposed as combination of the point-charge interaction and hybridization of 4f with ligand p states. Provided 4f^3 configurations dominate over 4f^1 as intermediate states, p-f hybridization favors the triplet, while point-charge interaction favors the singlet. For realistic parameters for hybridization as well as 4f^1 and 4f^3 levels, these singlet and triplet can form a nearly degenerate pseudo-quartet. It is found that one of two spin 1/2 objects composing the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The magnitude of each effective exchange depends strongly on a parameter characterizing the triplet wave function under the T_h symmetry. It is argued that differences of this parameter among Pr skutterdudites are responsible for the apparent diversity of their physical properties. Numerical renormalization group is used to derive the renormalization flows going toward singlet, doublet, triplet or quaret according to the CEF splitting and exchange interactions.Comment: 19 pages, 6 figures, to be published in Special Invited Section (Kondo Effect) of Journal of Physical Society of Japa

A Taxonomy of Causality-Based Biological Properties

We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a theoretical point of view, biochemical reactions are abstractly represented as causal implications and the produced metabolites as causal consequences of the implication representing the corresponding reaction. The fact that a reactant is produced is represented by means of the chain of reactions that have made it exist. Such representation abstracts away from quantities, stoichiometric and thermodynamic parameters and constitutes the basis for the characterization of our properties. Moreover, we propose an effective method for verifying our properties based on an abstract model of system dynamics. This consists of a new abstract semantics for the system seen as a concurrent network and expressed using the Chemical Ground Form calculus. We illustrate an application of this framework to a portion of a real metabolic pathway

Efficient CSL Model Checking Using Stratification

For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. Their proof can be turned into an approximation algorithm with worse than exponential complexity. In 2000, Baier, Haverkort, Hermanns and Katoen presented an efficient polynomial-time approximation algorithm for the sublogic in which only binary until is allowed. In this paper, we propose such an efficient polynomial-time approximation algorithm for full CSL. The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. On a stratified CTMC, the probability to satisfy a CSL path formula can be approximated by a transient analysis in polynomial time (using uniformization). We present a measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one. This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to work only for stratified CTMCs. As an additional contribution, our measure-preserving transformation can be used to ensure the decidability for general CTMCs.Comment: 18 pages, preprint for LMCS. An extended abstract appeared in ICALP 201

Orbital ferromagnetism and anomalous Hall effect in antiferromagnets on distorted fcc lattice

The Berry phase due to the spin wavefunction gives rise to the orbital ferromagnetism and anomalous Hall effect in the non-coplanar antiferromagnetic ordered state on face centered cubic (fcc) lattice once the crystal is distorted perpendicular to (1,1,1) or (1,1,0)- plane. The relevance to the real systems $\gamma$-FeMn and NiS$_2$ is also discussed.Comment: 4 pages, 3 figure