Assessing the performance of protective winter covers for outdoor marble statuary: pilot investigation

Outdoor statuary in gardens and parks in temperate climates has a tradition of being covered during the winter, to protect against external conditions. There has been little scientific study of the environmental protection that different types of covers provide. This paper examines environmental conditions provided by a range of covers used to protect marble statuary at three sites in the UK. The protection required depends upon the condition of the marble. Although statues closely wrapped and with a layer of insulation provide good protection, this needs to be considered against the potential physical damage of close wrapping a fragile deteriorated surface

Quantum Spin Hall Effect and Topologically Invariant Chern Numbers

We present a topological description of quantum spin Hall effect (QSHE) in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a $2\times 2$ traceless matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlin's gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states, and determine a phase diagram for the QSHE.Comment: 4 pages and 4 figure

Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property

The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be controlled by Berry phases accumulated by adiabatic motion of quasiparticles on the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi sea property like Landau diamagnetism, as has been previously supposed. Berry phases are a new topological ingredient that must be added to Landau Fermi-liquid theory in the presence of broken inversion or time-reversal symmetry.Comment: 4 pages, 0 figures; to appear in Physical Review Letters; cleaner form of main formula+note added confirming continued validity of result in interacting Fermi liquids: + improved summary paragraph stating result; final published version (minor changes

Persistent Currents in Quantum Chaotic Systems

The persistent current of ballistic chaotic billiards is considered with the help of the Gutzwiller trace formula. We derive the semiclassical formula of a typical persistent current $I^{typ}$ for a single billiard and an average persistent current $$ for an ensemble of billiards at finite temperature. These formulas are used to show that the persistent current for chaotic billiards is much smaller than that for integrable ones. The persistent currents in the ballistic regime therefore become an experimental tool to search for the quantum signature of classical chaotic and regular dynamics.Comment: 4 pages (RevTex), to appear in Phys. Rev. B, No.59, 12256-12259 (1999

Quantum Flux and Reverse Engineering of Quantum Wavefunctions

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wavefunction, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wavefunction.Comment: Accepted to EP

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Fluctuations of wave functions about their classical average

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.

Holonomic quantum computation in the presence of decoherence

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian decoherence.Comment: I. F-G. Now publishes under name I. Fuentes-Schuller Published versio

Periodic-Orbit Theory of Anderson Localization on Graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in one dimension. The exact expression for the probability to return of an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families are performed analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe