A contradiction between quantum hydrodynamics and the existence of particles

A. I. Laptukhov

L. S. Kuz’menkov, Сергей Геннадьевич Максимов

R. K. Vadapalli, Charles A. Weatherford, Ioana Banicescu +2 more

Abstract This article scrutinizes anomalies in accuracy studies by Brook et al. Int J Quantum Chem 2001, 85, 263–271 for a moving free particle. These studies were carried out in the framework of the quantum trajectory method developed from Bohm's hydrodynamic formalism. These accuracy studies exhibited a strange behavior of the relative error in the probability density that apparently contradicts the quantum fluid dynamic formalism. It is found that improper initialization of the pseudoparticle velocities is responsible for the observed anomalies. This article presents a method for appropriate initialization of the pseudoparticle velocities. It also evaluates the accuracy of this method by reinvestigating accuracy studies by Brook et al. for a moving free particle. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 1–6, 2003

Mario Schönberg

Serguei Maximov, L. S. Kuz’menkov, J.L. Guardado

Abstract The quantum distribution function is derived to reach an accordance with quantum hydrodynamics and to conserve quantum properties of the system. This distribution function, when calculating statistical averages, leads to correct local values of the fundamental physical quantities; and the local conservation laws of the microscopic quantum hydrodynamics can be obtained from such statistics by passing to mathematical expectatives. The equation for the one‐particle distribution function generates the many‐particle distribution functions. Then, the BBGKY hierarchy equations are obtained. The one‐particle statistical operator of a system of fermions in the local equilibrium at arbitrary temperatures is calculated. The dynamics of local hydrodynamic functions (chemical potential, hydrodynamic velocity, and temperature) completely determine the dynamics of the one‐particle statistical operator. The quantum hydrodynamic equations for the proton‐neutron system at low temperatures are obtained from the equation for one‐particle distribution function. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Moise Bonilla–Licea, Dieter Schuch