Inverse kinetic theory for quantum hydrodynamic equations
Abstract
A remarkable feature of standard quantum mechanics is its analogy with classical fluid dynamics. This has motivated in the past efforts to formulate phasespace techniques based on various statistical models of quantum hydrodynamic equations. In this work an inverse kinetic theory for the Schrödinger equation has been constructed in order to formally describe the standard quantum dynamics by means of a classical dynamical system (to be denoted as phasespace Schrödinger dynamical system). It is shown that the inverse kinetic theory can be (non)uniquely determined under suitable mathematical prescriptions. In particular, when the quantum linear momentum is identified with a suitable linear kinetic momentum, it follows that the fluctuations of the position vector and the kinetic linear momentum satisfy identically the Heisenberg theorem.
 Publication:

Physical Review A
 Pub Date:
 January 2007
 DOI:
 10.1103/PhysRevA.75.012105
 arXiv:
 arXiv:quantph/0606091
 Bibcode:
 2007PhRvA..75a2105T
 Keywords:

 03.65.Ca;
 47.10.Fg;
 47.15.km;
 11.10.Cd;
 Formalism;
 Dynamical systems methods;
 Potential flows;
 Axiomatic approach;
 Quantum Physics