Shear viscosity: velocity gradient as a constraint on wave function
Abstract
By viewing a velocity gradient in a fluid as an internal disturbance and treating it as a constraint on the wave function of a system, a linear evolution equation for the wave function is obtained from the Lagrange multiplier method. It allows us to define the microscopic response to a velocity gradient in a pure state. Taking a spatial coarse-graining average over this microscopic response and averaging it over admissible initial states, we achieve the observed macroscopic response and transport coefficient. In this scheme, temporal coarse-graining is not needed. The dissipation caused by a velocity gradient depends on the square of initial occupation probability, whereas the dissipation caused by a mechanical perturbation depends on the initial occupation probability itself. We apply the method of variation of constants to solve the time-dependent Schrodinger equation with constraints. The various time scales appearing in the momentum transport are estimated. The relation\ between the present work and previous theories is discussed.
Cite
@article{arxiv.1211.2362,
title = {Shear viscosity: velocity gradient as a constraint on wave function},
author = {M. -L. Zhang and D. A. Drabold},
journal= {arXiv preprint arXiv:1211.2362},
year = {2012}
}
Comments
16 pages, 1 figure, submitted to Phys. Rev. E