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]

Structure in a Loitering Universe

We study the formation of structure for a universe that undergoes a recent loitering phase. We compare the nonlinear mass distribution to that in a standard, matter dominated cosmology. The statistical aspects of the clustered matter are found to be robust to changes in the expansion law, an exception being that the peculiar velocities are lower by a factor of $\sim 3$ in the loitering model. Further, in the loitering scenario, nonlinear growth of perturbation occurs more recently ($z\sim 3-5$) than in the matter dominated case. Differences in the high redshift appearances of the two models will result but observable consequences depend critically on the chosen form, onset and duration of the loitering phase.Comment: 8 pages, (uses revtex.sty), 5 figures not included, available on request, UM AC 92-

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

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

Projective measurement in nuclear magnetic resonance

It is demonstrated that nuclear magnetic resonance experiments using pseudopure spin states can give possible outcomes of projective quantum measurement and probabilities of such outcomes. The physical system is a cluster of six dipolar-coupled nuclear spins of benzene in a liquid-crystalline matrix. For this system with the maximum total spin S=3, the results of measuring $S_X$ are presented for the cases when the state of the system is one of the eigenstates of $S_Z$.Comment: 9 pages incluing 3 figure

Extracting predictive models from marked-p free-text documents at the Royal Botanic Gardens, Kew, London

In this paper we explore the combination of text-mining, un-supervised and supervised learning to extract predictive models from a corpus of digitised historical floras. These documents deal with the nomenclature, geographical distribution, ecology and comparative morphology of the species of a region. Here we exploit the fact that portions of text in the floras are marked up as different types of trait and habitat. We infer models from these different texts that can predict different habitat-types based upon the traits of plant species. We also integrate plant taxonomy data in order to assist in the validation of our models. We have shown that by clustering text describing the habitat of different floras we can identify a number of important and distinct habitats that are associated with particular families of species along with statistical significance scores. We have also shown that by using these discovered habitat-types as labels for supervised learning we can predict them based upon a subset of traits, identified using wrapper feature selection

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