The Melody of Living Water: Music Ministry and Holy Baptism

(Excerpt) And It came to pass, when Paul was at Corinth, he and certain disciples came upon a mob that was stoning an organist. And Paul said unto them, What then hath he done unto thee that his head should be bruised? And the people cried with one voice, He hath played too loud. Yea, in the singing of psalms, he maketh our heads to ring as if they were beaten with hammers. Behold, he sitteth up high in the loft, and mighty are the pipes and mighty is the noise thereof, and though there be few of us below, he nonetheless playeth with all the stops, the Assyrian trumpet stop and the stop of the ram\u27s hom and the stop that soundeth like the sawing of stone, and we cannot hear the words that cometh out of our own mouths. He / always tosseth in variations that confuse us mightily and he playeth loud an discordant and always in a militant tempo, so that we have not time to breathe as we sing. Lo, he is a plague upon the faith and should be chastised. Paul, hearing this, had himself picked up a small stone, and was about to cast it, but he set It down, and bade the organist come forward. He was a narrow man, pale of complexion, dry flaking, thin of hair. And Paul said unto him, Why hath thou so abused thy brethren? And the organist replied, I could not hear them singing from where I sat, and therefore played the louder so as to encourage them. And Paul turned round to the mob and said loudly, Let him who has never played an organ cast the first stone. And they cast stones for a while until their arms were tired and Paul bade the organist repent and he did. And Paul said unto him, Thou shalt take up the flute and play It for thirty days, to cleanse thy spirit, and afterwards they returned to Corinth and sang psalms unaccompanied and then had coffee and were refreshed in the faith

Complex non-equilibrium dynamics in plasmas

Two new forms of strongly coupled plasmas will be discussed. They have become possible to create and observe in the laboratory only recently and exhibit a wealth of intriguing complex behavior which can be studied, in many cases for the first time, experimentally. Plasmas, gases of charged particles, are universal in the sense that certain properties of complex behavior do only depend on ratios of characteristic parameters of the plasma, not on the parameters themselves. Therefore, it is of fundamental and far reaching consequence, to be able to create and observe a strongly coupled plasma since its behavior is paradigmatic for an entire class of plasmas.Comment: 14 pages, to be published in European Revie

Dissipative Dicke Model with Collective Atomic Decay: Bistability, Noise-Driven Activation and Non-Thermal First Order Superradiance Transition

The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to e.g. atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced, collective decay of an excitation that is shared by $N$ atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by non-thermal, markovian noise. The interplay between dissipative and coherent elements leads to a genuine non-equilibrium dynamics in the bistable regime, which is expressed via a non-conservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke Model become exact in the large-$N$-limit. The absence of an effective free energy functional, however, necessitates to include fluctuation corrections with $\mathcal{O}(1/N)$ for finite $N<\infty$ to locate the non-thermal first-order phase transition between the superradiant and the empty cavity.Comment: as published in Physical Review

Large isoperimetric surfaces in initial data sets

We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all sufficiently large volumes, and that they are close to centered coordinate spheres. This implies that the volume-preserving stable constant mean curvature spheres constructed by G. Huisken and S.-T. Yau as well as R. Ye as perturbations of large centered coordinate spheres minimize area among all competing surfaces that enclose the same volume. This confirms a conjecture of H. Bray. Our results are consistent with the uniqueness results for volume-preserving stable constant mean curvature surfaces in initial data sets obtained by G. Huisken and S.-T. Yau and strengthened by J. Qing and G. Tian. The additional hypotheses that the surfaces be spherical and far out in the asymptotic region in their results are not necessary in our work.Comment: 29 pages. All comments welcome! This is the final version to appear in J. Differential Geo

Preferred Parameterisations on Homogeneous Curves

We show how to specify preferred parameterisations on a homogeneous curve in an arbitrary homogeneous space. We apply these results to limit the natural parameters on distinguished curves in parabolic geometries.Comment: 10 page

Conformally Fedosov manifolds

We introduce the notion of a conformally Fedosov structure and construct an associated Cartan connection. When an appropriate curvature vanishes, this allows us to construct a family of natural differential complexes akin to the BGG complexes from parabolic geometry.Comment: 28 pages. This is a substantial update to include BGG machinery and the construction of differential complexe