Nonlinear description of Yang-Mills cosmology： cosmic inflation and the accompanying Hannay's angle  

作　　者：Yacine Bouguerra Mustapha Maamache Jeong Ryeol Choi 

机构地区：[1]Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences,Universite Ferhat Abbas Setif 1, Setif 19000, Algeria [2]Département de Physique, Facultédes Sciences, Université de Jijel, BP 98,Ouled Aissa, Jijel 18000, Algeria [3]Department of Radiologic Technology, Daegu Health College, Yeongsong-ro 15, Buk-gu, Daegu 41453, Republic of Korea

出　　处：《Chinese Physics C》2017年第6期115-121,共7页中国物理C（英文版）

基　　金：Supported by Basic Science Research Program through National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2016R1D1A1A09919503)

摘　　要：Hannay＇s angle is a classical analogue of the ＂geometrical phase factor＂ found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay＇s angle is derived from a rigorous evaluation. The obtained Hannay＇s angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay＇s angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation,and its physical nature is addressed. Hannay＇s angle, together with its quantum counterpart Berry＇s phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation.Hannay＇s angle is a classical analogue of the ＂geometrical phase factor＂ found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay＇s angle is derived from a rigorous evaluation. The obtained Hannay＇s angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay＇s angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation,and its physical nature is addressed. Hannay＇s angle, together with its quantum counterpart Berry＇s phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation.

关 键 词：Yang-Mills cosmology Hannay angle time-dependent quartic Hamiltnian INFLATION 

分 类 号：P159[天文地球—天文学]