On the Aubry-Mather theory in statistical mechanics

被引：26

作者：

Candel, A ^{[1
]}

de la Llave, R

机构：

[1] CALTECH, Dept Math, Pasadena, CA 91125 USA

[2] Univ Texas, Dept Math, Austin, TX 78712 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1998年 / 192卷 / 03期

关键词：

Phase Space; Group Action; Statistical Mechanics; Mild Condition; Rotation Number;

D O I：

10.1007/s002200050313

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We generalize Aubry-Mather theory for configurations on the line to general sets with a group action. Cocycles on the group play the role of rotation numbers. The notion of Birkhoff configuration can be generalized to this setting. Under mild conditions on the group, we show how to find Birkhoff pound states for many-body interactions which are ferromagnetic, invariant under the group action and having periodic phase space.

引用

页码：649 / 669

页数：21

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