摘要
In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.
In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.
作者
Angelo Plastino
Mario Carlos Rocca
Diana Monteoliva
Alberto Hernando
Angelo Plastino;Mario Carlos Rocca;Diana Monteoliva;Alberto Hernando(Departamento de Física, Universidad Nacional de La Plata, La Plata, Argentina;Kido Dynamics SA, Lausanne, Switzerland;Departamento de Mateática, Universidad Nacional de La Plata, La Plata, Argentina;Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. C. 727, La Plata, Argentina;Comisión de Investigaciones Científicas, Provincia de Buenos Aires La Plata, La Plata, Argentina)
