2021/04/30 by T. Koide · 1 citation
Physics and Astronomy · #quant-ph #hep-th #nucl-th
paper · pdf · doi:10.1088/1742-5468/ac50b0
10 pages, 2 figures, discussions were added, accepted for the publication in JSTAT
arxiv created 2022/01/25 · arxiv updated 2022/02/28
A minimum uncertainty state for position and momentum of a fluid element is obtained. We consider a general fluid described by the Navier-Stokes-Korteweg (NSK) equation, which reproduces the behaviors of a standard viscous fluid, a fluid with the capillary action and a quantum fluid, with the proper choice of parameters. When the parameters of the NSK equation is adjusted to reproduce Madelung's hydrodynamic representation of the Schreodinger equation, the uncertainty relation of a fluid element reproduces the Kennard and the Robertson-Schreodinger inequalities in quantum mechanics. The derived minimum uncertainty state is the generalization of the coherent state and its uncertainty is given by a function of the shear viscosity. The viscous uncertainty can be smaller than the inviscid minimum value when the shear viscosity is smaller than a critical value which is similar in magnitude to the Kovtun-Son-Starinets (KSS) bound. This uncertainty reflects the information of the fluctuating microscopic degrees of freedom in the fluid and will modify the standard hydrodynamic scenario, for example, in heavy-ion collisions.