An explicit Schr\"odinger picture for Aharonov's Modular Variable concept

We propose to address in a natural manner, the modular variable concept explicitly in a Schr\"odinger picture. The idea of Modular Variables was introduced in 1969 by Aharonov, Pendleton and Petersen to explain certain non-local properties of quantum mechanics. Our approach to this subject is based on Schwinger's finite quantum kinematics and it's continuous limit.Comment: 16 pages, 9 figure

Theta Vectors and Quantum Theta Functions

In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector in comparison with the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no more meaningful. We explain why Manin's quantum theta function obtained via algebra (quantum tori) valued inner product of the theta vector is a natural choice for quantum version of the classical theta function (kq representation). We then show that this approach holds for a more general theta vector with constant obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in the Manin's construction. We further discuss the properties of the theta vector and of the quantum theta function, both of which have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in the tex

Peptide-mediated growth and dispersion of Au nanoparticles in water via sequence engineering

YesThe use of peptides to nucleate, grow, and stabilize nanoparticles in aqueous media via non-covalent interactions offers new possibilities for creating functional, water-dispersed inorganic/organic hybrid materials, particularly for Au nanoparticles. Numerous previous studies have identified peptide sequences that both possess a strong binding affinity for Au surfaces and are capable of supporting nanoparticle growth in water. However, recent studies have shown that not all such peptide sequences can produce stable dispersions of these nanoparticles. Here, via integrated experiments and molecular modeling, we provide new insights into the many factors that influence Au nanoparticle growth and stabilization in aqueous media. We define colloidal stability by the absence of visible precipitation after at least 24 hours post-synthesis. We use binding affinity measurements, nanoparticle synthesis, characterization and stabilization assays, and molecular modeling, to investigate a set of sequences based on two known peptides with strong affinity for Au. This set of biomolecules is designed to probe specific sequence and context effects using both point mutations and global reorganization of the peptides. Our data confirm, for a broader range of sequences, that Au nanoparticle/peptide binding affinity alone is not predictive of peptide-mediated colloidal stability. By comparing nanoparticle stabilization assay outcomes with molecular simulations, we establish a correlation between the colloidal stability of the Au nanoparticles and the degree of conformational diversity in the surface-adsorbed peptides. Our findings suggest future routes to engineer peptide sequences for bio-based growth and dispersion of functional nanoparticles in aqueous media.Air Office of Scientific Research, grant number FA9550-12-1-0226

Novel Nanocrystalline Intermetallic Coatings for Metal Alloys in Coal-fired Environments

Intermetallic coatings (iron aluminide and nickel aluminide) were prepared by a novel reaction process. In the process, the aluminide coating is formed by an in-situ reaction between the aluminum powder fed through a plasma transferred arc (PTA) torch and the metal substrate (steel or Ni-base alloy). Subjected to the high temperature within an argon plasma zone, aluminum powder and the surface of the substrate melt and react to form the aluminide coatings. The prepared coatings were found to be aluminide phases that are porosity-free and metallurgically bonded to the substrate. The coatings also exhibit excellent high-temperature corrosion resistance under the conditions which simulate the steam-side and fire-side environments in coal-fired boilers. It is expected that the principle demonstrated in this process can be applied to the preparation of other intermetallic and alloy coatings

Development of Bulk Nanocrystalline Cemented Tungsten Carbide for Industrial Applicaitons

This report contains detailed information of the research program entitled "Development of Bulk Nanocrystalline Cemented Tungsten Carbide Materials for Industrial Applications". The report include the processes that were developed for producing nanosized WC/Co composite powders, and an ultrahigh pressure rapid hot consolidation process for sintering of nanosized powders. The mechanical properties of consolidated materials using the nanosized powders are also reported

Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands

We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a DC or AC electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and the energy subbands in the Hofstadter spectrum. Based on this formalism, the pattern of band splitting, the distribution of Hall conduct- ivities, and the positions of energy subbands in the Hofstadter spectrum can be understood in a simple and unified picture.Comment: 26 pages, Revtex, 6 figures included, submitted to Phys.Rev.

Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.Comment: 12 pages, RevTe

Conductivity of 2D lattice electrons in an incommensurate magnetic field

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\phi$ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we consider a series of systems with commensurate fluxes which converge to the irrational value. We have calculated a real part of the longitudinal conductivity $\sigma_{xx}(\omega)$. Using a scaling analysis, we have found $\Re\sigma_{xx}(\omega)$ behaves as $1/\omega ^{\gamma}$ \,$(\gamma =0.55)$ when $\phi =\tau,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.Comment: 16 pages, postscript files are available on reques