Strongly Coupled Matter-Field and Non-Analytic Decay Rate of Dipole Molecules in a Waveguide

The decay rate \gam of an excited dipole molecule inside a waveguide is evaluated for the strongly coupled matter-field case near a cutoff frequency \ome_c without using perturbation analysis. Due to the singularity in the density of photon states at the cutoff frequency, we find that \gam depends non-analytically on the coupling constant $\ggg$ as $\ggg^{4/3}$. In contrast to the ordinary evaluation of \gam which relies on the Fermi golden rule (itself based on perturbation analysis), \gam has an upper bound and does not diverge at \ome_c even if we assume perfect conductance in the waveguide walls. As a result, again in contrast to the statement found in the literature, the speed of emitted light from the molecule does not vanish at \ome_c and is proportional to $c\ggg^{2/3}$ which is on the order of $10^3 \sim 10^4$ m/s for typical dipole molecules.Comment: 4 pages, 2 figure

Hydrodynamical Modeling of a Multiple‐Inlet Estuary/Barrier System: Insight Into Tidal Inlet Formation and Stability

Two specific questions are addressed concerning the role of tidal hydrodynamics in determining the long‐term morphologic evolution of the Nauset Beach‐Monomoy Island barrier system and the Chatham Harbor‐Pleasant Bay tidal estuary, Massachusetts: (1) why do the barrier and estuary exhibit a long‐term (∼150 yr) cycle of new inlet formation, and (2) once a new inlet forms, why is the resulting multiple inlet system unstable? To address these questions, a branched 1‐d numerical model is used to recreate the basic flow patterns in the tidal estuary at ten‐year intervals during the last half century and also to recreate flow conditions shortly before and shortly after the formation of the new inlet. Results suggest that an inlet will form through Nauset Beach once southerly elongation of the barrier has led to a critical head across the barrier at high tide. If this critical head (enhanced by storm surge and wave set‐up) exists at high tide during consecutive tidal cycles, flood currents can deepen the overwash channel sufficiently to enable the stronger ebb currents to complete the formation process. Once a new inlet has formed, the surface gradient and tidal discharge are drastically reduced along the pre‐existing channel to the south of the inlet. This reduction eliminates the tidal scouring action needed to keep the channel open. Rapid shoaling within the channel to the south of the new inlet completes the hydrodynamic decoupling of the northern and southern sections of the estuary.https://scholarworks.wm.edu/vimsbooks/1037/thumbnail.jp

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio

Smooth adiabatic evolutions with leaky power tails

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

On hybrid states of two and three level atoms

We calculate atom-photon resonances in the Wigner-Weisskopf model, admitting two photons and choosing a particular coupling function. We also present a rough description of the set of resonances in a model for a three-level atom coupled to the photon field. We give a general picture of matter-field resonances these results fit into.Comment: 33 pages, 12 figure

Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation

Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. Here, we introduce a new class of moves based on nonequilibrium dynamics: candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution. The acceptance rule is similar to the Metropolis acceptance probability, but related to the nonequilibrium work rather than the instantaneous energy difference. Our method is applicable to sampling from both a single thermodynamic state or a mixture of thermodynamic states, and allows both coordinates and thermodynamic parameters to be driven in nonequilibrium proposals. While generating finite-time switching trajectories incurs an additional cost, driving some degrees of freedom while allowing others to evolve naturally can lead to large enhancements in acceptance probabilities, greatly reducing structural correlation times. Using nonequilibrium driven processes vastly expands the repertoire of useful Monte Carlo proposals in simulations of dense solvated systems

Mechanisms Driving Decadal Changes in the Carbonate System of a Coastal Plain Estuary

Understanding decadal changes in the coastal carbonate system is essential for predicting how the health of these waters responds to anthropogenic drivers, such as changing atmospheric conditions and riverine inputs. However, studies that quantify the relative impacts of these drivers are lacking. In this study, the primary drivers of decadal trends in the surface carbonate system, and the spatiotemporal variability in these trends, are identified for a large coastal plain estuary: the Chesapeake Bay. Experiments using a coupled three-dimensional hydrodynamic-biogeochemical model highlight that, over the past three decades, the changes in the surface carbonate system of Chesapeake Bay have strong seasonal and spatial variability. The greatest surface pH and aragonite saturation state (ΩAR) reductions have occurred in the summer in the middle (mesohaline) Bay: −0.24 and −0.9 per 30 years, respectively, with increases in atmospheric CO2 and reductions in nitrate loading both being primary drivers. Reductions in nitrate loading have a strong seasonal influence on the carbonate system, with the most pronounced decadal decreases in pH and ΩAR occurring during the summer when primary production is strongly dependent on nutrient availability. Increases in riverine total alkalinity and dissolved inorganic carbon have raised surface pH in the upper oligohaline Bay, while other drivers such as atmospheric warming and input of acidified ocean water through the Bay mouth have had comparatively minor impacts on the estuarine carbonate system. This work has significant implications for estuarine ecosystem services, which are typically most sensitive to surface acidification in the spring and summer seasons

The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System

It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for this matter model as many families of this type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweighted Sobolev spaces for a wave equation satisfied by the second fundamental form of a maximal foliation.Comment: 24 pages, plain TE

Secchi disk measurements in turbid water

In the classical theory of the Secchi disk depth, diffuse sunlight falling on the disk is reflected back to the observer’s eye along the most direct route, as a beam. The disappearance depth, ZSD, of the disk is then expected to vary inversely with the sum of the beam and diffuse attenuation coefficients: c+KD. Observations presented here show that, in the most turbid waters sampled, the Secchi disk is visible at greater depths (by a factor of up to 4) than predicted by this theory. In these conditions, the disk appears blurry and it seems likely that some of the light reflected by the disk returns to the eye as diffuse light, photons being scattered one or more times on their journey from the disk surface to the observer. We have modified the theory of the Secchi disk in turbid water to allow for a mixture of beamed and diffuse light contributing to disk visibility. The modified theory corrects the under-estimate of Secchi depths in turbid waters and gives good agreement with observations over a wide range of turbidity. The insight gained allows a more informed interpretation of Secchi disk measurements in turbid water. Supplemental data files: https://doi.org/10.25773/z8qm-c77