6,965 research outputs found
The QCD Trace Anomaly as a Vacuum Effect (The vacuum is a medium is the message!)
We use arguments taken from the electrodynamics of media to deduce the QCD
trace anomaly from the expression for the vacuum energy in the presence of an
external color magnetic field.Comment: 18 pages, USITP 94-1
Dynamics of the Modulational Instability in Microresonator Frequency Combs
A study is made of frequency comb generation described by the driven and
damped nonlinear Schr\"odinger equation on a finite interval. It is shown that
frequency comb generation can be interpreted as a modulational instability of
the continuous wave pump mode, and a linear stability analysis, taking into
account the cavity boundary conditions, is performed. Further, a truncated
three-wave model is derived, which allows one to gain additional insight into
the dynamical behaviour of the comb generation. This formalism describes the
pump mode and the most unstable sideband and is found to connect the coupled
mode theory with the conventional theory of modulational instability. An
in-depth analysis is done of the nonlinear three-wave model. It is demonstrated
that stable frequency comb states can be interpreted as attractive fixed points
of a dynamical system. The possibility of soft and hard excitation states in
both the normal and the anomalous dispersion regime is discussed.
Investigations are made of bistable comb states, and the dependence of the
final state on the way the comb has been generated. The analytical predictions
are verified by means of direct comparison with numerical simulations of the
full equation and the agreement is discussed.Comment: 9 pages, 6 figures, submitted to Phys. Rev.
Modulational instability of nonlinear polarization mode coupling in microresonators
We investigate frequency comb generation in the presence of polarization
effects induced by nonlinear mode coupling in microresonator devices. A set of
coupled temporal Lugiato-Lefever equations are derived to model the propagation
dynamics, and an in-depth study is made of the modulational instability of
their multistable homogeneous steady-state solutions. It is shown that new
kinds of instabilities can occur for co-propagating fields that interact
through nonlinear cross-phase modulation. These instabilities display
properties that differ from their scalar counterpart, and are shown to result
in the generation of new types of incoherently coupled frequency comb states.Comment: 8 pages, 7 figure
On the numerical simulation of Kerr frequency combs using coupled mode equations
It is demonstrated that Kerr frequency comb generation described by coupled
mode equations can be numerically simulated using Fast Fourier Transform
methods. This allows broadband frequency combs spanning a full octave to be
efficiently simulated using standard algorithms, resulting in orders of
magnitude improvements in the computation time.Comment: 3 pages, 1 figure, submitted to Optics Communication
Anyons on Higher Genus Surfaces - a Constructive Approach
We reconsider the problem of anyons on higher genus surfaces by embedding
them in three dimensional space. From a concrete realization based on three
dimensional flux tubes bound to charges moving on the surface, we explicitly
derive all the representations of the spinning braid group. The component
structure of the wave functions arises from winding the flux tubes around the
handles. We also argue that the anyons in our construction must fulfil the
generalized spin-statistics relation.Comment: 8 pages, LaTex, 2 figures available on request ([email protected]),
USITP-93-1
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