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

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

QED for a Fibrillar Medium of Two-Level Atoms

We consider a fibrillar medium with a continuous distribution of two-level atoms coupled to quantized electromagnetic fields. Perturbation theory is developed based on the current algebra satisfied by the atomic operators. The one-loop corrections to the dispersion relation for the polaritons and the dielectric constant are computed. Renormalization group equations are derived which demonstrate a screening of the two-level splitting at higher energies. Our results are compared with known results in the slowly varying envelope and rotating wave approximations. We also discuss the quantum sine-Gordon theory as an approximate theory.Comment: 32 pages, 4 figures, uses harvmac and epsf. In this revised version, infra-red divergences are more properly handle

Witten's Vertex Made Simple

The infinite matrices in Witten's vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.Comment: 24 pages, 2 figures, RevTeX style, typos correcte

S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case

A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S-matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c /T_F is approximately 0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3 approximately 1.3 where n is the density and lambda the thermal wavelength, which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure

Is the String Coupling Constant invariant under T-duality?

It is well known that under T-duality the sigma model dilaton (which is normally thought to be related to the string coupling constant through the simple formula $\kappa = exp$), undergoes an additive shift. On the other hand, Kugo and Zwiebach, using a simplified form of string field theory, claim that the string coupling constant does not change under the T-duality. Obviously, what seems to happen is that two different coupling constants, associated to different dilatons, are used. In this contribution we shall try to clarify this, and related issues.Comment: LaTeX, 13 pag. Contributions to Santa Margherita and S. Petersburg meeting

The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.Comment: 36 pages, 12 figure

Quantum Clifford-Hopf Algebras for Even Dimensions

In this paper we study the quantum Clifford-Hopf algebras $\widehat{CH_q(D)}$ for even dimensions $D$ and obtain their intertwiner $R-$matrices, which are elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of these new algebras we find the possibility to connect with extended supersymmetry. We also analyze the corresponding spin chain hamiltonian, which leads to Suzuki's generalized $XY$ model.Comment: 12 pages, LaTeX, IMAFF-12/93 (final version to be published, 2 uuencoded figures added