We use a density matrix formalism to derive a kinetic theory for a quantum gas. Generalized kinetic fields are introduced and, employing the Wigner function, a certain hierarchy of quantum hydrodynamic (QHD) equations for the corresponding macroscopic variables is obtained. We assert a maximum entropy principle to obtain closure of the QHD system. For the explicit incorporation of statistics a proper quantum entropy is analyzed in terms of the reduced density matrix. The determination of the reduced Wigner function for equilibrium and non-equilibrium conditions is found to become possible only by assuming that the Lagrange multipliers can be expanded in powers of ℏ^2. Quantum contributions are expressed in powers of ℏ^2 while classical results are recovered in the limit ℏ→0.
|Titolo:||Quantum hydrodynamic models from a maximum entropy principle|
|Autori interni:||TROVATO, Massimo|
|Data di pubblicazione:||2010|
|Rivista:||JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL|
|Appare nelle tipologie:||1.1 Articolo in rivista|