Errata for: Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point

We present some important corrections to our work which appeared in Nucl. Phys. B426 (1994) 534 (hep-th/9402144). Our previous results for the correlation functions $\langle e^{i\alpha \Phi(x)} e^{i\alpha' \Phi (0) } \rangle$ were only valid for $\alpha = \alpha'$, due to the fact that we didn't find the most general solution to the differential equations we derived. Here we present the solution corresponding to $\alpha \neq \alpha'$.Comment: 4 page

Holographic classification of Topological Insulators and its 8-fold periodicity

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the boundary states of topological insulators are Dirac fermions, we thereby holographically reproduce the Periodic Table of topological insulators found by Kitaev and Ryu. et. al, without using topological invariants nor K-theory. In addition we find candidate Z_2 topological insulators in classes AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table

Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models

We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. The critical exponents are computed to two-loop order. Possible applications to condensed matter physics in 3 space-time dimensions are discussed.Comment: v2: Published version, minor typose correcte

Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis

We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.Comment: version 3: additional appendix explains how the $\nu$ to $1-\nu$ duality of Riemann's $\zeta (\nu)$ follows from a special modular transformation in a massless relativistic theor

The Scattering Theory of Oscillator Defects in an Optical Fiber

We examine harmonic oscillator defects coupled to a photon field in the environs of an optical fiber. Using techniques borrowed or extended from the theory of two dimensional quantum fields with boundaries and defects, we are able to compute exactly a number of interesting quantities. We calculate the scattering S-matrices (i.e. the reflection and transmission amplitudes) of the photons off a single defect. We determine using techniques derived from thermodynamic Bethe ansatz (TBA) the thermodynamic potentials of the interacting photon-defect system. And we compute several correlators of physical interest. We find the photon occupancy at finite temperature, the spontaneous emission spectrum from the decay of an excited state, and the correlation functions of the defect degrees of freedom. In an extension of the single defect theory, we find the photonic band structure that arises from a periodic array of harmonic oscillators. In another extension, we examine a continuous array of defects and exactly derive its dispersion relation. With some differences, the spectrum is similar to that found for EM wave propagation in covalent crystals. We then add to this continuum theory isolated defects, so as to obtain a more realistic model of defects embedded in a frequency dependent dielectric medium. We do this both with a single isolated defect and with an array of isolated defects, and so compute how the S-matrices and the band structure change in a dynamic medium.Comment: 32 pages, TeX with harvmac macros, three postscript figure

Review of the Ochsenius Theory for Salt Generation in the Transylvanian Basin, Romania

This short study aims to highlight contradictions in Ochsenius’s model for the basin-wide salt generation (Kara-Bogas bay desiccation). Without claiming completeness, and through numerous records cited from the specific literature, we attempt to point at crucial incoherencies in the classical evaporitic model. In our presupposition, these might have led our ancestors to conclude that basin-wide salt generation needs theoretically well-based models. This is emphatically true for the Transylvanian Basin,Romania.The selected records are basic for the specific topic. We checked their validity by logical reasoning and by literature references.As for salt generation, the classical Ochsenius model has been upheld for the generation of evaporates even though it has been known that there are records denying the exclusivity of the evaporation model. It has also been proven that deep-sea salt exists, yet terminology is reluctant to follow the new discoveries. If non-evaporitic salt generation exists, it entails that huge salt deposits may exist, which are not remnants of a desiccation process.These cannot be considered as part of the classical theory of evaporation.Former researchers left important but neglected records, which should have updated the model of Ochsenius by now. Well-documented historical observation uncovered some contradictions in the salt generation of the Transylvanian Basin, Romania.Hereby we list 10 important contradictions,which may reveal that the well-known theory of Ochsenius (i.e. drying of Kara Bogaz bay) ought to be challenged for the Transylvanian Basin

Super Spin-Charge Separation for class A, C, and D disorder

We prove versions of super spin-charge separation for all three of the symmetry groups SU(N), Sp(2N), and SO(N) of disordered Dirac fermions in 2+1 dimensions, which involve the supercurrent-algebras gl (1|1)_{N}, osp(2|2)_{-2N}, and osp(2|2)_N respectively. For certain restricted classes of disordered potentials, the latter supercurrent algebra based conformal field theories can arise as non-trivial low energy fixed points. For all cases with such a fixed point, we compute the density of states exponents as a function of N.Comment: 10 pages; section 3 adde

On modeling the variability of bedform dimensions

ABSTRACT: Bedforms are irregular features that cannot easily be described by mean values. The variations in the geometric dimensions affect the bed roughness, and they are important in the modeling of vertical sorting and in modeling the thickness of cross-strata sets. The authors analyze the variability of bedform dimensions for three sets of flume experiments, considering PDFs of bedform height, trough elevation and crest elevation divided by its mean value. It appears that the dimensionless standard deviation of the bedform height is within a narrow range for nearly all experiments. This appears to be valid for the trough elevation and crest elevation, as well. For some modeling purposes, it seems sufficient to assume that the standard deviation is a constant, so that the variation in bedform dimension can be modeled by only predicting the mean bedform dimension.

Stochastics of bedform dimensions

Often river dunes are considered as regular bed patterns, with a mean dune height and a mean dune length. In reality however, river dunes are threedimensional and irregular features that cannot be fully described by their mean values. In fact, dune dimensions can be considered as stochastic variables. Their probability distribution can be characterized by a mean value and variance. The stochastic properties of dune dimensions are relevant for (see e.g. Van der Mark et al., 2005):\ud • Shipping - highest crests\ud • Pipelines & cables - deepest troughs\ud • Modelling cross-strata sets - troughs, dune heights\ud • Modelling vertical sorting - troughs\ud • Modelling bed roughness - dune heights\ud In the present research the stochastics of crest elevation, trough elevation and dune height are investigated by analysing three sets of flume experiments