Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases

We prove regularity properties of the self-energy, to all orders in perturbation theory, for systems with singular Fermi surfaces which contain Van Hove points where the gradient of the dispersion relation vanishes. In this paper, we show for spatial dimensions $d \ge 3$ that despite the Van Hove singularity, the overlapping loop bounds we proved together with E. Trubowitz for regular non--nested Fermi surfaces [J. Stat. Phys. 84 (1996) 1209] still hold, provided that the Fermi surface satisfies a no-nesting condition. This implies that for a fixed interacting Fermi surface, the self-energy is a continuously differentiable function of frequency and momentum, so that the quasiparticle weight and the Fermi velocity remain close to their values in the noninteracting system to all orders in perturbation theory. In a companion paper, we treat the more singular two-dimensional case.Comment: 48 pages LaTeX with figure

Homogenization of the Oscillating Dirichlet Boundary Condition in General Domains

We prove the homogenization of the Dirichlet problem for fully nonlinear elliptic operators with periodic oscillation in the operator and of the boundary condition for a general class of smooth bounded domains. This extends the previous results of Barles and Mironescu in half spaces. We show that homogenization holds despite a possible lack of continuity in the homogenized boundary data. The proof is based on a comparison principle with partial Dirichlet boundary data which is of independent interest.Comment: Version to appear in J. Math. Pures Appl. Added Remarks 1.2 and 1.7. Removed some extraneous statements of previous results (previously Corollaries 2.7 and 2.12). Changed the statement and proof of Lemma 3.1 to fix a small error and R^{-\alpha} is now (N/R)^{\alpha} here and in later uses of the Lemma. 23 page

A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant $\lambda$ for $|\lambda| |\log T| \le K$ where $K$ is some numerical constant and $T$ is the temperature. Furthermore in that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior which is that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our results prove also that in dimension two any transition temperature must be non-perturbative in the coupling constant, a result expected on physical grounds. The proof exploits the specific momentum conservation rules in two dimensions.Comment: 4 pages, no figure

Current Knowledge and Attitudes Concerning Cost-Effectiveness in Glaucoma Pharmacotherapy: A Glaucoma Specialists Focus Group Study.

Background:Rising healthcare costs motivate continued cost-reduction efforts. To help lower costs associated with open-angle glaucoma (OAG), a prevalent, progressive disease with substantial direct and indirect costs, clinicians need to understand the cost-effectiveness of intraocular pressure (IOP)-lowering pharmacotherapies. There is little published information on clinicians' knowledge and attitudes about cost-effectiveness in glaucoma treatment. Purpose:This pilot focus group study aimed to explore clinician attitudes and perspectives around the costs and cost drivers of glaucoma therapy; the implementation of cost-effectiveness decisions; the clinical utility of cost-effectiveness studies; and the cost-effectiveness of available treatments. Methods:Six US glaucoma specialists participated in two separate teleconferencing sessions (three participants each), managed by an independent, skilled moderator (also a glaucoma specialist) using a discussion guide. Participants reviewed recent publications (n=25) on health economics outcomes research in glaucoma prior to the sessions. Results:Participants demonstrated a clear understanding of the economic burden of glaucoma therapy and identified medications, diagnostics, office visits, and treatment changes as key cost drivers. They considered cost-effectiveness an appropriate component of treatment decision-making but identified the need for additional data to inform these decisions. Participants indicated that there were only a few recent studies on health economics outcomes in glaucoma which evaluate parameters important to patient care, such as quality of life and medication adherence, and that longitudinal data were scant. In addition to efficacy, participants felt patient adherence and side-effect profile should be included in economic evaluations of glaucoma pharmacotherapy. Recently approved medications were evaluated in this context. Conclusion:Clinicians deem treatment decisions based on cost-effectiveness data as clinically appropriate. Newer IOP-lowering therapies with potentially greater efficacy and favorable side-effect and adherence profiles may help optimize cost-effectiveness. Future studies should include: clinicians' perspectives; lack of commercial bias; analysis of long-term outcomes/costs; more comprehensive parameters; real-world (including quality-of-life) data; and a robust Markov model