It is found that in a quantum system with cyclic Hamiltonian the time-dependent Schrodinger equation admits the Bloch type solutions which have the form of Bloch function with respect to the time. These solutions cons...It is found that in a quantum system with cyclic Hamiltonian the time-dependent Schrodinger equation admits the Bloch type solutions which have the form of Bloch function with respect to the time. These solutions constitute an orthonormal basis of the solution space and lead to a new type of quantum phases. The new phases, called Bloch phases by the authors, are the special Aharonov-Anandan phases, and reduce to the Berry phases under the adiabatic approximation if the degeneracy of instantaneous eigen-energy is time-independent. The above conclusions are proved and calculation for the evolution of spin magnetic moments in a magnetic field precessing with constant angular velocity is exemplified.展开更多
The aim of this article is twofold.One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method.The other is to obtain the p...The aim of this article is twofold.One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method.The other is to obtain the precise values of Bloch constants for certain log-p-harmonic mappings.These results improve upon the corresponding results given in Bai et al.(Complex Anal.Oper.Theory,13(2):321-340,2019).展开更多
This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of C^n with critical points. Furthermore, the estimates of Bloch constant with respect to the...This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of C^n with critical points. Furthermore, the estimates of Bloch constant with respect to these subclasses are given.展开更多
In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses...In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.展开更多
文摘It is found that in a quantum system with cyclic Hamiltonian the time-dependent Schrodinger equation admits the Bloch type solutions which have the form of Bloch function with respect to the time. These solutions constitute an orthonormal basis of the solution space and lead to a new type of quantum phases. The new phases, called Bloch phases by the authors, are the special Aharonov-Anandan phases, and reduce to the Berry phases under the adiabatic approximation if the degeneracy of instantaneous eigen-energy is time-independent. The above conclusions are proved and calculation for the evolution of spin magnetic moments in a magnetic field precessing with constant angular velocity is exemplified.
基金supported by Guangdong Natural Science Foundation(2018A030313508)。
文摘The aim of this article is twofold.One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method.The other is to obtain the precise values of Bloch constants for certain log-p-harmonic mappings.These results improve upon the corresponding results given in Bai et al.(Complex Anal.Oper.Theory,13(2):321-340,2019).
基金Supported by the National Natural Science Foundation of China(11471111,11571105,11671362)Supported by the Natural Science Foundation of Zhejiang Province(LY16A010004)
文摘This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of C^n with critical points. Furthermore, the estimates of Bloch constant with respect to these subclasses are given.
基金supported by the National Natural Science Foundation of China(51178037,10632020)the 973 State Key Development Program for Basic Research of China(2010CB732104)
文摘In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.
