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systems with symmetry breaking and restoration系统与对称破坏和修复.pdf

发布：2017-09-09约9.36万字共29页下载文档

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Symmetry 2010, 2, 40 - 68; doi:10.3390/sym2010040 OPEN ACCESS symmetry ISSN 2073-8994 /journal/symmetry Article Systems with Symmetry Breaking and Restoration Vyacheslav I. Yukalov Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia; E-Mail: yukalov@theor.jinr.ru, Tel.: 7 (496) 216-3947; 7 (496) 213-3824 Received: 15 December 2009 / Accepted: 29 December 2009 / Published: 11 January 2010 Abstract: Statistical systems, in which spontaneous symmetry breaking can be accompanied by spontaneous local symmetry restoration, are considered. A general approach to describing such systems is formulated, based on the notion of weighted Hilbert spaces and conﬁguration averaging. The approach is illustrated by the example of a ferroelectric with mesoscopic ﬂuctuations of paraelectric phase. The inﬂuence of the local symmetry restoration on the system characteristics, such as sound velocity and Debye-Waller factor, is discussed. Keywords: spontaneous symmetry breaking; spontaneous symmetry restoration; weighted Hilbert spaces; ferroelectric-paraelectric phase transition, relaxor ferroelectrics Classiﬁcation: PACS 05.30.Ch, 05.70.Ce, 05.70.Fh, 05.70.Jk, 77.22.Ej, 77.80.Jk 1. Introduction It is generally accepted that phase transitions are related to symmetry changes, so that the transfor- mation from a disordered to an ordered phase is accompanied by spontaneous symmetry breaking [ 1–3]. There also exist more complicated cases, when the symmetry, being broken in the major part of

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