Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.Comment: 8 pages, version to appear in Eur. Phys. J.

Preparation of high density heavy metal fluoride glasses with extended ultraviolet and infra red ranges, and such high density heavy metal fluoride glasses

A heavy metal fluoride glass composition range (in mol percent) consisting essentially of: (16-30)BaF.sub.2.(8-26)HfF.sub.4.(6-24)InF.sub.3 or GaF.sub.3.(4-16)CdF.sub.2.(6-24)YbF.sub.3.(4-22)ZnF.sub.2. In an alternative embodiment, a heavy metal fluoride glass composition range (in mol percent) comprises (16-30)BaF.sub.2.(8-26)HfF.sub.4.(6-24) of (0-24)InF.sub.3, (0-24)GaF.sub.3 and (0-19)AlF.sub.3.(1-16)CdF.sub.2.(6-24)YbF.sub.3.(4-26)ZnF.sub.2. A preferred heavy metal fluoride glass produced in accordance with the present invention comprises a composition (in mol %) and comprises about 26BaF.sub.2.18HfF.sub.4.7InF.sub.3.5GaF.sub.3.10CdF.sub.2.18YbF.sub.3. 16ZnF.sub.2. A preferred heavy metal fluoride glass has maximum thickness of most preferably about 3 mm. Another preferred heavy metal fluoride glass comprises a composition (in mol %) and comprises about 26BaF.sub.2.18HfF.sub.4.12AlF.sub.3.10CdF.sub.2.18YbF.sub.3.16ZnF.sub.2

Stimulus Responsive Nanoparticles

Disclosed are various embodiments of methods and systems related to stimulus responsive nanoparticles. In one embodiment includes a stimulus responsive nanoparticle system, the system includes a first electrode, a second electrode, and a plurality of elongated electro-responsive nanoparticles dispersed between the first and second electrodes, the plurality of electro-responsive nanorods configured to respond to an electric field established between the first and second electrodes

G-actions with close orbit spaces

The classification of G-spaces by Palais is refined for the case where the orbit space satisfies certain mild topological hypotheses. It is shown that when a sequence of such orbit spaces is "close" to a limit orbit space, in some suitable sense, within a larger ambient orbit space, the G-spaces in the tail of the sequence are strongly equivalent to the limit G-space.Comment: 12 pages, 1 figure. The result as previously stated in v1 was incorrect; the hypotheses were insufficien

Renormalisation and fixed points in Hilbert Space

The energies of low-lying bound states of a microscopic quantum many-body system of particles can be worked out in a reduced Hilbert space. We present here and test a specific non-perturbative truncation procedure. We also show that real exceptional points which may be present in the spectrum can be identified as fixed points of coupling constants in the truncation procedure.Comment: 4 pages, 1 tabl

The state of peer-to-peer network simulators

Networking research often relies on simulation in order to test and evaluate new ideas. An important requirement of this process is that results must be reproducible so that other researchers can replicate, validate and extend existing work. We look at the landscape of simulators for research in peer-to-peer (P2P) networks by conducting a survey of a combined total of over 280 papers from before and after 2007 (the year of the last survey in this area), and comment on the large quantity of research using bespoke, closed-source simulators. We propose a set of criteria that P2P simulators should meet, and poll the P2P research community for their agreement. We aim to drive the community towards performing their experiments on simulators that allow for others to validate their results

Representations of the Weyl Algebra in Quantum Geometry

The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. Additional assumptions concern the dimension of the underlying analytic manifold (at least three), the finite wide triangulizability of surfaces in it to be used for the fluxes and the naturality of the action of diffeomorphisms -- but neither any domain properties of the represented Weyl operators nor the requirement that the diffeomorphisms act by pull-backs. For this, the general behaviour of C*-algebras generated by continuous functions and pull-backs of homeomorphisms, as well as the properties of stratified analytic diffeomorphisms are studied. Additionally, the paper includes also a short and direct proof of the irreducibility of A.Comment: 71 pages, 1 figure, LaTeX. Changes v2 to v3: previous results unchanged; some addings: inclusion of gauge transforms, several comments, Subsects. 1.5, 3.7, 3.8; comparison with LOST paper moved to Introduction; Def. 2.5 modified; some typos corrected; Refs. updated. Article now as accepted by Commun. Math. Phy