Perturbation Theory around Non-Nested Fermi Surfaces I. Keeping the Fermi Surface Fixed

The perturbation expansion for a general class of many-fermion systems with a non-nested, non-spherical Fermi surface is renormalized to all orders. In the limit as the infrared cutoff is removed, the counterterms converge to a finite limit which is differentiable in the band structure. The map from the renormalized to the bare band structure is shown to be locally injective. A new classification of graphs as overlapping or non-overlapping is given, and improved power counting bounds are derived from it. They imply that the only subgraphs that can generate $r$ factorials in the $r^{\rm th}$ order of the renormalized perturbation series are indeed the ladder graphs and thus give a precise sense to the statement that `ladders are the most divergent diagrams'. Our results apply directly to the Hubbard model at any filling except for half-filling. The half-filled Hubbard model is treated in another place.Comment: plain TeX with postscript figures in a uuencoded gz-compressed tar file. Put it on a separate directory before unpacking, since it contains about 40 files. If you have problems, requests or comments, send e-mail to [email protected]

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

A Proof of Luttinger Theorem

A rigorous and simple perturbative proof of Luttinger's theorem is sketched for Fermi liquids in two and three dimensions. It is proved that in the finite volume, the quasi-particle density is independent of the interaction strength. The thermodynamic limit is then controlled to all orders in perturbation theory.Comment: 7 page

A First Look at Airborne Imaging Spectrometer (AIS) Data in an Area of Altered Volcanic Rocks and Carbonate Formations, Hot Creek Range, South Central Nevada

Three flight lines of Airborne Imaging Spectrometer (AIS) data were collected in 128 bands between 1.2 and 2.4 microns in the Hot Creek Range, Nevada on July 25, 1984. The flight lines are underlain by hydrothermally altered and unaltered Paleozoic carbonates and Tertiary rhyolitic to latitic volcanics in the Tybo mining district. The original project objectives were to discriminate carbonate rocks from other rock types, to distinguish limestone from dolomite, and to discriminate carbonate units from each other using AIS imagery. Because of high cloud cover over the prime carbonate flight line and because of the acquisition of another flight line in altered and unaltered volcanics, the study has been extended to the discrimination of alteration products. In an area of altered and unaltered rhyolites and latites in Red Rock Canyon, altered and unaltered rock could be discriminated from each other using spectral features in the 1.16 to 2.34 micron range. The altered spectral signatures resembled montmorillonite and kaolinite. Field samples were gathered and the presence of montmorillonite was confirmed by X-ray analysis

Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems

It is known that perturbation theory converges in fermionic field theory at weak coupling if the interaction and the covariance are summable and if certain determinants arising in the expansion can be bounded efficiently, e.g. if the covariance admits a Gram representation with a finite Gram constant. The covariances of the standard many--fermion systems do not fall into this class due to the slow decay of the covariance at large Matsubara frequency, giving rise to a UV problem in the integration over degrees of freedom with Matsubara frequencies larger than some Omega (usually the first step in a multiscale analysis). We show that these covariances do not have Gram representations on any separable Hilbert space. We then prove a general bound for determinants associated to chronological products which is stronger than the usual Gram bound and which applies to the many--fermion case. This allows us to prove convergence of the first integration step in a rather easy way, for a short--range interaction which can be arbitrarily strong, provided Omega is chosen large enough. Moreover, we give - for the first time - nonperturbative bounds on all scales for the case of scale decompositions of the propagator which do not impose cutoffs on the Matsubara frequency.Comment: 29 pages LaTe

Spectral Function of 2D Fermi Liquids

We show that the spectral function for single-particle excitations in a two-dimensional Fermi liquid has Lorentzian shape in the low energy limit. Landau quasi-particles have a uniquely defined spectral weight and a decay rate which is much smaller than the quasi-particle energy. By contrast, perturbation theory and the T-matrix approximation yield spurious deviations from Fermi liquid behavior, which are particularly pronounced for a linearized dispersion relation.Comment: 6 pages, LaTeX2e, 5 EPS figure

Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

Nonequilibrium quantum phase transition in itinerant electron systems

We study the effect of the voltage bias on the ferromagnetic phase transition in a one-dimensional itinerant electron system. The applied voltage drives the system into a nonequilibrium steady state with a non-zero electric current. The bias changes the universality class of the second order ferromagnetic transition. While the equilibrium transition belongs to the universality class of the uniaxial ferroelectric, we find the mean-field behavior near the nonequilibrium critical point.Comment: Final version as accepted to Phys. Rev. Let

A general numerical analysis program for the superconducting quasiparticle mixer

A user-oriented computer program SISCAP (SIS Computer Analysis Program) for analyzing SIS mixers is described. The program allows arbitrary impedance terminations to be specified at all LO harmonics and sideband frequencies. It is therefore able to treat a much more general class of SIS mixers than the widely used three-frequency analysis, for which the harmonics are assumed to be short-circuited. An additional program, GETCHI, provides the necessary input data to program SISCAP. The SISCAP program performs a nonlinear analysis to determine the SIS junction voltage waveform produced by the local oscillator. The quantum theory of mixing is used in its most general form, treating the large signal properties of the mixer in the time domain. A small signal linear analysis is then used to find the conversion loss and port impedances. The noise analysis includes thermal noise from the termination resistances and shot noise from the periodic LO current. Quantum noise is not considered. Many aspects of the program have been adequately verified and found accurate

A murine model for developmental dysplasia of the hip: ablation of CX3CR1 affects acetabular morphology and gait.

BACKGROUND: Developmental dysplasia of the hip (DDH) is a debilitating condition whose distinguishing signs include incomplete formation of the acetabulum leading to dislocation of the femur, accelerated wear of the articular cartilage and joint laxity resulting in osteoarthritis. It is a complex disorder having environmental and genetic causes. Existing techniques fail to detect milder forms of DDH in newborns leading to hip osteoarthritis in young adults. A sensitive, specific and cost effective test would allow identification of newborns that could be non-invasively corrected by the use of a Pavlik harness. Previously, we identified a 2.5 MB candidate region on human chromosome 3 by using linkage analysis of a 4 generation, 72 member family. Whole exome sequencing of the DNA of 4 severely affected members revealed a single nucleotide polymorphism variant, rs3732378 co-inherited by all 11 affected family members. This variant causes a threonine to methionine amino acid change in the coding sequence of the CX3CR1 chemokine receptor and is predicted to be harmful to the function of the protein To gain further insight into the function of this mutation we examined the effect of CX3CR1 ablation on the architecture of the mouse acetabulum and on the murine gait. METHODS: The hips of 5 and 8 weeks old wild type and CX3CR1 KO mice were analyzed using micro-CT to measure acetabular diameter and ten additional dimensional parameters. Eight week old mice were gait tested using an inclined treadmill with and without load and then underwent micro-CT analysis. RESULTS: (1) KO mice showed larger a 5-17% larger diameter left acetabula than WT mice at both ages. (2) At 8 weeks the normalized area of space (i.e. size discrepancy) between the femur head and acetabulum is significantly larger [38% (p = 0.001)-21% (p = 0.037)] in the KO mice. (3) At 8 weeks gait analysis of these same mice shows several metrics that are consistent with impairment in the KO but not the WT mice. These deficits are often seen in mice and humans who develop hip OA. CONCLUSION: The effect of CX3CR1 deletion on murine acetabular development provides suggestive evidence of a susceptibility inducing role of the CX3CR1 gene on DDH