422 research outputs found
A 1D Model for N-level Atoms Coupled to an EM Field
We construct a model for n-level atoms coupled to quantized electromagnetic
fields in a fibrillar geometry. In the slowly varying envelope and rotating
wave approximations, the equations of motion are shown to satisfy a zero
curvature representation, implying integrability of the quantum system.Comment: 8 pages, Plain Te
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 to
duality of Riemann's 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
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
The full set of -invariant factorized -matrices
We use the method of the tensor product graph to construct rational (Yangian
invariant) solutions of the Yang-Baxter equation in fundamental representations
of and thence the full set of -invariant factorized -matrices.
Brief comments are made on their bootstrap structure and on Belavin's scalar
Yangian conserved charges.Comment: 10p
Form-factors computation of Friedel oscillations in Luttinger liquids
We show how to analytically determine for the "Friedel
oscillations" of charge density by a single impurity in a 1D Luttinger liquid
of spinless electrons.Comment: Revtex, epsf, 4pgs, 2fig
Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes
We develop a finite temperature field theory formalism in any dimension that
has the filling fractions as the basic dynamical variables. The formalism
efficiently decouples zero temperature dynamics from the quantum statistical
sums. The zero temperature `data' is the scattering amplitudes. A saddle point
condition leads to an integral equation which is similar in spirit to the
thermodynamic Bethe ansatz for integrable models, and effectively resums
infinite classes of diagrams. We present both relativistic and non-relativistic
versions
Descent Relations and Oscillator Level Truncation Method
We reexamine the oscillator level truncation method in the bosonic String
Field Theory (SFT) by calculation the descent relation =Z_3<V_2|. For
the ghost sector we use the fermionic vertices in the standard oscillator
basis. We propose two new schemes for calculations. In the first one we assume
that the insertion satisfies the overlap equation for the vertices and in the
second one we use the direct calculations. In both schemes we get the correct
structures of the exponent and pre-exponent of the vertex <V_2|, but we find
out different normalization factors Z_3.Comment: 21 pages, 10 figures, Late
A central extension of \cD Y_{\hbar}(\gtgl_2) and its vertex representations
A central extension of \cD Y_{\hbar}(\gtgl_2) is proposed. The bosonization
of level module and vertex operators are also given.Comment: 10 pages, AmsLatex, to appear in Lett. in Math. Phy
Quantum Clifford-Hopf Algebras for Even Dimensions
In this paper we study the quantum Clifford-Hopf algebras
for even dimensions and obtain their intertwiner 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 model.Comment: 12 pages, LaTeX, IMAFF-12/93 (final version to be published, 2
uuencoded figures added
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