10,978 research outputs found
Dual pumped microresonator frequency combs
A study is made of the nonlinear dynamics of dual pumped microresonator Kerr
frequency combs described by a driven and damped nonlinear Schr\"odinger
equation, with an additional degree of freedom in the form of the modulation
frequency. A truncated four wave model is derived for the pump modes and the
dominant sideband pair which is found to be able to describe much of the
essential dynamical behaviour of the full equation. The stability of stationary
states within the four wave model is investigated and numerical simulations are
made to demonstrate that a large range of solutions, including cavity solitons,
are possible beyond previously considered low intensity patterns.Comment: 7 pages, 9 figures, submitted to Phys. Rev.
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
Is Dark Matter made up of Massive Quark Objects?
We suggest that dark matter is made up of massive quark objects that have
survived from the Big Bang, representing the ground state of ``baryonic''
matter. Hence, there was no overall phase transition of the original quark
matter, but only a split-up into smaller objects. We speculate that normal
hadronic matter comes about through enforced phase transitions when such
objects merge or collide, which also gives rise to the cosmic gamma-ray bursts.Comment: 8 pages Latex, no figures; to be published in the Proceedings of Dark
'98, Heidelberg, July 199
Distributed Interior-point Method for Loosely Coupled Problems
In this paper, we put forth distributed algorithms for solving loosely
coupled unconstrained and constrained optimization problems. Such problems are
usually solved using algorithms that are based on a combination of
decomposition and first order methods. These algorithms are commonly very slow
and require many iterations to converge. In order to alleviate this issue, we
propose algorithms that combine the Newton and interior-point methods with
proximal splitting methods for solving such problems. Particularly, the
algorithm for solving unconstrained loosely coupled problems, is based on
Newton's method and utilizes proximal splitting to distribute the computations
for calculating the Newton step at each iteration. A combination of this
algorithm and the interior-point method is then used to introduce a distributed
algorithm for solving constrained loosely coupled problems. We also provide
guidelines on how to implement the proposed methods efficiently and briefly
discuss the properties of the resulting solutions.Comment: Submitted to the 19th IFAC World Congress 201
Quantum Hall Physics - hierarchies and CFT techniques
The fractional quantum Hall effect, being one of the most studied phenomena
in condensed matter physics during the past thirty years, has generated many
groundbreaking new ideas and concepts. Very early on it was realized that the
zoo of emerging states of matter would need to be understood in a systematic
manner. The first attempts to do this, by Haldane and Halperin, set an agenda
for further work which has continued to this day. Since that time the idea of
hierarchies of quasiparticles condensing to form new states has been a pillar
of our understanding of fractional quantum Hall physics. In the thirty years
that have passed since then, a number of new directions of thought have
advanced our understanding of fractional quantum Hall states, and have extended
it in new and unexpected ways. Among these directions is the extensive use of
topological quantum field theories and conformal field theories, the
application of the ideas of composite bosons and fermions, and the study of
nonabelian quantum Hall liquids. This article aims to present a comprehensive
overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure
Higgs Pain? Take a Preon!
The Higgs mechanism is the favourite cure for the main problem with
electroweak unification, namely how to reconcile a gauge theory with the need
for massive gauge bosons. This problem does not exist in preon models for quark
and lepton substructure with composite and s, which, consequently,
also avoid all other theoretical complications and paradoxes with the Higgs
mechanism. We present a new, minimal preon model, which explains the family
structure, and predicts several new, heavy quarks, leptons and vector bosons.
Our preons obey a phenomenological supersymmetry, but without so-called squarks
and sleptons, since this SUSY is effective only on the composite scale.Comment: The preon contents of some quarks and leptons have been changed in
order to achieve a more consistent scheme. A few new comments have been
added. 13 pages, LaTeX, no figures. To be published in Proc. of the Meeting
on 'The Fundamental Structure of Matter' and 'Tests of the Electroweak
Symmetry Breaking', Ouranoupolis, Greece, May 199
Preon Trinity
We present a new minimal model for the substructure of all known quarks,
leptons and weak gauge bosons, based on only three fundamental and stable
spin-1/2 preons. As a consequence, we predict three new quarks, three new
leptons, and six new vector bosons. One of the new quarks has charge .
The model explains the apparent conservation of three lepton numbers, as well
as the so-called Cabibbo-mixing of the and quarks, and predicts
electromagnetic decays or oscillations between the neutrinos
() and (). Other neutrino oscillations, as well
as rarer quark mixings and CP violation can come about due to a small
quantum-mechanical mixing of two of the preons in the quark and lepton wave
functions.Comment: 5 pages, Latex, no figure
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