Kinetic approach for quantum hydrodynamic equations

M. Tessarotto, M. Ellero, P. Nicolini

Research output: Contribution to journalConference articlepeer-review


A striking feature of standard quantum mechanics (SQM) is its analogy with classical fluid dynamics. In particular it is well known the Schrödinger equation can be viewed as describing a classical compressible and non-viscous fluid, described by two (quantum) fluid fields {p, V}, to be identified with the quantum probability density and velocity field. This feature has suggested the construction of a phase-space hidden-variable description based on a suitable inverse kinetic theory (IKT; Tessarotto et al., 2007). The discovery of this approach has potentially important consequences since it permits to identify the classical dynamical system which advances in time the quantum fluid fields. This type of approach, however requires the identification of additional fluid fields. These can be generally identified with suitable directional fluid temperatures Tqm, i (for i = 1, 2, 3), to be related to the expectation values of momentum fluctuations appearing in the Heisenberg inequalities. Nevertheless the definition given previously for them (Tessarotto et al., 2007) is non-unique. In this paper we intend to propose a criterion, based on the validity of a constant H-theorem, which provides an unique definition for the quantum temperatures.

Original languageEnglish (US)
Pages (from-to)33-38
Number of pages6
JournalAIP Conference Proceedings
StatePublished - 2009
Event26th International Symposium on Rarefied Gas Dynamics, RGD26 - Kyoto, Japan
Duration: Jul 20 2008Jul 25 2008


  • Classical statistical mechanics
  • Kinetic theory
  • Standard quantum mechanics

ASJC Scopus subject areas

  • General Physics and Astronomy


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