https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

We report a synthesis of highly luminescent (CdSe)ZnS composite quantum dots with CdSe cores ranging in diameter from 23 to 55 A. The narrow photoluminescence (fwhm ≤ 40 nm) from these composite dots spans most of the visible spectrum from blue through red with quantum yields of 30−50% at room temperature. We characterize these materials using a range of optical and structural techniques. Optical absorption and photoluminescence spectroscopies probe the effect of ZnS passivation on the electronic structure of the dots. We use a combination of wavelength dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, small and wide angle X-ray scattering, and transmission electron microscopy to analyze the composite dots and determine their chemical composition, average size, size distribution, shape, and internal structure. Using a simple effective mass theory, we model the energy shift for the first excited state for (CdSe)ZnS and (CdSe)CdS dots with varying shell thickness. Finally, we characterize the...

(CdSe)ZnS Core-Shell Quantum Dots - Synthesis and Characterization of a Size Series of Highly Luminescent Nanocrystallites

The field of nanoparticle research has drawn much attention in the past decade as a result of the search for new materials. Size confinement results in new electronic and optical properties, possibly suitable for many electronic and optoelectronic applications. A characteristic feature of noble metal nanoparticles is the strong color of their colloidal solutions, which is caused by the surface plasmon absorption. This article describes our studies of the properties of the surface plasmon absorption in metal nanoparticles that range in size between 10 and 100 nm. The effects of size, shape, and composition on the plasmon absorption maximum and its bandwidth are discussed. Furthermore, the optical response of the surface plasmon absorption due to excitation with femtosecond laser pulses allowed us to follow the electron dynamics (electron−electron and electron−phonon scattering) in these metal nanoparticles. It is found that the electron−phonon relaxation processes in nanoparticles, which are smaller than t...

Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods

Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

Diffusion in regular and disordered lattices

The problems associated with the poor convergence of the Fourier transform of the hard-sphere dielectric function are discussed. A significant band gap between the eighth and ninth levels has been found for air spheres in fcc. We also consider a periodic array of Gaussian spheres, which converges well and allows a consistent and reliable determination of the general features of photonic bands. It is found that when \ensuremath{\epsilon}(r) is sharply peaked, photonic levels become almost degenerate throughout the Brillouin zone, corresponding to standing waves.

Photonic bands: Convergence problems with the plane-wave method.

We present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear ${\ensuremath{\chi}}^{(2)}$ medium. We show that a 20-period, 12-\ensuremath{\mu}m structure can generate short SH pulses (similar in duration to pump pulses) whose energy and power levels may be 2--3 orders of magnitude larger than the energy and power levels produced by an equivalent length of a phase-matched, bulk medium. This phenomenon comes about as a result of the combination of high electromagnetic mode density of states, low group velocity, and spatial phase locking of the fields near the photonic band edge. The structure is designed so that the pump pulse is tuned near the first-order photonic band edge, and the SH signal is generated near the band edge of the second-order gap. This maximizes the density of available field modes for both the pump and SH field. Our results show that the ${\ensuremath{\chi}}^{(2)}$ response is effectively enhanced by several orders of magnitude. Therefore, mm- or cm-long, quasi-phase-matched devices could be replaced by these simple layered structures of only a few micrometers in length. This has important applications to high-energy lasers, Raman-type sources, and frequency up- and down-conversion schemes.

Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures

Controlled synthesis and quantum-size effect in gold-coated nanoparticles.

A novel basis for beam steering with electrowetting microprisms (EMPs) is reported. EMPs utilize electrowetting modulation of liquid contact angle in order to mimic the refractive behavior for various classical prism geometries. Continuous beam steering through an angle of 14 degrees (+/-7 degrees ) has been demonstrated with a liquid index of n=1.359. Experimental results are well-matched to theoretical behavior up to the point of electrowetting contact-angle saturation. Projections show that use of higher index liquids (n~1.6) will result in steering through ~30 degrees (+/-15 degrees ). Fundamental factors defining achievable deflection range, and issues for Ladar use, are reviewed. This approach is capable of good switching speed (~ms), polarization independent operation, modulation of beam field-of-view (lensing), and high steering efficiency that is independent of deflection angle.

Joseph W. Haus

Papers

Diffusion in regular and disordered lattices

Photonic bands: Convergence problems with the plane-wave method.

Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures

Controlled synthesis and quantum-size effect in gold-coated nanoparticles.

Agile wide-angle beam steering with electrowetting microprisms