We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. T...We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. The clustered vortex states are specified by the inverse temperature β and the rotation frequency ω, which are the conjugate variables of energy E and angular momentum L,respectively. The formation of the axis-symmetric clustered vortex states(azimuthal angle independent) involves the separating of vortices with opposite circulation and the clustering of vortices with the same circulation around the origin and edge. The state preserves SO(2) symmetry while breaking Z_2 symmetry. We find that, near the uniform state, the rotation-free clustered state(ω = 0) emerges at particular values of L^(2)/E and β. At large energies, we obtain asymptotically exact vortex density distributions, whose validity condition gives rise to the lower bound of β for the rotation-free states. Noticeably, the obtained vortex density distribution near the edge at large energies provides a novel exact vortex density distribution for the corresponding chiral vortex system.展开更多
Shortcut to adiabaticity(STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxili...Shortcut to adiabaticity(STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper,an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.展开更多
基金support from the National Natural Science Foundation of China (Grant No. 12175215)the National Key Research and Development Program of China (Grant No. 2022YFA 1405300)NSAF (Grant No. U1930403)。
文摘We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. The clustered vortex states are specified by the inverse temperature β and the rotation frequency ω, which are the conjugate variables of energy E and angular momentum L,respectively. The formation of the axis-symmetric clustered vortex states(azimuthal angle independent) involves the separating of vortices with opposite circulation and the clustering of vortices with the same circulation around the origin and edge. The state preserves SO(2) symmetry while breaking Z_2 symmetry. We find that, near the uniform state, the rotation-free clustered state(ω = 0) emerges at particular values of L^(2)/E and β. At large energies, we obtain asymptotically exact vortex density distributions, whose validity condition gives rise to the lower bound of β for the rotation-free states. Noticeably, the obtained vortex density distribution near the edge at large energies provides a novel exact vortex density distribution for the corresponding chiral vortex system.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308)。
文摘Shortcut to adiabaticity(STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper,an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.
