Lie algebra cohomology and group structure of gauge theories

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other charge $Q^{\dagger}$.Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy

Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models

Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing recent work we compare various periodic and quasiperiodic models, where the couplings and/or the lattice may be aperiodic, and where the Ising couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign. We present some of our results on the square-lattice fully-frustrated Ising model. Finally, we make a few remarks on our recent works on the pentagrid Ising model and on overlapping unit cells in three dimensions and how these works can be utilized once more detailed results for pair correlations in, e.g., the eight-vertex model or the chiral Potts model or even three-dimensional Yang-Baxter integrable models become available.Comment: LaTeX2e using iopart.cls, 10 pages, 5 figures (5 eps files), Dunk Island conference in honor of 60th birthday of A.J. Guttman

Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introductio

Spin-orbital coupling effect on Josephson current through a superconductor heterojunction

We study spin-orbital coupling effect on the Josephson current through a superconductor (SC) heterojunction, consisting of two s-wave superconductors and a two-dimensional electron gas (2DEG) layer between them. The Rashba-type (RSOC) and/or Dresselhaus-type (DSOC) of spin-orbital coupling are considered in the 2DEG region. By using the lattice Bogoliubov-de Gennes equation and the Keldysh formalism, we calculate the DC supercurrent flowing through the junction and find that the critical current $I_c$ exhibits a damped oscillation with both the strength of SOC and the layer length of 2DEG; especially, the strength ratio between RSOC and DSOC can also induce switching between the $0$ state and the $\pi$ state of the SC/2DEG/SC junction as well. This $0$-$\pi$ transition results from the fact that SOC in a two-dimension system can lead to a pseudo-magnetic effect on the flowing electrons like the effect of a ferromagnet, since the time reversal symmetry of the system has already been broken by two SC leads with different macroscopic phases.Comment: 5 pages, 5 figure

Multiple Timescale Energy Scheduling for Wireless Communication with Energy Harvesting Devices

The primary challenge in wireless communication with energy harvesting devices is to efficiently utilize the harvesting energy such that the data packet transmission could be supported. This challenge stems from not only QoS requirement imposed by the wireless communication application, but also the energy harvesting dynamics and the limited battery capacity. Traditional solar predictable energy harvesting models are perturbed by prediction errors, which could deteriorate the energy management algorithms based on this models. To cope with these issues, we first propose in this paper a non-homogenous Markov chain model based on experimental data, which can accurately describe the solar energy harvesting process in contrast to traditional predictable energy models. Due to different timescale between the energy harvesting process and the wireless data transmission process, we propose a general framework of multiple timescale Markov decision process (MMDP) model to formulate the joint energy scheduling and transmission control problem under different timescales. We then derive the optimal control policies via a joint dynamic programming and value iteration approach. Extensive simulations are carried out to study the performances of the proposed schemes

Joint multicast routing and channel assignment in multiradio multichannel wireless mesh networks using tabu search

Copyright @ 2009 IEEE Computer SocietyThis paper proposes a tabu search (TS) based optimization approach to search a minimum-interference multicast tree which satisfies the end-to-end delay constraint and optimizes the usage of the scarce radio network resource in wireless mesh networks. The path-oriented encoding method is adopted and each candidate solution is represented by a tree data structure (i.e., a set of paths). Since we expect the multicast trees on which the minimum-interference channel assignment can be produced, a fitness function that returns the total channel conflict is devised. The techniques for controlling the tabu search procedure are well developed. A simple yet effective channel assignment algorithm is proposed to reduce the channel conflict. Simulation results show that the proposed TS multicast algorithm can produce the multicast trees which have better performance in terms of both the total channel conflict and the tree cost than that of a well known multicast algorithm in wireless mesh networks.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

Identified Particle Production in d+Au and p+p collisions at RHIC

The BRAHMS experiment at RHIC has measured the transverse momentum spectra of charged pions, kaons and (anti-)protons over a wide range of rapidity in d+Au and p+p collisions at $\sqrt{s_{NN}}=200$GeV. The nuclear modification factor $R_{dAu}$ at forward rapidities shows a clear suppression for $\pi^{+}$. The measured net-proton yields in p+p collisions are compared to PYTHIA and HIJING/B and seem to be better described by the latter.Comment: 4 pages, 3 figures, presented at the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions, "Quark Matter 2006", Shanghai, China, November 14-20, 2006. to appear in the proceedings of Quark Matter 2006 as a special issue of Journal of Physics G: Nuclear and Particle Physic

Spontaneous Magnetization of the Integrable Chiral Potts Model

We show how $Z$-invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrable eigenvectors. When the distance between the two spins in the correlation function becomes infinite it becomes the square of the order parameter. In this way, we show that the spontaneous magnetization can be expressed in terms of the inner products of the eigenvectors of the $N$ asymptotically degenerate maximum eigenvalues. Using our previous results on these eigenvectors, we are able to obtain the order parameter as a sum almost identical to the one given by Baxter. This gives the known spontaneous magnetization of the chiral Potts model by an entirely different approach.Comment: LaTeX 2E document, using iopart.cls with iopams packages, 22 pages, 1 eps figure. Presented at the Simons Center for Geometry and Physics Workshop on Correlation Functions for Integrable Models 2010: January 18-22, 2010. Version 2: The identity conjectured in version 1 is now proved and its proof is presented in arXiv:1108.4713; various small corrections and improvements have been made als