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
While quantum-classical correspondence for a system is a very fundamental problem in modern physics,the understanding of its mechanism is often elusive,so the methods used and the results of detailed theoretical analy...While quantum-classical correspondence for a system is a very fundamental problem in modern physics,the understanding of its mechanism is often elusive,so the methods used and the results of detailed theoretical analysis have been accompanied by active debate.In this study,the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution.The inverted oscillator model plays an important role in several branches of cosmology and particle physics.The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them.It is shown from illustrations of the probability density that,although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one,the difference becomes relatively small when the classical excitation is sufficiently high.We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave.From these main interpretations and others in the text,we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system,which is a crucial concept in quantum mechanics.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Supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2016R1D1A1A09919503)
文摘While quantum-classical correspondence for a system is a very fundamental problem in modern physics,the understanding of its mechanism is often elusive,so the methods used and the results of detailed theoretical analysis have been accompanied by active debate.In this study,the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution.The inverted oscillator model plays an important role in several branches of cosmology and particle physics.The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them.It is shown from illustrations of the probability density that,although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one,the difference becomes relatively small when the classical excitation is sufficiently high.We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave.From these main interpretations and others in the text,we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system,which is a crucial concept in quantum mechanics.
