In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation be...In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.展开更多
We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exp...We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.展开更多
The synthesized monoclinic（B-type） phase of Y2O3 has been investigated by in situ angle-dispersive x-ray diffraction in a diamond anvil cell up to 44 GPa at room temperature. A phase transition occurs from monoclini...The synthesized monoclinic（B-type） phase of Y2O3 has been investigated by in situ angle-dispersive x-ray diffraction in a diamond anvil cell up to 44 GPa at room temperature. A phase transition occurs from monoclinic（B-type） to hexagonal（A-type） phase at 23.5 GPa and these two phases coexist even at the highest pressure. Parameters of isothermal equation of state are V0= 69.0（1）A3, K0= 159（3） GPa, K0= 4（fixed） for the B-type phase and V0= 67.8（2） A3, K0= 156（3） GPa,K＇0= 4fixed for the A-type phase. The structural anisotropy increases with increasing pressure for both phases.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11204012 and 91321103
文摘In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.
基金Project supported by the National Natural Science Foundation of China (Grand No. 10575055)K. C. Wong Magna Fund in Ningbo University
文摘We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1232204 and 41502029)China Postdoctoral Science Foundation(Grant No.2015M580679)
文摘The synthesized monoclinic（B-type） phase of Y2O3 has been investigated by in situ angle-dispersive x-ray diffraction in a diamond anvil cell up to 44 GPa at room temperature. A phase transition occurs from monoclinic（B-type） to hexagonal（A-type） phase at 23.5 GPa and these two phases coexist even at the highest pressure. Parameters of isothermal equation of state are V0= 69.0（1）A3, K0= 159（3） GPa, K0= 4（fixed） for the B-type phase and V0= 67.8（2） A3, K0= 156（3） GPa,K＇0= 4fixed for the A-type phase. The structural anisotropy increases with increasing pressure for both phases.
