352 research outputs found
Ion implantation damage of silicon as observed by optical reflection spectroscopy in the 1 to 6 eV region
Optical reflection spectra of crystalline, sputtered, and ion implanted silicon specimens are presented. Characteristic aspects of the spectra of ion implanted specimens are related to lattice damage
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Individual complex Dirac eigenvalue distributions from random matrix theory and lattice QCD at nonzero chemical potential
We analyze how individual eigenvalues of the QCD Dirac operator at nonzero chemical potential are distributed in the complex plane. Exact and approximate analytical results for such distributions are derived from non-Hermitian random matrix theory. When comparing these to lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class
Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results
For QCD at non-zero chemical potential , the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from random matrix theory (RMT). We distinguish two cases depending on the parameter , where is the volume and is the familiar low-energy constant of chiral perturbation theory. For small , we use a Fredholm determinant expansion and observe that already the first few terms give an excellent approximation. For large , all spectral correlations are rotationally invariant, and exact results can be derived. We compare the RMT predictions to lattice data and in both cases find excellent agreement in the topological sectors
Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
We analyze how individual eigenvalues of the QCD Dirac operator at nonzero
quark chemical potential are distributed in the complex plane. Exact and
approximate analytical results for both quenched and unquenched distributions
are derived from non-Hermitian random matrix theory. When comparing these to
quenched lattice QCD spectra close to the origin, excellent agreement is found
for zero and nonzero topology at several values of the quark chemical
potential. Our analytical results are also applicable to other physical systems
in the same symmetry class.Comment: 4 pages, 4 figures, minor changes, as published in Phys. Rev. Let
Optical Reflection Studies of Damage in Ion Implanted Silicon
Optical (3–6.5 eV) reflection spectra are presented for crystalline Si implanted at room temperature with 40 keV Sb ions to doses of less than 2×10^15/cm^2. These spectra, and their deviation from the reflection spectrum of crystalline Si, are discussed in terms of a model based on the average dielectric properties of the implanted region. For samples having a high ion dose (>10^15/cm^2) the observed spectra resemble the spectra of sputtered Si films. Anneal characteristics of the reflection spectra are found to be dose dependent. These observations are compared to, and found to substantiate, the results of other experimental techniques for studying lattice damage in Si
Inflectional loci of scrolls
Let be a scroll over a smooth curve and let
\L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special
geometry of implies that some sheaves related to the principal part bundles
of \L are locally free. The inflectional loci of can be expressed in
terms of these sheaves, leading to explicit formulas for the cohomology classes
of the loci. The formulas imply that the only uninflected scrolls are the
balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif
Two dimensional fermions in three dimensional YM
Dirac fermions in the fundamental representation of SU(N) live on the surface
of a cylinder embedded in and interact with a three dimensional SU(N)
Yang Mills vector potential preserving a global chiral symmetry at finite .
As the circumference of the cylinder is varied from small to large, the chiral
symmetry gets spontaneously broken in the infinite limit at a typical bulk
scale. Replacing three dimensional YM by four dimensional YM introduces
non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table
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