12 research outputs found
Topological Modes in Dual Lattice Models
Lattice gauge theory with gauge group is reconsidered in four
dimensions on a simplicial complex . One finds that the dual theory,
formulated on the dual block complex , contains topological modes
which are in correspondence with the cohomology group ,
in addition to the usual dynamical link variables. This is a general phenomenon
in all models with single plaquette based actions; the action of the dual
theory becomes twisted with a field representing the above cohomology class. A
similar observation is made about the dual version of the three dimensional
Ising model. The importance of distinct topological sectors is confirmed
numerically in the two dimensional Ising model where they are parameterized by
.Comment: 10 pages, DIAS 94-3
Theory of Pump Depletion and Spike Formation in Stimulated Raman Scattering
By using the inverse spectral transform, the SRS equations are solved and the
explicit output data is given for arbitrary laser pump and Stokes seed profiles
injected on a vacuum of optical phonons. For long duration laser pulses, this
solution is modified such as to take into account the damping rate of the
optical phonon wave. This model is used to interprete the experiments of Druhl,
Wenzel and Carlsten (Phys. Rev. Lett., (1983) vol. 51, p. 1171), in particular
the creation of a spike of (anomalous) pump radiation. The related nonlinear
Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike
is not a soliton.Comment: LaTex file, includes two figures in LaTex format, 9 page
General duality for abelian-group-valued statistical-mechanics models
We introduce a general class of statistical-mechanics models, taking values
in an abelian group, which includes examples of both spin and gauge models,
both ordered and disordered. The model is described by a set of ``variables''
and a set of ``interactions''. A Gibbs factor is associated to each variable
and to each interaction. We introduce a duality transformation for systems in
this class. The duality exchanges the abelian group with its dual, the Gibbs
factors with their Fourier transforms, and the interactions with the variables.
High (low) couplings in the interaction terms are mapped into low (high)
couplings in the one-body terms. The idea is that our class of systems extends
the one for which the classical procedure 'a la Kramers and Wannier holds, up
to include randomness into the pattern of interaction. We introduce and study
some physical examples: a random Gaussian Model, a random Potts-like model, and
a random variant of discrete scalar QED. We shortly describe the consequence of
duality for each example.Comment: 26 pages, 2 Postscript figure
INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING
Zakharov-Shabat--Ablowitz-Kaup-Newel-Segur representation for
Stokes-anti-Stokes stimulated Raman scattering is proposed. Periodical waves,
solitons and self-similarity solutions are derived. Transient and bright
threshold solitons are discussed.Comment: 16 pages, LaTeX, no figure
Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus. II. Triangular and hexagonal lattices
We compute the finite-size corrections to the free energy, internal energy
and specific heat of the critical two-dimensional spin-1/2 Ising model on a
triangular and hexagonal lattices wrapped on a torus. We find the general form
of the finite-size corrections to these quantities, as well as explicit
formulas for the first coefficients of each expansion. We analyze the
implications of these findings on the renormalization-group description of the
model.Comment: 45 pages (LaTeX2e). Self-unpacking file containing the tex file and
three macros (indent.sty, eqsection.sty, subeqnarray.sty). Paper I
corresponds to cond-mat/0009054. Final versio
Three-Wave Backward Optical Solitons
Three-wave solitons backward propagating with respect to a pump wave are generated in nonlinear optical media through stimulated Brillouin scattering (SBS) in optical fibers or through the non-degenerate three-wave interaction in quadratic (χ (2) ) nonlinear media. In an optical fiber-ring cavity, nanosecond solitary wave morphogenesis takes place when it is pumped with a continuous wave (c.w.). A backward dissipative Stokes soliton is generated from the hypersound waves stimulated by electrostriction between the forward pump wave and the counterpropagating Stokes wave. Superluminous and subluminous dissipative solitons are controlled via a single parameter: the feedback or reinjection for a given pump intensity or the pump intensity for a given feedback. In a c.w. pumped optical parametric oscillator (OPO), backward picosecond soliton generation takes place for non-degenerate three-wave interaction in the quadratic medium. The resonant condition is automatically satisfied in stimulated Brillouin backscattering when the fiber-ring laser contains a large number of longitudinal modes beneath the Brillouin gain curve. However, in order to achieve quasiphase matching between the three optical waves (the forward pump wave and the backwar