In-betweenness: a geometric monotonicity property for operator means

We introduce the notions of in-betweenness and monotonicity with respect to a metric, for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity. We exhibit two classes of non-trivial means that are monotonic with respect to the Euclidean metric. We also show that all Kubo-Ando means are monotonic with respect to the trace metric, which is the natural metric for the geometric mean.Comment: 15 pages; a preliminary version has been presented at the June 2010 ILAS Conference in Pisa, Ital

Fermi edge singularities in X-ray spectra of strongly correlated fermions

We discuss the problem of the X-ray absorption in a system of interacting fermions and, in particular, those features in the X-ray spectra that can be used to discriminate between conventional Fermi-liquids and novel "strange metals". Focusing on the case of purely forward scattering off the core-hole potential, we account for the relevant interactions in the conduction band by means of the bosonization technique. We find that the X-ray Fermi edge singularities can still be present, although modified, even if the density of states vanishes at the Fermi energy, and that, in general, the relationship between the two appears to be quite subtle.Comment: Latex, 16 pages, Princeton preprin

Alignment verification for electron beam lithography

Alignment between lithography layers is essential for device fabrication. A minor defect in a single marker can lead to incorrect alignment and this can be the source of wafer reworks. In this paper we show that this can be prevented by using extra alignment markers to check the alignment during patterning, rather than inspecting vernier patterns after the exposure is completed. Accurate vernier patterns can often only be read after pattern transfer has been carried out. We also show that by using a Penrose tile as a marker it is possible to locate the marker to about 1 nm without fully exposing the resist. This means that the marker can be reused with full accuracy, thus improving the layer to layer alignment accuracy. Lithography tool noise limits the process

Stability Walls in Heterotic Theories

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure

Relativistic Solenoids

We construct a general relativistic analogy of an infinite solenoid, i.e., of an infinite cylinder with zero electric charge and non-zero electric current in the direction tangential to the cylinder and perpendicular to its axis. We further show that the solution has a good weak-field limit.Comment: 9 pages, 2 figure

Odd Parity and Line Nodes in Heavy Fermion Superconductors

Group theory arguments have demonstrated that a general odd parity order parameter cannot have line nodes in the presence of spin-orbit coupling. In this paper, it is shown that these arguments do not hold on the $k_z = \pi/c$ zone face of a hexagonal close packed lattice. In particular, three of the six odd parity representations vanish identically on this face. This has potential relevance to the heavy fermion superconductor $UPt_3$.Comment: 5 pages, revte

Ground State Energy of the One-Dimensional Discrete Random Schr\"{o}dinger Operator with Bernoulli Potential

In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable \ell_N, the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that for almost every realization of the potential the ground state energy behaves asymptotically as $\frac{\pi^2}{\ell_N+1)^2}$ in the sense that the ratio of the quantities goes to one

Vacuum polarization in two-dimensional static spacetimes and dimensional reduction

We obtain an analytic approximation for the effective action of a quantum scalar field in a general static two-dimensional spacetime. We apply this to the dilaton gravity model resulting from the spherical reduction of a massive, non-minimally coupled scalar field in the four-dimensional Schwarzschild geometry. Careful analysis near the event horizon shows the resulting two-dimensional system to be regular in the Hartle-Hawking state for general values of the field mass, coupling, and angular momentum, while at spatial infinity it reduces to a thermal gas at the black-hole temperature.Comment: REVTeX 4, 23 pages. Accepted by PRD. Minor modifications from original versio

Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

Analytical approximations for ${}$ and ${}$ of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state. The expressions for ${}$ and ${}$ are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to ${}$ and ${}$ are calculated in asymptotically flat spacetimes in a quantum state corresponding to the Minkowski vacuum (Boulware quantum state). The limits of the applicability of these approximations are discussed.Comment: revtex4, 17 pages; v2: three references adde

Photoemission and the Origin of High Temperature Superconductivity

The condensation energy can be shown to be a moment of the change in the occupied part of the spectral function when going from the normal to the superconducting state. As a consequence, there is a one to one correspondence between the energy gain associated with forming the superconducting ground state, and the dramatic changes seen in angle resolved photoemission spectra. Some implications this observation has are offered.Comment: 4 pages, M2S conference proceeding