Some boundary effects in quantum field theory

We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators, respectively, of a quantum harmonic oscillator on a circle. An expression for the effective coupling constant is obtained showing explicitly its dependence on the dimension of the box.Comment: 12 pages, Late

Semiclassical description of resonant tunneling

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field is used. The resulting semiclassical expression is written as the sum over special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall.Comment: LaTeX, 8 page

Atomic and nano-scale characterization of a 50-year-old hydrated C3S paste

This paper investigates the atomic and nano-scale structures of a 50-year-old hydrated alite paste. Imaged by TEM, the outer product C-S-H fibers are composed of particles that are 1.5-2 nm thick and several tens of nanometers long. 29Si NMR shows 47.9% Q1 and 52.1% Q2, with a mean SiO4 tetrahedron chain length (MCL) of 4.18, indicating a limited degree of polymerization after 50 years' hydration. A Scanning Transmission X-ray Microscopy (STXM) study was conducted on this late-age paste and a 1.5 year old hydrated C3S solution. Near Edge X-ray Absorption Fine Structure (NEXAFS) at Ca L3,2-edge indicates that Ca2 + in C-S-H is in an irregular symmetric coordination, which agrees more with the atomic structure of tobermorite than that of jennite. At Si K-edge, multi-scattering phenomenon is sensitive to the degree of polymerization, which has the potential to unveil the structure of the SiO44 - tetrahedron chain

Theory of 2δ\delta-kicked Quantum Rotors

We examine the quantum dynamics of cold atoms subjected to {\em pairs} of closely spaced $\delta$-kicks from standing waves of light, and find behaviour quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments [Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a regime of chaotic, anomalous classical diffusion. We show that the corresponding quantum phase-space has a cellular structure, arising from a unitary matrix with oscillating band-width. The corresponding eigenstates are exponentially localized, but scale with a fractional power, $L \sim \hbar^{-0.75}$, in contrast to the QKR for which $L \sim \hbar^{-1}$. The effect of inter-cell (and intra-cell) transport is investigated by studying the spectral fluctuations with both periodic as well as `open' boundary conditions.Comment: 12 pages with 14 figure

Using the critical set to induce bifurcations

For a function $F: X \to Y$ between real Banach spaces, we show how continuation methods to solve $F(u) = g$ may improve from basic understanding of the critical set $C$ of $F$. The algorithm aims at special points with a large number of preimages, which in turn may be used as initial conditions for standard continuation methods applied to the solution of the desired equation. A geometric model based on the sets $C$ and $F^{-1}(F(C))$ substantiate our choice of curves $c \in X$ with abundant intersections with $C$. We consider three classes of examples. First we handle functions $F: R^2 \to R^2$, for which the reasoning behind the techniques is visualizable. The second set of examples, between spaces of dimension 15, is obtained by discretizing a nonlinear Sturm-Liouville problem for which special points admit a high number of solutions. Finally, we handle a semilinear elliptic operator, by computing the six solutions of an equation of the form $-\Delta - f(u) = g$ studied by Solimini.Comment: 23 pages, 14 figure