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 varia...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.展开更多
In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these ...In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay＇s angle suitable for calculating the Berry curvature in the atom- molecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay＇s angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.展开更多
基金Supported by Basic Science Research Program through National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2016R1D1A1A09919503)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10825417)
文摘In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay＇s angle suitable for calculating the Berry curvature in the atom- molecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay＇s angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.
