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.

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

Friends and Symptom Dimensions in Patients with Psychosis: A Pooled Analysis

PMCID: PMC3503760This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Gamma-Ray Bursts from Primordial Quark Objects in Space

We investigate the possibility that gamma-ray bursts originate in a concentric spherical shell with a given average redshift and find that this is indeed compatible with the data from the third BATSE (3B) catalog. It is also shown that there is enough freedom in the choice of unknown burst properties to allow even for extremely large distances to the majority of bursts. Therefore, we speculate about an early, and very energetic, origin of bursts, and suggest that they come from phase transitions in massive objects of pure quark matter, left over from the Big Bang.Comment: 11 pages, Latex, 3 postscript figures, to be publ in the Proc of the Joint Meeting of the Networks 'The Fundamental Structure of Matter' and 'Tests of the Electroweak Symmetry Breaking', Ouranoupolis, Greece, May 199

Charge and Current in the Quantum Hall Matrix Model

We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low momenta -- this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. These results show that the classical quantum Hall matrix models describe important aspects of the dynamics of electrons in the lowest Landau level. In the quantum theory the ordering ambiguities are more severe; we discuss possible strategies, but we have not been able to construct a good density operator, satisfying the pertinent lowest Landau level commutator algebra.Comment: 12 pages, no figures; a logical error below the proposed density operator (46) in version 1 is corrected, and the claim that this density operator satisfy the magnetic algebra (2) is withdrawn. Some formulations have been changed and a few misprints correcte