Integrability in the mesoscopic dynamics

JOURNAL OF GEOMETRY AND PHYSICS

卷:55

Article

关键词: mesoscopic dynamics;    Schrodinger equation integrable;    nonlinear differential equation;    operator evolution equation;    correlated electrons;   

DOI  :  10.1016/j.geomphys.2004.11.005

来源: Elsevier

【 摘 要 】

The Mesoscopic Mechanics (MeM), as introduced in [51, is relevant to the electron gas confined to two spatial dimensions. It predicts a special way of collective response of correlated electrons to the external magnetic field. The dynamic variable of this theory is a finite-dimensional operator, which is required to satisfy the mesoscopic Schrodinger equation, cf. (2) below. In this article, we describe general solutions of the mesoscopic Schrodinger equation. Our approach is specific to the problem at hand. It relies on the unique structure of the equation and makes no reference to any other techniques, with the exception of the geometry of unitary groups. In conclusion, a surprising fact comes to light. Namely, the mesoscopic dynamics filters through the (microscopic) Schrodinger dynamics as the latter turns out to be a clearly separable part, in fact an autonomous factor, of the evolution. This is a desirable result also from the physical standpoint. (c) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free