We analyze the effect of stochastic dephasing on geometric phases. The result implies that the correction of geometric phases relies on not only the fluctuation of the random variable in the stochastic process, but al...We analyze the effect of stochastic dephasing on geometric phases. The result implies that the correction of geometric phases relies on not only the fluctuation of the random variable in the stochastic process, but also the frequency of the system.展开更多
There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.
We utilize the general displacement operator proposed recently [C.Y. Chen, et al., Phys. Rev. A 74 （2006） 032328] to investigate a high-speed geometric quantum computation via vibrational mode decay of two trapped t...We utilize the general displacement operator proposed recently [C.Y. Chen, et al., Phys. Rev. A 74 （2006） 032328] to investigate a high-speed geometric quantum computation via vibrational mode decay of two trapped thermal ions. We find that, under some special conditions, the geometric phase gating is somewhat faster in the heating case than in the ideal case. We also investigate analytically the influence from the vibrational mode heating on the fidelity and the success probability of the implementation.展开更多
As one kind of key lightweight components with enormous quantities and diversities, the bent tubular parts have attracted in- creasing applications in aerospace, automobile, etc. Thus, how the inevitable springback be...As one kind of key lightweight components with enormous quantities and diversities, the bent tubular parts have attracted in- creasing applications in aerospace, automobile, etc. Thus, how the inevitable springback behaves under different bending specifications should be fully addressed to efficiently achieve the precision forming of various bent tubes. Taking the medium strength thin-walled 6061-T4 Al-alloy tube as the objective, via the deformation theory of plasticity, explicit/implicit FE method and experimental approaches, we explored and clarified the nonlinear springback rules of the tubes and corresponding mechanisms in universal rotary draw bending regarding angular springback and radius growth by deliberately changing the tube diameter D and wall thickness t. The geometry dependent springback behaviors of thin-walled tube upon cold bending are thus revealed: 1) With the increasing of D, the tangent tensile strain increases and the proportional coefficient decreases, which causes the angular springback to decrease, while the radius springback increases due to the larger bending radius. 2) With the increasing of t, the tangent tensile strain decreases and the proportional coefficient increases, resulting in the increase of both angular springback and radius springback. 3) Under the same D/t, the angular springback varies little, while the radius springback increases with the larger diameter D. 4) The D/t can be used as a reasonable nondimensional index to evaluate the springback angle; as to the radius growth, the individual effects of the D and t should be considered. 5) The verification of the above results was conducted by experiments and analytical analysis.展开更多
In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Prenet formulae for curves in similarity symplectic geometry are ob...In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Prenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations.展开更多
Quantum phase transitions (QPTs) play a central role for understanding many-body physics [1]. Different from classical phase transitions which are driven by thermal fluctuations, QPTs are driven by quantum fluctuation...Quantum phase transitions (QPTs) play a central role for understanding many-body physics [1]. Different from classical phase transitions which are driven by thermal fluctuations, QPTs are driven by quantum fluctuations at zero temperature and can be accessed by varying some physical parameters of the many-body system. Characterizing QPTs, which normally needs complicated theoretical calculations, becomes a fundamental problem to further study quantum matters. Here a group of physicists proposed to connect the geometrical properties of reduced density matrices (RDMs) of the physical system with its quantum phase transitions [2,3]展开更多
A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition i...A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.60573008
文摘We analyze the effect of stochastic dephasing on geometric phases. The result implies that the correction of geometric phases relies on not only the fluctuation of the random variable in the stochastic process, but also the frequency of the system.
文摘There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.
基金Supported by the National Natural Science Foundation of China under Grant No. 10774042the Natural Science Fondation of Hunan Province under Grant No. 09JJ3121the National Fundamental Research Program of China under Grant Nos. 2005CB724500 and60490280
文摘We utilize the general displacement operator proposed recently [C.Y. Chen, et al., Phys. Rev. A 74 （2006） 032328] to investigate a high-speed geometric quantum computation via vibrational mode decay of two trapped thermal ions. We find that, under some special conditions, the geometric phase gating is somewhat faster in the heating case than in the ideal case. We also investigate analytically the influence from the vibrational mode heating on the fidelity and the success probability of the implementation.
基金supported by the National Natural Science Foundation of China (Grant No. 50905144)Program for New Century Excellent Talentsin University+2 种基金the fund of the State Key Laboratory of Solidification Processing in NWPUthe Natural Science Basic Research Plan in Shaanxi Province (Grant No. 2011JQ6004)the 111 Project (Grant No.B08040)
文摘As one kind of key lightweight components with enormous quantities and diversities, the bent tubular parts have attracted in- creasing applications in aerospace, automobile, etc. Thus, how the inevitable springback behaves under different bending specifications should be fully addressed to efficiently achieve the precision forming of various bent tubes. Taking the medium strength thin-walled 6061-T4 Al-alloy tube as the objective, via the deformation theory of plasticity, explicit/implicit FE method and experimental approaches, we explored and clarified the nonlinear springback rules of the tubes and corresponding mechanisms in universal rotary draw bending regarding angular springback and radius growth by deliberately changing the tube diameter D and wall thickness t. The geometry dependent springback behaviors of thin-walled tube upon cold bending are thus revealed: 1) With the increasing of D, the tangent tensile strain increases and the proportional coefficient decreases, which causes the angular springback to decrease, while the radius springback increases due to the larger bending radius. 2) With the increasing of t, the tangent tensile strain decreases and the proportional coefficient increases, resulting in the increase of both angular springback and radius springback. 3) Under the same D/t, the angular springback varies little, while the radius springback increases with the larger diameter D. 4) The D/t can be used as a reasonable nondimensional index to evaluate the springback angle; as to the radius growth, the individual effects of the D and t should be considered. 5) The verification of the above results was conducted by experiments and analytical analysis.
基金supported by National Natural Science Foundation of China(Grant Nos.11471174 and 11101332)Natural Science Foundation of Shaanxi Province(Grant No.2014JM-1002)the Natural Science Foundation of Xianyang Normal University of Shaanxi Province(Grant No.14XSYK004)
文摘In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Prenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations.
文摘Quantum phase transitions (QPTs) play a central role for understanding many-body physics [1]. Different from classical phase transitions which are driven by thermal fluctuations, QPTs are driven by quantum fluctuations at zero temperature and can be accessed by varying some physical parameters of the many-body system. Characterizing QPTs, which normally needs complicated theoretical calculations, becomes a fundamental problem to further study quantum matters. Here a group of physicists proposed to connect the geometrical properties of reduced density matrices (RDMs) of the physical system with its quantum phase transitions [2,3]
基金Supported by National Natural Science Foundation of China under Grant No.11005002 and 11475004 New Century Excellent Talent of M.O.E（NCET-11-0937） Sponsoring Program of Excellent Younger Teachers in universities in Henan Province under Grant No.2010GGJS-181
文摘A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model.
