Superfluid to Mott-insulator transition in Bose-Hubbard models

We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidences that, across the transition,most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].Comment: 4 pages, 4 figures, based on cond-mat/061130

Polyakov Lines in Yang-Mills Matrix Models

We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations which are convenient for finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper bounds which decay as a power law at large momentum p. We argue that these capture the full asymptotic behaviour. We also indicate how to extend the results to some correlation functions of Polyakov lines.Comment: 19 pages, v2 typos corrected, v3 ref adde

Adding a Myers Term to the IIB Matrix Model

We show that Yang-Mills matrix integrals remain convergent when a Myers term is added, and stay in the same topological class as the original model. It is possible to add a supersymmetric Myers term and this leaves the partition function invariant.Comment: 8 pages, v2 2 refs adde

On the Quantum Geometry of String Theory

The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space--time appears dynamically. It is possible that lower dimensional universes dominate the theory, therefore providing a dynamical solution to the reduction of space--time dimensionality. We summarize recent works that show the central role of the phase of the fermion determinant in the possible realization of such a scenario.Comment: 3 pages, 2 figures, Lattice2001(surfaces

Assemblage of Hymenoptera Arriving at Logs Colonized by \u3cem\u3eIps pini\u3c/em\u3e (Coleoptera: Curculionidae: Scolytinae) and its Microbial Symbionts in Western Montana

Colonization of a tree by bark beetles and their symbionts creates a new habitat for a diverse assemblage of arthropods, including competing herbivores, xylophages, fungivores, saprophages, predators, and parasitoids. Understanding these assemblages is important for evaluating nontarget effects of various management tactics and for subsequently evaluating how changes in climate, the presence of invasive species, and altered forestry practices and land-use tenure may affect biodiversity. We characterized the assemblage of hymenopterans attracted to logs of ponderosa pine (Pinus ponderosa C. Lawson (Pinaceae)) colonized by the bark beetle Ips pini (Say) and its microbial symbionts. In one experiment, the composition and relative abundances of species arriving at hosts colonized by I. pini, and possible sources of attraction, were determined. Treatments consisted of a log containing I. pini with its natural complement of microorganisms, a log alone, and a blank control. A second experiment was carried out to determine whether or not Hymenoptera were attracted to microbial symbionts of I. pini. Treatments consisted of a blank control, a log alone, a log containing I. pini with its natural complement of microorganisms, either Ophiostoma ips, Burkholderia sp., or Pichia scolyti, and a log inoculated with a combination of these three microorganisms. Over 2 years, 5163 Hymenoptera were captured, of which over 98% were parasitoids. Braconidae, Platygastridae, Encyrtidae, Pteromalidae, and Ichneumonidae were the most abundant. Seven known species of bark beetle parasitoids (all Pteromalidae) were captured. However, parasitoids of Diptera, Lepidoptera, Hymenoptera, and non-wood-boring Coleoptera were also common. Nineteen species showed preferential attraction to host plants infested with I. pini and its complement of microorganisms, host plants inoculated with I. pini microbial symbionts, or host plants alone. Interestingly, many of these species were parasitoids of phytophagous, fungivorous, and saprophytic insects rather than of bark beetles themselves. These results suggest that a diverse assemblage of natural enemies that attack various feeding guilds within a common habitat exploit common olfactory cues

Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail

Phase Diagram of Bosonic Atoms in Two-Color Superlattices

We investigate the zero temperature phase diagram of a gas of bosonic atoms in one- and two-color standing-wave lattices in the framework of the Bose-Hubbard model. We first introduce some relevant physical quantities; superfluid fraction, condensate fraction, quasimomentum distribution, and matter-wave interference pattern. We then discuss the relationships between them on the formal level and show that the superfluid fraction, which is the relevant order parameter for the superfluid to Mott-insulator transition, cannot be probed directly via the matter wave interference patterns. The formal considerations are supported by exact numerical solutions of the Bose-Hubbard model for uniform one-dimensional systems. We then map out the phase diagram of bosons in non-uniform lattices. The emphasis is on optical two-color superlattices which exhibit a sinusoidal modulation of the well depth and can be easily realized experimentally. From the study of the superfluid fraction, the energy gap, and other quantities we identify new zero-temperature phases, including a localized and a quasi Bose-glass phase, and discuss prospects for their experimental observation.Comment: 18 pages, 17 figures, using REVTEX