Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

PDF

City University of New York (CUNY)

Series

2021

Articles 121 - 122 of 122

Full-Text Articles in Physical Sciences and Mathematics

A Twisted Generalization Of The Classical Dedekind Sum, Brad Isaacson Jan 2021

A Twisted Generalization Of The Classical Dedekind Sum, Brad Isaacson

Publications and Research

In this paper, we express three different, yet related, character sums in terms of generalized Bernoulli numbers. Two of these sums are generalizations of sums introduced and studied by Berndt and Arakawa–Ibukiyama–Kaneko in the context of the theory of modular forms. A third sum generalizes a sum already studied by Ramanujan in the context of theta function identities. Our methods are elementary, relying only on basic facts from algebra and number theory.

Go to article

Exclusion Statistics For Particles With A Discrete Spectrum, Stéphane Ouvry, Alexios P. Polychronakos Jan 2021

Exclusion Statistics For Particles With A Discrete Spectrum, Stéphane Ouvry, Alexios P. Polychronakos

Publications and Research

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a …

Go to article

First Prev