Progress In Mathematical Physics Research Articles

Ubiquity of Superconducting Domes in the Bardeen-Cooper-Schrieffer Theory with Finite-Range Potentials.

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature T_{c} with the carrier density n predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasilocal. In contrast, we show that any well-defined nonlocal potential leads to a "superconducting dome," i.e., a nonmonotonic T_{c}(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity.

Algebraic equivalence of locally normal representations

It will be shown that (i) the absolute value of every locally normal linear functional is again locally normal; (ii) two locally normal representations πi and π2 of S/ generate isomorphic von Neumann algebras ^(πϊ) and ^^(π 2) if and only if there exists an automorphism a of S>/ such that πx o β and π2 are quasi-equivalent, provided that either ^(πϊ) or ^^(τr 2) is afinite. This paper is motivated by a recent work [6] of R. Haag. R. V. Kadison and D. Kastler. As they mentioned, the recent progress in mathematical physics has made a precise analysis of representatio ns of a C*-algebra furnished with a net of von Neumann algebras a growing necessity. In the first half of this paper, we shall show that the space of all locally normal linear functionals of a C*-algebra with a net of von Neumann algebras is a closed invariant subspace of the conjugate space in the sense of [14], which will imply that the absolute value of a locally normal linear functional is locally normal too. The last half of this paper will be devoted to extending a result of Powers [11] for UHF algebra to a C*-algebra sf with a proper sequential type 1^ funnel. Namely it will be shown that two locally normal representations πλ and π2 of the C*-algebra s%? generate isomorphic von Neumann algebras if and only if they are connected by an automorphism of s^. This is proven under the assumption that one of the generated von Neumann algebras is σ-finite. 2* The locally normal conjugate space of a C*-algebra with a net of von Neumann algebras* Let Szf be a C*-algebra. Suppose a system % = (jQ (ϋ) \}a^fa is dense in s^ with respect to the norm topology. The system % = {s/a} is called a net (in Ssf) of von Neumann algebras and each j^ς is called local subalgebra of DEFINITION 1. A continuous linear functional φ (resp. representa

Annales de l'Institut Henri Poincaré: recueil de conférences et mémoires de calcul des probabilitiés et physique théorique

THE Henri Poincaré Institute invites leading scientific workers to lecture on recent progress in mathematical physics. The “Annales”, of which the first number has just appeared, will contain a French translation of these lectures. In the present number we have Einstein on the unitary field theory, C. G. Darwin on the wave theory of matter, and Fermi on the theory of radiation.

Lectures delivered at the Celebration of the Twentieth Anniversary of the Foundation of Clark University, under the auspices of the Department of Physics

THE system of holding conferences at which a number of lectures are given by eminent special ists is a noticeable feature of American universi ties, and is being adopted with success in other countries. Clark University was founded in 1889, and under the invitaton of its Department of Physics courses of lectures were given to celebrate its twentieth anniversary. Those published in this volume are by Prof. Vito Volterra on recent pro gress in mathematical physics (in French), by Prof. Rutherford on the history of the alpha rays, by Prof. R. W. Wood on optical properties of metallic vapours, and by Prof. C. Barus on physical pro perties of iron carbides. Other lectures by Profs. Michelson and E. F. Nichols are not published. The volume will be of interest to those who at tended the conferences or who desire a not too extensive summary of our knowledge in the branches of study covered by the lectures.