Possible enhancements of collective flow anisotropy induced by uncertainty relation for fluid element

Abstract

In the stochastic formulation of viscous hydrodynamics, the velocity of a fluid element fluctuates satisfying a similar relation to the quantum-mechanical uncertainty relation. Using a non-relativistic toy model, we show that the presence of such a velocity fluctuation increases the local anisotropy of the momentum distributions of produced hadrons, and thus the collective flow parameters such as v 2 is emphasized.

Uncertainty relation in viscous hydrodynamics and its effects in collective flow observables

“…Here, the conditional ensemble average is calculated by fixing the value of the stochastic position rt at t. See for example, Matos et al (2020) for more detail. Applying the mean forward derivative to Equation (2), we find…”

“…and thus the complex function is interpreted as the wave function. See, for example, Matos et al (2020) for details.…”

“…Recently, the two of the present authors proposed an alternative formulation of the quantum-mechanical uncertainty relations (Gazeau & Koide 2020; Koide 2020; Koide & Kodama 2018;Matos et al 2020). In this approach, the origin of uncertainty is kinematically interpreted: the finite minimum uncertainty is attributed to the nondifferentiability of a particle trajectory.…”

“…It is known that dynamics of fluid is represented by the motions of fluid elements. In the variational formulation of the Navier-Stokes-Fourier equation, the viscous terms are induced through the stochastic motions of the fluid elements (Koide & Kodama 2012;Matos et al 2020). Therefore, an inequality, which is analogous to the quantum-mechanical one, will be satisfied between the fluctuations of the position and momentum of the fluid element.…”

“…In Koide & Kodama (2018) and Matos et al (2020), the minimum value of uncertainty was estimated for water at room temperature. The magnitude is much larger than the quantum-mechanical one but still much smaller than the observation scale of fluids.…”