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VOL. 20 | 2019 Geometric Flow Appearing in Conservation Law in Classical and Quantum Mechanics
Naohisa Ogawa

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional curved surface with thickness $\epsilon$ embedded in $\mathbb E^3$. In such a system, two-dimensional conservation law needs an additional term just like an anomaly. The additional term can be obtained by the $\epsilon$ expansion. This term has a Gaussian and a mean curvature dependence and can be written as the total divergence of geometric flow $J^i_{G}$. This fact holds in both classical and quantum mechanics.

Information

Published: 1 January 2019
First available in Project Euclid: 21 December 2018

zbMATH: 1414.81139
MathSciNet: MR3887752

Digital Object Identifier: 10.7546/giq-20-2019-215-226

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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