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arXiv · 1710.07995

On fluctuations of cycles in a finite CW complex

Michael J. Catanzaro·Vladimir Y. Chernyak·John R. Klein
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Abstract

We use algebraic topology to study the stochastic mo- tion of cellular cycles in a finite CW complex. Inspired by statis- tical mechanics, we introduce a homological observable called the average current. The latter measures the average flux of the prob- ability in the process. In the low temperature, adiabatic limit, we prove that the average current fractionally quantizes, in which the denominators are combinatorial invariants of the CW complex.

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Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein. 2017-10-22. On fluctuations of cycles in a finite CW complex. https://arxiv.org/abs/1710.07995

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