Periodic Ising Correlations

In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis", by using representation theory. Our approach leads to a simpler and more direct way of deriving the spectrum of the transfer matrix for the finite periodic Ising model. We then determine formulas for the spin correlation functions that depend on the matrix elements of the induced rotation associated with the spin operator in a basis of eigenvectors for the transfer matrix. The representation of the spin matrix elements is obtained by considering the spin operator as an intertwining map. We exhibit the "new" elements V+ and V- in the Bugrij-Lisovyy formula as part of a holomorphic factorization of the periodic and anti-periodic summability kernels on the spectral curve associated with the induced rotation for the transfer matrix.Comment: 36 page

Mesoscopic effects in superconductor-ferromagnet-superconductor junctions

We show that at zero temperature the supercurrent through the superconductor - ferromagnetic metal - superconductor junctions does not decay exponentially with the thickness $L$ of the junction. At large $L$ it has a random sample-specific sign which can change with a change in temperature. In the case of mesoscopic junctions the phase of the order parameter in the ground state is a random sample-specific quantity. In the case of junctions of large area the ground state phase difference is $\pm \pi/2$.Comment: 4 pages, 1 figur

Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the "almost-isolated" trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.Comment: 39 pages, 6 figures, version to appear in PRD : a few minor changes and many typos corrected in equation

Phase coherent transport in SrTiO3/LaAlO3 interfaces

The two dimensional electron gas formed between the two band insulators SrTiO3 and LaAlO3 exhibits a variety of interesting physical properties which make it an appealing material for use in future spintronics and/or quantum computing devices. For this kind of applications electrons have to retain their phase memory for sufficiently long times or length. Using a mesoscopic size device we were able to extract the phase coherence length, and its temperature variation. We find the dephasing rate to have a power law dependence on temperature. The power depends on the temperature range studied and sheet resistance as expected from dephasing due to strong electron-electron interactions.Comment: Submitted to Phys. Rev

Characterisation and representation of non-dissipative electromagnetic medium with a double light cone

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in isotropic medium the Fresnel surface is at each point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L. Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is for example the behaviour of uniaxial medium like calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates

Covariant coarse-graining of inhomogeneous dust flow in General Relativity

A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant, coordinate-independent manner. The coarse--grained quantities are all quasi-local functionals, depending only on the geometry of the boundary of the considered domain. They can be thought of as relativistic generalizations of simple volume averages of local quantities in a flat space. The procedure is based on the isometric embedding theorem for S^2 surfaces and thus requires the boundary of the domain in question to have spherical topology and positive scalar curvature. We prove that in the limit of infinitesimally small volume the proposed quantities reproduce the local expansion, shear and vorticity. In case of irrotational flow we derive the time evolution for the coarse-grained quantities and show that its structure is very similar to the evolution equation for their local counterparts. Additional terms appearing in it may serve as a measure of the backreacton of small-scale inhomogeneities of the flow on the large-scale motion of the fluid inside the domain and therefore the result may be interesting in the context of the cosmological backreaction problem. We also consider the application of the proposed coarse-graining procedure to a number of known exact solutions of Einstein equations with dust and show that it yields reasonable results.Comment: 17 pages, 5 figures. Version accepted in Classical and Quantum Gravity

The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.Comment: 4 pages, 1 figur

Critical disorder effects in Josephson-coupled quasi-one-dimensional superconductors

Effects of non-magnetic randomness on the critical temperature T_c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T_c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-coherence breaking. The interplay between disorder and quantum phase fluctuations results in quantum critical behavior at T=0, manifesting itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.Comment: 4 pages, 2 figure

Drag resistance of 2D electronic microemulsions

Motivated by recent experiments of Pillarisetty {\it et al}, \prl {\bf 90}, 226801 (2003), we present a theory of drag in electronic double layers at low electron concentration. We show that the drag effect in such systems is anomolously large, it has unusual temperature and magnetic field dependences accociated with the Pomeranchuk effect, and does not vanish at zero temperature

Band structures of P-, D-, and G-surfaces

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.Comment: 21 pages, 8 figures, 3 tables, submitted to Phys. Rev.