Domain Wall Fermions with Exact Chiral Symmetry

We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note that the method can be used for both quenched and dynamical calculations. We test the method using smooth and thermalized gauge field configurations. We also make comparisons of the performance (cost) of the domain wall operator for spectroscopy compared to other methods such as the overlap-Dirac operator and find both methods are comparable in cost.Comment: revtex, 37 pages, 11 color postscript figure

Signal enhancement of the in-plane and out-of-plane Rayleigh wave components

Several groups have reported an enhancement of the ultrasonic Rayleigh wave when scanning close to a surface-breaking defect in a metal sample. This enhancement may be explained as an interference effect where the waves passing directly between source and receiver interfere with those waves reflected back from the defect. We present finite element models of the predicted enhancement when approaching a defect, along with experiments performed using electromagnetic acoustic transducers sensitive to either in-plane or out-of-plane motion. A larger enhancement of the in-plane motion than the out-of-plane motion is observed and can be explained by considering ultrasonic reflections and mode conversion at the defect

Residual Chiral Symmetry Breaking in Domain-Wall Fermions

We study the effective quark mass induced by the finite separation of the domain walls in the domain-wall formulation of chiral fermion as the function of the size of the fifth dimension ($L_s$), the gauge coupling $\beta$ and the physical volume $V$. We measure the mass by calculating the small eigenvalues of the hermitian domain-wall Dirac operator ($H_{\rm DWF}(m_0))$ in the topologically-nontrivial quenched SU(3) gauge configurations. We find that the induced quark mass is nearly independent of the physical volume, decays exponentially as a function of $L_s$, and has a strong dependence on the size of quantum fluctuations controlled by $\beta$. The effect of the choice of the lattice gluon action is also studied.Comment: 12 pages, 7 figure

Non-linear enhancement of laser generated ultrasonic Rayleigh waves by cracks

Laser generated ultrasound has been widely used for detecting cracks, surface and sub-surface defects in many different materials. It provides a non-contact wideband excitation source which can be focused into different geometries. Previous workers have reported enhancement of the laser generated Rayleigh wave when a crack is illuminated by pulsed laser beam irradiation. We demonstrate that the enhancement observed is due to a combination of source truncation, the free boundary condition at the edge of the crack and interference effects. Generating a Rayleigh wave over a crack can lead to enhancement of the amplitude of the Rayleigh wave signal, a shift in the dominant frequency of the wideband Rayleigh wave and strong enhancement of the high frequency components of the Rayleigh wave

Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background

In the domain-wall formulation of chiral fermion, the finite separation between domain-walls ($L_s$) induces an effective quark mass ($m_{\rm eff}$) which complicates the chiral limit. In this work, we study the size of the effective mass as the function of $L_s$ and the domain-wall height $m_0$ by calculating the smallest eigenvalue of the hermitian domain-wall Dirac operator in the topologically-nontrivial background fields. We find that, just like in the free case, $m_{\rm eff}$ decreases exponentially in $L_s$ with a rate depending on $m_0$. However, quantum fluctuations amplify the wall effects significantly. Our numerical result is consistent with a previous study of the effective mass from the Gell-Mann-Oakes-Renner relation.Comment: 10 pages, an appendix and minor changes adde

An alternative to domain wall fermions

We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of $H$ and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alternative to domain wall fermions in the context of numerical QCD.Comment: Revtex Latex, 26 pages, 1 figure, a few minor change

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

A size-dependent strain relaxation and its effects on the optical properties of InGaN/GaN multiple quantum wells (QWs) in micro-pillars have been investigated through a combination of high spatial resolution cathodoluminescence (CL) hyperspectral imaging and numerical modeling. The pillars have diameters (d) ranging from 2 to 150 μm and were fabricated from a III-nitride light-emitting diode (LED) structure optimized for yellow-green emission at ∼560 nm. The CL mapping enables us to investigate strain relaxation in these pillars on a sub-micron scale and to confirm for the first time that a narrow (≤2 μm) edge blue-shift occurs even for the large InGaN/GaN pillars (d > 10 μm). The observed maximum blue-shift at the pillar edge exceeds 7 nm with respect to the pillar centre for the pillars with diameters in the 2–16 μm range. For the smallest pillar (d = 2 μm), the total blue-shift at the edge is 17.5 nm including an 8.2 nm “global” blue-shift at the pillar centre in comparison with the unetched wafer. By using a finite element method with a boundary condition taking account of a strained GaN buffer layer which was neglected in previous simulation works, the strain distribution in the QWs of these pillars was simulated as a function of pillar diameter. The blue-shift in the QWs emission wavelength was then calculated from the strain-dependent changes in piezoelectric field, and the consequent modification of transition energy in the QWs. The simulation and experimental results agree well, confirming the necessity for considering the strained buffer layer in the strain simulation. These results provide not only significant insights into the mechanism of strain relaxation in these micro-pillars but also practical guidance for design of micro/nano LEDs