Overlapping Unit Cells in 3d Quasicrystal Structure

A 3-dimensional quasiperiodic lattice, with overlapping unit cells and periodic in one direction, is constructed using grid and projection methods pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are the vertices of a convex polytope P, and 4 are interior points also shared with other neighboring unit cells. Using Kronecker's theorem the frequencies of all possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final versio

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

The Chiral Potts Models Revisited

In honor of Onsager's ninetieth birthday, we like to review some exact results obtained so far in the chiral Potts models and to translate these results into language more transparent to physicists, so that experts in Monte Carlo calculations, high and low temperature expansions, and various other methods, can use them. We shall pay special attention to the interfacial tension $\epsilon_r$ between the $k$ state and the $k-r$ state. By examining the ground states, it is seen that the integrable line ends at a superwetting point, on which the relation $\epsilon_r=r\epsilon_1$ is satisfied, so that it is energetically neutral to have one interface or more. We present also some partial results on the meaning of the integrable line for low temperatures where it lives in the non-wet regime. We make Baxter's exact results more explicit for the symmetric case. By performing a Bethe Ansatz calculation with open boundary conditions we confirm a dilogarithm identity for the low-temperature expansion which may be new. We propose a new model for numerical studies. This model has only two variables and exhibits commensurate and incommensurate phase transitions and wetting transitions near zero temperature. It appears to be not integrable, except at one point, and at each temperature there is a point, where it is almost identical with the integrable chiral Potts model.Comment: J. Stat. Phys., LaTeX using psbox.tex and AMS fonts, 69 pages, 30 figure

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

Symmetries of Large N Matrix Models for Closed Strings

We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known results of solvable spin chain systems.Comment: 12 pages, 1 eps figure, RevTex, some minor typos in the publised version are correcte

sl(N) Onsager's Algebra and Integrability

We define an $sl(N)$ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of $sl(N)$ Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonian linear in the generators of $sl(N)$ Onsager's Algebra is shown to posses an infinite number of mutually commuting integrals of motion

A wideband linear tunable CDTA and its application in field programmable analogue array

This document is the Accepted Manuscript version of the following article: Hu, Z., Wang, C., Sun, J. et al. ‘A wideband linear tunable CDTA and its application in field programmable analogue array’, Analog Integrated Circuits and Signal Processing, Vol. 88 (3): 465-483, September 2016. Under embargo. Embargo end date: 6 June 2017. The final publication is available at Springer via https://link.springer.com/article/10.1007%2Fs10470-016-0772-7 © Springer Science+Business Media New York 2016In this paper, a NMOS-based wideband low power and linear tunable transconductance current differencing transconductance amplifier (CDTA) is presented. Based on the NMOS CDTA, a novel simple and easily reconfigurable configurable analogue block (CAB) is designed. Moreover, using the novel CAB, a simple and versatile butterfly-shaped FPAA structure is introduced. The FPAA consists of six identical CABs, and it could realize six order current-mode low pass filter, second order current-mode universal filter, current-mode quadrature oscillator, current-mode multi-phase oscillator and current-mode multiplier for analog signal processing. The Cadence IC Design Tools 5.1.41 post-layout simulation and measurement results are included to confirm the theory.Peer reviewedFinal Accepted Versio

Density Profiles in Random Quantum Spin Chains

We consider random transverse-field Ising spin chains and study the magnetization and the energy-density profiles by numerically exact calculations in rather large finite systems ($L\le 128$). Using different boundary conditions (free, fixed and mixed) the numerical data collapse to scaling functions, which are very accurately described by simple analytic expressions. The average magnetization profiles satisfy the Fisher-de Gennes scaling conjecture and the corresponding scaling functions are indistinguishable from those predicted by conformal invariance.Comment: 4 pages RevTeX, 4 eps-figures include

Quasinormal Modes of Dirty Black Holes

Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.Comment: 4 pages. Published in PR

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.Comment: Published in PR