IKT approach for quantum hydrodynamic equations

A striking feature of standard quantum mechanics is its analogy with classical fluid dynamics. In particular it is well known the Schr\"{o}dinger equation can be viewed as describing a classical compressible and non-viscous fluid, described by two (quantum) fluid fields {\rho ,% \mathbf{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 $T_{QM,i}$ (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.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

IKT-approach to MHD turbulence

An open issue in turbulence theory is related to the determination of the exact evolution equation for the probability density associated to the relevant (stochastic) fluid fields. Such an equation in the usual approaches to turbulence reproduces, at most in an approximate sense, the correct fluid equations. In this paper we present a statistical model which applies to an incompressible, resistive and quasi-neutral magnetofluid. The approach is based on the formulation of an inverse kinetic theory (IKT) for the full set of MHD equations appropriate for an incompressible, viscous, quasi-neutral, isentropic, isothermal and resistive magnetofluid. Basic feature of the new approach is that it relies on first principles - including in particular the exact validity of the fluid equations - and thus permits the determination of the correct evolution equation for the probability density. Specific application of the theory here considered concerns the case of statistically homogeneous and stationary MHD turbulence