The Hausdorff moments in statistical mechanics

Scalas, E and Viano, G A (1993) The Hausdorff moments in statistical mechanics. Journal of Mathematical Physics, 34. pp. 5781-5800. ISSN 0022-2488

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A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L 2 space and the moments are finite in number and affected by noise or round‐off errors, the approximation converges asymptotically in the L 2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(β) (β=1/k BT ) is obtained which coincides with a Watson resummation of the high‐temperature series for Z(β).

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Enrico Scalas
Date Deposited: 03 Oct 2014 13:39
Last Modified: 28 Mar 2017 21:34

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