Cluster expansion in the canonical ensemble

We consider a system of particles confined in a box \La\subset\R^d interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer's virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof

Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

A deficit of ultraluminous X-ray sources in luminous infrared galaxies

We present results from a Chandra study of ultraluminous X-ray sources (ULXs) in a sample of 17 nearby (DL < 60 Mpc) luminous infrared galaxies (LIRGs), selected to have star formation rates (SFRs) in excess of 7 M⊙ yr−1 and low foreground Galactic column densities (NH ≲ 5 × 1020 cm−2). A total of 53 ULXs were detected and we confirm that this is a complete catalogue of ULXs for the LIRG sample. We examine the evolution of ULX spectra with luminosity in these galaxies by stacking the spectra of individual objects in three luminosity bins, finding a distinct change in spectral index at luminosity ∼2 × 1039 erg s−1. This may be a change in spectrum as 10 M⊙ black holes transit from an ∼ Eddington to a super-Eddington accretion regime, and is supported by a plausible detection of partially ionized absorption imprinted on the spectrum of the luminous ULX (LX ≈ 5 × 1039 erg s−1) CXOU J024238.9-000055 in NGC 1068, consistent with the highly ionized massive wind that we would expect to see driven by a super-Eddington accretion flow. This sample shows a large deficit in the number of ULXs detected per unit SFR (0.2 versus 2 ULXs, per M⊙ yr−1) compared to the detection rate in nearby (DL < 14.5 Mpc) normal star-forming galaxies. This deficit also manifests itself as a lower differential X-ray luminosity function normalization for the LIRG sample than for samples of other star-forming galaxies. We show that it is unlikely that this deficit is a purely observational effect. Part of this deficit might be attributable to the high metallicity of the LIRGs impeding the production efficiency of ULXs and/or a lag between the star formation starting and the production of ULXs; however, we argue that the evidence – including very low NULX/LFIR, and an even lower ULX incidence in the central regions of the LIRGs – shows that the main culprit for this deficit is likely to be the high column of gas and dust in these galaxies, that fuels the high SFR but also acts to obscure many ULXs from our view

Quantum field theory of metallic spin glasses

We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains reference to related work in cond-mat/950412

Second harmonic generation and birefringence of some ternary pnictide semiconductors

A first-principles study of the birefringence and the frequency dependent second harmonic generation (SHG) coefficients of the ternary pnictide semiconductors with formula ABC$_2$ (A = Zn, Cd; B = Si, Ge; C = As, P) with the chalcopyrite structures was carried out. We show that a simple empirical observation that a smaller value of the gap is correlated with larger value of SHG is qualitatively true. However, simple inverse power scaling laws between gaps and SHG were not found. Instead, the real value of the nonlinear response is a result of a very delicate balance between different intraband and interband terms.Comment: 13 pages, 12 figure

Optically induced coherent intra-band dynamics in disordered semiconductors

On the basis of a tight-binding model for a strongly disordered semiconductor with correlated conduction- and valence band disorder a new coherent dynamical intra-band effect is analyzed. For systems that are excited by two, specially designed ultrashort light-pulse sequences delayed by tau relatively to each other echo-like phenomena are predicted to occur. In addition to the inter-band photon echo which shows up at exactly t=2*tau relative to the first pulse, the system responds with two spontaneous intra-band current pulses preceding and following the appearance of the photon echo. The temporal splitting depends on the electron-hole mass ratio. Calculating the population relaxation rate due to Coulomb scattering, it is concluded that the predicted new dynamical effect should be experimentally observable in an interacting and strongly disordered system, such as the Quantum-Coulomb-Glass.Comment: to be published in Physical Review B15 February 200

Parabolic stable surfaces with constant mean curvature

We prove that if u is a bounded smooth function in the kernel of a nonnegative Schrodinger operator $-L=-(\Delta +q)$ on a parabolic Riemannian manifold M, then u is either identically zero or it has no zeros on M, and the linear space of such functions is 1-dimensional. We obtain consequences for orientable, complete stable surfaces with constant mean curvature $H\in\mathbb{R}$ in homogeneous spaces $\mathbb{E}(\kappa,\tau)$ with four dimensional isometry group. For instance, if M is an orientable, parabolic, complete immersed surface with constant mean curvature H in $\mathbb{H}^2\times\mathbb{R}$, then $|H|\leq 1/2$ and if equality holds, then M is either an entire graph or a vertical horocylinder.Comment: 15 pages, 1 figure. Minor changes have been incorporated (exchange finite capacity by parabolicity, and simplify the proof of Theorem 1)