arXiv quant-ph/98040571998-04-23quant-ph

开路径的绝热Berry相和Hannay角

Adiabatic Berry Phase and Hannay Angle for Open Paths

Arun Kumar Pati

备注：: Latex, no figures, 24 pages, submitted to Ann. Phys
发表信息：: Annals Phys.270:178-197,1998
DOI：: 10.1006/aphy.1998.5850

摘要：

我们通过定义一个广义规范位，其线积分给出了任意参数演化的相完整性，得到绝热Berry相。考虑到对于经典可积系统，如何获得开路Hannay角是一个很困难的问题，我们利用参数化相干态方法建立了开路Berry相位和Hannay角之间的联系.利用半经典波函数分析了开路Berry相位，得到开路Hannay角。进一步，通过用瞬时投影子的交换子及其微分表示绝热Berry相位，并利用算子的Wigner表示，得到分布函数及其微分之间的Poisson括号。这使我们能够讨论相位完整性的经典极限，它产生了开放路径的角度完整性。基于量子力学内积经典极限的思想，给出了汉内角的一个操作定义.本文还指出了开路Berry相位和Hannay角在波包复苏现象中的可能应用。

英文摘要：

We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain open-path Hannay angle, we establish a connection between the open-path Berry phase and Hannay angle by using the parametrised coherent state approach. Using the semiclassical wavefunction we analyse the open-path Berry phase and obtain the open-path Hannay angle. Further, by expressing the adiabatic Berry phase in terms of the commutator of instantaneous projectors with its differential and using Wigner representation of operators we obtain the Poisson bracket between distribution function and its differential. This enables us to talk about the classical limit of the phase holonomy which yields the angle holonomy for open-paths. An operational definition of Hannay angle is provided based on the idea of classical limit of quantum mechanical inner product. A probable application of the open-path Berry phase and Hannay angle to wave-packet revival phenomena is also pointed out.

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