Annealed lower tails for the energy of a polymer

We consider the energy of a randomly charged polymer. We assume that only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we obtain the correct temperature-scale for the Gibbs measure.Comment: 27 page

Many-particle quantum graphs and Bose-Einstein condensation

In this paper we propose quantum graphs as one-dimensional models with a complex topology to study Bose-Einstein condensation and phase transitions in a rigorous way. We fist investigate non-interacting many-particle systems on quantum graphs and provide a complete classification of systems that exhibit Bose-Einstein condensation. We then consider models of interacting particles that can be regarded as a generalisation of the well-known Tonks-Girardeau gas. Here our principal result is that no phase transitions occur in bosonic systems with repulsive hardcore interactions, indicating an absence of Bose-Einstein condensation

Study of a high spatial resolution 10B-based thermal neutron detector for application in neutron reflectometry: the Multi-Blade prototype

Although for large area detectors it is crucial to find an alternative to detect thermal neutrons because of the 3He shortage, this is not the case for small area detectors. Neutron scattering science is still growing its instruments' power and the neutron flux a detector must tolerate is increasing. For small area detectors the main effort is to expand the detectors' performances. At Institut Laue-Langevin (ILL) we developed the Multi-Blade detector which wants to increase the spatial resolution of 3He-based detectors for high flux applications. We developed a high spatial resolution prototype suitable for neutron reflectometry instruments. It exploits solid 10B-films employed in a proportional gas chamber. Two prototypes have been constructed at ILL and the results obtained on our monochromatic test beam line are presented here

Gaussian field theories, random Cantor sets and multifractality

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace numerical calculation

The Approximating Hamiltonian Method for the Imperfect Boson Gas

The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.Comment: 7 page

THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

Proof of Bose-Einstein Condensation for Interacting Gases with a One-Particle Spectral Gap

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems

Directed polymers on a Cayley tree with spatially correlated disorder

In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse direction i.e. within the shell. In this paper we take the transverse distance to be the hierarchical ultrametric distance, but other possibilities are discussed. We compute the free energy for the case of quenched disorder and show that there is a fundamental difference between the case of short range spatial correlations of the disorder which behaves similarly to the non-correlated case considered previously by Derrida and Spohn and the case of long range correlations which has a totally different overlap distribution which approaches a single delta function about q=1 for large L, where L is the length of the walk. In the latter case the free energy is not extensive in L for the intermediate and also relevant range of L values, although in the true thermodynamic limit extensivity is restored. We identify a crossover temperature which grows with L, and whenever T<T_c(L) the system is always in the low temperature phase. Thus in the case of long-ranged correlation as opposed to the short-ranged case a phase transition is absent.Comment: 23 pages, 1 figure, standard latex. J. Phys. A, accepted for publicatio

Deep subcutaneous application of poly-L-lactic acid as a filler for facial lipoatrophy in HIV-infected patients

Introduction: Facial lipoatrophy is a crucial problem of HIV-infected patients undergoing highly active antiretroviral therapy (HAART). Poly-L-lactic acid (PLA), provided as New-Fill(R)/Sculptra(TM), is known as one possible treatment option. In 2004 PLA was approved by the FDA as Sculptra(TM) for the treatment of lipoatrophy of the face in HIV-infected patients. While the first trials demonstrated relevant efficacy, this was to some extent linked to unwanted effects. As the depth of injection was considered relevant in this context, the application modalities of the preparation were changed. The preparation was to be injected more deeply into subcutaneous tissue, after increased dilution. Material and Methods: To test this approach we performed a pilot study following the new recommendations in 14 patients. Results: While the efficacy turned out to be about the same, tolerability was markedly improved. The increase in facial dermal thickness was particularly obvious in those patients who had suffered from lipoatrophy for a comparatively small period of time. Conclusion: With the new recommendations to dilute PLA powder and to inject it into the deeper subcutaneous tissue nodule formation is a minor problem. However, good treatment results can only be achieved if lipoatrophy is not too intense; treatment intervals should be about 2 - 3 weeks. Copyright (C) 2005 S. Karger AG, Basel

The Canonical Perfect Bose Gas in Casimir Boxes

We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose-Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.Comment: 23 page