Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms

Generation of energetic (hot) electrons is an intrinsic property of any plasmonic nanostructure under illumination. Simultaneously, a striking advantage of metal nanocrystals over semiconductors lies in their very large absorption cross sections. Therefore, metal nanostructures with strong and tailored plasmonic resonances are very attractive for photocatalytic applications. However, the central questions regarding plasmonic hot electrons are how to quantify and extract the optically-excited energetic electrons in a nanocrystal. We develop a theory describing the generation rates and the energy-distributions of hot electrons in nanocrystals with various geometries. In our theory, hot electrons are generated owing to surfaces and hot spots. The formalism predicts that large optically-excited nanocrystals show the excitation of mostly low-energy Drude electrons, whereas plasmons in small nanocrystals involve mostly hot electrons. The energy distributions of electrons in an optically-excited nanocrystal show how the quantum many-body state in small particles evolves towards the classical state described by the Drude model when increasing nanocrystal size. We show that the rate of surface decay of plasmons in nanocrystals is directly related to the rate of generation of hot electrons. Based on a detailed many-body theory involving kinetic coefficients, we formulate a simple scheme describing the plasmon's dephasing. In most nanocrystals, the main decay mechanism of a plasmon is the Drude friction-like process and the secondary path comes from generation of hot electrons due to surfaces and electromagnetic hot spots. This latter path strongly depends on the size, shape and material of the nanocrystal, correspondingly affecting its efficiency of hot-electron production. The results in the paper can be used to guide the design of plasmonic nanomaterials for photochemistry and photodetectors.Comment: 90 pages, 21 figures, including Supplementary Informatio

Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2{\pi}]2 torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously (Chandler & Kerswell 2013) and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Over the extended torus at low forcing amplitudes, some extracted states mimick the statistics of the spatially-localised chaos present surprisingly well recalling the striking finding of Kawahara & Kida (2001) in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed

Clustering of spectra and fractals of regular graphs

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labelled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind.Comment: 10 pages, 5 figure

Efimov Physics in 6Li Atoms

A new narrow 3-atom loss resonance associated with an Efimov trimer crossing the 3-atom threshold has recently been discovered in a many-body system of ultracold 6Li atoms in the three lowest hyperfine spin states at a magnetic field near 895 G. O'Hara and coworkers have used measurements of the 3-body recombination rate in this region to determine the complex 3-body parameter associated with Efimov physics. Using this parameter as the input, we calculate the universal predictions for the spectrum of Efimov states and for the 3-body recombination rate in the universal region above 600 G where all three scattering lengths are large. We predict an atom-dimer loss resonance at (672 +/- 2) G associated with an Efimov trimer disappearing through an atom-dimer threshold. We also predict an interference minimum in the 3-body recombination rate at (759 +/- 1) G where the 3-spin mixture may be sufficiently stable to allow experimental study of the many-body system.Comment: 27 pages, 9 figures, REVTeX4, published versio

Three-body Recombination of Lithium-6 Atoms with Large Negative Scattering Lengths

The 3-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex valued. We provide semi-analytic expressions for the cases of 2 or 3 equal scattering lengths and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of Lithium-6 atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.Comment: 4 pages, 4 figures, agrees with published versio

Land classification of south-central Iowa from computer enhanced images

The author has identified the following significant results. Enhanced LANDSAT imagery was most useful for land classification purposes, because these images could be photographically printed at large scales such as 1:63,360. The ability to see individual picture elements was no hindrance as long as general image patterns could be discerned. Low cost photographic processing systems for color printings have proved to be effective in the utilization of computer enhanced LANDSAT products for land classification purposes. The initial investment for this type of system was very low, ranging from $100 to$200 beyond a black and white photo lab. The technical expertise can be acquired from reading a color printing and processing manual

Land Classification of South-central Iowa from Computer Enhanced Images

The author has identified the following significant results. Two enhanced false color negatives from multispectral scanner scenes, dated 15 April 1974 and 29 August 1972, were printed at a scale of 1:125,000 to form the basis for land use interpretations in the Wapello County, Iowa test site. The use of geomorphic principles proved valuable in the interpretation of the April scene to form valuable generalizations for planning purposes on soil associations, topography, alluvial valleys, and agricultural land use. The August scene was superior in providing information on urban extent, transportation networks, forest cover, and water bodies

Land classification of south-central Iowa from computer enhanced images

There are no author-identified singificant results in this report