# Crossover from Selberg's type to Ruelle's type Zeta function in classical kinetics

Source: [Crossover from Selberg's type to Ruelle's type Zeta function in classical kinetics](<https://www.sota2.com/research/paper/68fa1e887a2b558e29322e88>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T15:16:13.163Z

Authors: Daniel L. Miller

Published: 1997-12-15T22:36:45.000Z

## Abstract

The decay rates of the density-density correlation function are computed for a chaotic billiard with some amount of disorder inside. In the case of the clean system the rates are zeros of Ruelle's Zeta function and in the limit of strong disorder they are roots of Selberg's Zeta function. We constructed the interpolation formula between two limiting Zeta functions by analogy with the case of the integrable billiards. The almost clean limit is discussed in some detail. PACS numbers: 05.20.Dd, 05.45.+b, 51.10.+y

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9712156>)

[PDF](<https://arxiv.org/pdf/cond-mat/9712156.pdf>)