Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Electromagnetic field angular momentum in condensed matter systems

Various electromagnetic systems can carry an angular momentum in their {\bf E} and {\bf B} fields. The electromagnetic field angular momentum (EMAM) of these systems can combine with the spin angular momentum to give composite fermions or composite bosons. In this paper we examine the possiblity that an EMAM could provide an explanation of the fractional quantum Hall effect (FQHE) which is complimentary to the Chern-Simons explanation. We also examine a toy model of a non-BCS superconductor (e.g. high $T_c$ superconductors) in terms of an EMAM. The models presented give a common, simple picture of these two systems in terms of an EMAM. The presence of an EMAM in these systems might be tested through the observation of the decay modes of a charged, spin zero unstable particle inside one of these systems.Comment: 17 pages, no figures, to be published in Phys. Rev.

Quantum Locality

It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is no reason to suspect any conflict between quantum theory and special relativity.Comment: Introduction has been revised, references added, minor corrections elsewhere. To appear in Foundations of Physic

Organic film thickness influence on the bias stress instability in Sexithiophene Field Effect Transistors

In this paper, the dynamics of bias stress phenomenon in Sexithiophene (T6) Field Effect Transistors (FETs) has been investigated. T6 FETs have been fabricated by vacuum depositing films with thickness from 10 nm to 130 nm on Si/SiO2 substrates. After the T6 film structural analysis by X-Ray diffraction and the FET electrical investigation focused on carrier mobility evaluation, bias stress instability parameters have been estimated and discussed in the context of existing models. By increasing the film thickness, a clear correlation between the stress parameters and the structural properties of the organic layer has been highlighted. Conversely, the mobility values result almost thickness independent

Substructures in lens galaxies: PG1115+080 and B1555+375, two fold configurations

We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in several cases the observed value differs significantly. The most plausible solution is to invoke the presence of substructures, as for instance predicted by the Cold Dark Matter scenario, located near the two images. In particular, we analyze the two fold lens systems PG1115+080 and B1555+375, for which there are not yet satisfactory models which explain the observed anomalous flux ratios. We add to a smooth lens model, which reproduces well the positions of the images but not the anomalous fluxes, one or two substructures described as singular isothermal spheres. For PG1115+080 we consider a smooth model with the influence of the group of galaxies described by a SIS and a substructure with mass $\sim 10^{5} M_{\odot}$ as well as a smooth model with an external shear and one substructure with mass $\sim 10^{8} M_{\odot}$ . For B1555+375 either a strong external shear or two substructures with mass $\sim 10^{7} M_{\odot}$ reproduce the data quite well.Comment: 26 pages, updated bibliography, Accepted for publication in Astrophysics & Space Scienc

A quasilocal calculation of tidal heating

We present a method for computing the flux of energy through a closed surface containing a gravitating system. This method, which is based on the quasilocal formalism of Brown and York, is illustrated by two applications: a calculation of (i) the energy flux, via gravitational waves, through a surface near infinity and (ii) the tidal heating in the local asymptotic frame of a body interacting with an external tidal field. The second application represents the first use of the quasilocal formalism to study a non-stationary spacetime and shows how such methods can be used to study tidal effects in isolated gravitating systems.Comment: REVTex, 4 pages, 1 typo fixed, standard sign convention adopted for the Newtonian potential, a couple of lines added to the discussion of gauge dependent term

Potts model on recursive lattices: some new exact results

We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths $L_y=2,3,4,5$. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width $L_y=3$ and $L_y=m+2$, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.Comment: 17 pages, 19 figures. v2 typos corrected, title changed and references, acknowledgements and two further original examples added. v3 one further example added. v4 final versio

Momentum-Resolved Tunneling into Fractional Quantum Hall Edges

Tunneling from a two-dimensional contact into quantum-Hall edges is considered theoretically for a case where the barrier is extended, uniform, and parallel to the edge. In contrast to previously realized tunneling geometries, details of the microscopic edge structure are exhibited directly in the voltage and magnetic-field dependence of the differential tunneling conductance. In particular, it is possible to measure the dispersion of the edge-magnetoplasmon mode, and the existence of additional, sometimes counterpropagating, edge-excitation branches could be detected.Comment: 4 pages, 3 figures, RevTex

Measuring the cosmological bulk flow using the peculiar velocities of supernovae

We study large-scale coherent motion in our universe using the existing Type IA supernovae data. If the recently observed bulk flow is real, then some imprint must be left on supernovae motion. We run a series of Monte Carlo Markov Chain runs in various redshift bins and find a sharp contrast between the z 0.05 data. The$z < 0.05 data are consistent with the bulk flow in the direction (l,b)=({290^{+39}_{-31}}^{\circ}, {20^{+32}_{-32}}^{\circ}) with a magnitude of v_bulk = 188^{+119}_{-103} km/s at 68% confidence. The significance of detection (compared to the null hypothesis) is 95%. In contrast, z > 0.05 data (which contains 425 of the 557 supernovae in the Union2 data set) show no evidence for bulk flow. While the direction of the bulk flow agrees very well with previous studies, the magnitude is significantly smaller. For example, the Kashlinsky, et al.'s original bulk flow result of v_bulk > 600 km/s is inconsistent with our analysis at greater than 99.7% confidence level. Furthermore, our best-fit bulk flow velocity is consistent with the expectation for the \Lambda CDM model, which lies inside the 68% confidence limit.Comment: Version published in JCA