Generalization of Uncertainty Relation for Quantum and Stochastic Systems
arXiv:1208.0258 · doi:10.1016/j.physleta.2018.04.008
Abstract
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.
11 pages, 1 figure, the Robertson-Schroedinger uncertainty relation is discussed. Accepted for publication in Phys, Lett. A