NDLI: Quantum Moment Hydrodynamics and the Entropy Principle

Content Provider	Springer Nature Link
Author	Degond, P. Ringhofer, C.
Copyright Year	2003
Abstract	This paper presents how a non-commutative version of the entropy extremalization principle allows to construct new quantum hydrodynamic models. Our starting point is the moment method, which consists in integrating the quantum Liouville equation with respect to momentum p against a given vector of monomials of p. Like in the classical case, the so-obtained moment system is not closed. Inspired from Levermore's procedure in the classical case,$^{(26)}$ we propose to close the moment system by a quantum (Wigner) distribution function which minimizes the entropy subject to the constraint that its moments are given. In contrast to the classical case, the quantum entropy is defined globally (and not locally) as the trace of an operator. Therefore, the relation between the moments and the Lagrange multipliers of the constrained entropy minimization problem becomes nonlocal and the resulting moment system involves nonlocal operators (instead of purely local ones in the classical case). In the present paper, we discuss some practical aspects and consequences of this nonlocal feature.
Starting Page	587
Ending Page	628
Page Count	42
File Format	PDF
ISSN	00224715
Journal	Journal of Statistical Physics
Volume Number	112
Issue Number	3-4
e-ISSN	15729613
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2003-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Physical Chemistry Quantum Physics Mathematical and Computational Physics Statistical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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