2006/06/10 by Massimo Tessarotto, Marco Ellero, Piero Nicolini
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Kinetic energy #Method of quantum characteristics #Momentum (technical analysis) #Phase space #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum operation #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.75.012105
published as Phys.Rev.A75:012105,2007
arxiv created 2006/06/10 · openalex publication_date 2007/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A remarkable feature of standard quantum mechanics is its analogy with classical fluid dynamics. This has motivated in the past efforts to formulate phase-space techniques based on various statistical models of quantum hydrodynamic equations. In this work an inverse kinetic theory for the Schr"odinger equation has been constructed in order to formally describe the standard quantum dynamics by means of a classical dynamical system (to be denoted as phase-space Schr"odinger 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.