The Quantum Hydrodynamic Formulation of Dirac Equation and Its Generalized Stochastic and Non-linear Analogs
Physical Science International Journal · pp. 93–114 · Published 6 Nov 2014
10.9734/PSIJ/2015/12534Abstract
The quantum hydrodynamic-like equations as a function of two real sets of variables (i.e., the 4x4 action matrix and the 4-dimensional wave function modulus vector) of the Dirac equation are derived in the present work. The paper shows that in the low velocity limit the equations lead to the hydrodynamic representation of the Pauli’s equation for charged particle with spin given by Janossy [1] and by Bialynicki et al [2]. The Lorentz invariance of the relativistic quantum potential that generates the non-local behavior of the quantum mechanics is discussed.
References (19)
- 1 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? [DOI]
- 2 On the Einstein Podolsky Rosen paradox [DOI]
- 3 Bell’s theorem without inequalities [DOI]
- 4 Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement [DOI]
- 5 Statistical Mechanics of Elasticity [DOI]
- 6 The Quantum Hydrodynamic Model for Semiconductor Devices [DOI]
- 7 Plasmonics in Dirac systems: from graphene to topological insulators [DOI]
- 8 Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics [DOI]
- 9 Quantum fluctuations, decoherence of the mean field, and structure formation in the early Universe [DOI]
- 10 Theory of quanta
- 11 Zum hydrodynamischen Modell der Quantenmechanik [DOI]
- 12 A lower bound for the velocity of quantum communications in the preferred frame [DOI]
- 13 The speed of quantum information and the preferred frame: analysis of experimental data
- 14 Decoherence induced by zero-point fluctuations in quantum Brownian motion [DOI]
- 15 Stochastic Description of a Bose–Einstein Condensate [DOI]
- 16 The Classical Mechanics from the Quantum Equation
- 17 Particle Method for the Numerical Solution of the Time-Dependent Schrödinger Equation [DOI]
- 18 Exploring phase space localization of chaotic eigenstates via parametric variation [DOI]
- 19 Can fluctuating quantum states acquire the classical behavior on large scale? [DOI]
Cited by 4
P. Chiarelli · 2014
Chiarelli Piero · International Journal of Physical Sciences · 2015
Andika Kusuma Wijaya, Arief Hermanto, Muhammad Farchani Rosyid · International Journal of Geometric Methods in Modern Physics · 2022
Showing 3 of 4 known citations — external sources report more than can currently be individually listed.
Related research
- Quantum to Classical Transition in the Stochastic Hydrodynamic Analogy: The Explanation of the Lindemann Relation and the Analogies Between the Maximum of Density at He Lambda Point and that One at Water-Ice Phase Transition — shares topic coverage
- The Classical Mechanics from the Quantum Equation — shares topic coverage
Article metrics
Real usage data collected on this platform.
38
Page views
0
PDF downloads
8
Outbound clicks
4
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.