On invariant sets in Lagrangian graphs

In this exposition, we show that a Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are smooth enough. We also provide some counterexamples for the case that the Hamiltonians are not smooth enough.Comment: 4 page

Temperature can enhance coherent oscillations at a Landau-Zener transition

We consider sweeping a system through a Landau-Zener avoided-crossing, when that system is also coupled to an environment or noise. Unsurprisingly, we find that decoherence suppresses the coherent oscillations of quantum superpositions of system states, as superpositions decohere into mixed states. However, we also find an effect we call "Lamb-assisted coherent oscillations", in which a Lamb shift exponentially enhances the coherent oscillation amplitude. This dominates for high-frequency environments such as super-Ohmic environments, where the coherent oscillations can grow exponentially as either the environment coupling or temperature are increased. The effect could be used as an experimental probe for high-frequency environments in such systems as molecular magnets, solid-state qubits, spin-polarized gases (neutrons or He3) or Bose-condensates.Comment: 4 Pages & 4 Figs - New version: introduction extended & citations adde

A History of Flips in Combinatorial Triangulations

Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of the various attempts to answer it.Comment: Added a paragraph referencing earlier work in the vertex-labelled setting that has implications for the unlabeled settin

Nowhere minimal CR submanifolds and Levi-flat hypersurfaces

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces.Comment: 21 pages; conjecture 2.8 was removed in proof; to appear in J. Geom. Ana

Development of flashlamp-pumped Q-switched Ho:Tm:Cr:YAG lasers for mid-infrared LIDAR application

A flashlamp-pumped 2.1 micron Ho:Tm:Cr:YAG laser was studied for both normal mode and Q-switched operations under a wide variety of experimental conditions in order to optimize performance. Laser output energy, slope efficiency, threshold and pulselength were determined as a function of operating temperature, output mirror reflectivity, input electrical energy and Q-switch opening time. The measured normal-mode laser thresholds of a Ho(3+) (0.45 atomic percent):Tm(3+) (2.5 atomic percent):Cr(3+) (0.8 atomic percent):YAG crystal ranged form 26 to 50 J between 120 and 200 K with slope efficiencies up to 0.36 percent with a 60 percent reflective output mirror. Under Q-switched operation the slope efficiency was 90 percent of the normal-mode result. Development of solid state lasers with Ho(3+), Tm(3+) and/or Er(3+) doped crystals has been pursued by NASA for eye-dafe mid-infrared LIDAR (light detection and ranging) application. As a part of the project, the authors have been working on evaluating Ho(3+):Tm(3+):Cr(3+):YAG crystals for normal-mode and Q-switched 2.1 micron laser operations in order to determine an optimum Tm(3+) concentration under flashlamp pumping conditions. Lasing properties of the Ho(3+) in the mid-infrared region have been studied by many research groups since the early 1960's. However, the technology of those lasers is still premature for lidar application. In order to overcome the inefficiency related to narrow absorption bands of the Ho(3+), Tm(3+) and Er(3+), the erbium has been replaced by chromium. The improvement in flashlamp-pumped Ho(3+) laser efficiency has been demonstrated recently by several research groups by utilizing the broad absorption spectrum of Cr(3+) which covers the flashlamp's emission spectrum. Efficient energy transfer to the Tm(3+) and then the Ho(3+) occurs subsequently. It is known that high Tm(3+) concentration and low Ho(3+) concentration are preferred to achieve a quantum efficiency approaching two and to avoid large reabsorption losses. However, determination of the optimum Tm(3+) concentration required to ensure efficient energy transfer from Cr(3+) to Tm(3+) and from Tm(3+) to Ho(3+) has not been made in the Ho:Tm:CR:YAG crystal. The results obtained so far are given

Twistor theory on a finite graph

We show how the description of a shear-free ray congruence in Minkowski space as an evolving family of semi-conformal mappings can naturally be formulated on a finite graph. For this, we introduce the notion of holomorphic function on a graph. On a regular coloured graph of degree three, we recover the space-time picture. In the spirit of twistor theory, where a light ray is the more fundamental object from which space-time points should be derived, the line graph, whose points are the edges of the original graph, should be considered as the basic object. The Penrose twistor correspondence is discussed in this context

Suppression of non-adiabatic phases by a non-Markovian environment: easier observation of Berry phases

We consider a two-level system coupled to a highly non-Markovian environment when the coupling axis rotates with time. The environment may be quantum (for example a bosonic bath or a spin bath) or classical (such as classical noise). We show that an Anderson orthogonality catastrophe suppresses transitions, so that the system's instantaneous eigenstates (parallel and anti-parallel to the coupling axis) can adiabatically follow the rotation. These states thereby acquire Berry phases; geometric phases given by the area enclosed by the coupling axis. Unlike in earlier proposals for environment-induced Berry phases, here there is little decoherence, so one does not need a decoherence-free subspace. Indeed we show that this Berry phase should be much easier to observe than a conventional one, because it is not masked by either the dynamic phase or the leading non-adiabatic phase. The effects that we discuss should be observable in any qubit device where one can drive three parameters in the Hamiltonian with strong man-made noise.Comment: 14 pages - v4 Extended and improved presentation (complete change of method and results w.r.t. version 1

Scientific investigations in the Gulf of Mexico and Caribbean Sea during the 1974-1975 Calypso cruise, parts 1 and 2

The distribution and concentrations of the standing crop of phytoplankton and nutrient salts in the Gulf of Mexico and the Caribbean Sea were investigated to provide ground truth for correlating temperature and chlorophyll-a measurements with observations from NASA U-2 aircraft equipped with specially designed sensors for measuring ocean color phenomena. The physical, chemical, and biological data obtained is summarized. Sampling procedures and methods used for determining plant pigments, species composition of phytoplankton, nutrient salt analysis, and the euphotic zones are described

On a Subposet of the Tamari Lattice

We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page