In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,...In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.展开更多
We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for...We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau-Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau-Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau-Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.展开更多
We investigate the quantum dynamical behaviors of bosons in a diamond chain with weak magnetic flux(WMF),including Landau–Zener tunnelling,Bloch oscillations,localization phenomenon,and collapses-revivals phenomena.W...We investigate the quantum dynamical behaviors of bosons in a diamond chain with weak magnetic flux(WMF),including Landau–Zener tunnelling,Bloch oscillations,localization phenomenon,and collapses-revivals phenomena.We observed that collapses-revivals phenomena can occur in diamond chain with WMF and cannot exist in the strong magnetic flux case as the previous study(Chang N N and Xue J K,2018,Chin.Phys.B 27105203).Induced by WMF,the energy band for the system varies from gapless to gapped structure.The position of the extrema of probability amplitude for ground state can also be altered by WMF within a single diamond plaquette.As a consequence,the transitions between different dynamical behaviors of bosons in diamond chain can be manipulated by WMF,depending on its initial configurations.展开更多
We analyze the effect of tilting and artificial magnetic flux, on the energy bands structure for the system and the corresponding tunneling dynamics for bosons with various initial configurations in the diamond lattic...We analyze the effect of tilting and artificial magnetic flux, on the energy bands structure for the system and the corresponding tunneling dynamics for bosons with various initial configurations in the diamond lattice chain, where intriguing and significant phenomena occur, including Landau–Zener tunneling, Bloch oscillations, and localization phenomenon.Both vertical tilting and artificial magnetic flux may alter the structure of energy levels（dispersion structure or flat band）,and enforce the occurrence of Landau–Zener tunneling, which scans the whole of the Bloch bands. We find that, transitions among Landau–Zener tunneling, Bloch oscillations, and localization phenomenon, are not only closely related to the energy bands structure, but also depends on the initial configuration of bosons in the diamond lattice chain. As a consequence,Landau–Zener tunneling, Bloch oscillations, and localization phenonmenon of bosons always counteract and are complementary with each other in the diamond lattice chain.展开更多
In this paper,we give a definition of Bloch mappings defined in the unit polydisk D^n, which generalizes the concept of Bloch functions defined in the unit disk D.It is known that Bloch theorem fails unless we have so...In this paper,we give a definition of Bloch mappings defined in the unit polydisk D^n, which generalizes the concept of Bloch functions defined in the unit disk D.It is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex variables.We shall establish the corresponding distortion theorems for subfamiliesβ(K)andβ_(loc)(K) of Bloch mappings defined in the polydisk D^n,which extend the distortion theorems of Liu and Minda to higher dimensions.As an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in D^n.In particular,our results reduce to the classical results of Ahlfors and Landau when n=1.展开更多
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)。
文摘In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
基金Project supported by the National Natural Science Foundation of China (Grant No 10874251)
文摘We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau-Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau-Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau-Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.
基金Project supported the National Natural Science Foundation of China(Grant Nos.11974053,11674026,11274255,11305132,and 11475027)China Scholarship Council(CSC)
文摘We investigate the quantum dynamical behaviors of bosons in a diamond chain with weak magnetic flux(WMF),including Landau–Zener tunnelling,Bloch oscillations,localization phenomenon,and collapses-revivals phenomena.We observed that collapses-revivals phenomena can occur in diamond chain with WMF and cannot exist in the strong magnetic flux case as the previous study(Chang N N and Xue J K,2018,Chin.Phys.B 27105203).Induced by WMF,the energy band for the system varies from gapless to gapped structure.The position of the extrema of probability amplitude for ground state can also be altered by WMF within a single diamond plaquette.As a consequence,the transitions between different dynamical behaviors of bosons in diamond chain can be manipulated by WMF,depending on its initial configurations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11764039,11475027,11865014,11865014,11274255,and 11305132)the Natural Science Foundation of Gansu Province,China(Grant No.17JR5RA076)the Scientific Research Project of the Higher Education of Gansu Province,China(Grant No.2016A-005)
文摘We analyze the effect of tilting and artificial magnetic flux, on the energy bands structure for the system and the corresponding tunneling dynamics for bosons with various initial configurations in the diamond lattice chain, where intriguing and significant phenomena occur, including Landau–Zener tunneling, Bloch oscillations, and localization phenomenon.Both vertical tilting and artificial magnetic flux may alter the structure of energy levels（dispersion structure or flat band）,and enforce the occurrence of Landau–Zener tunneling, which scans the whole of the Bloch bands. We find that, transitions among Landau–Zener tunneling, Bloch oscillations, and localization phenomenon, are not only closely related to the energy bands structure, but also depends on the initial configuration of bosons in the diamond lattice chain. As a consequence,Landau–Zener tunneling, Bloch oscillations, and localization phenonmenon of bosons always counteract and are complementary with each other in the diamond lattice chain.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10571164)Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(Grant No.20050358052)
文摘In this paper,we give a definition of Bloch mappings defined in the unit polydisk D^n, which generalizes the concept of Bloch functions defined in the unit disk D.It is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex variables.We shall establish the corresponding distortion theorems for subfamiliesβ(K)andβ_(loc)(K) of Bloch mappings defined in the polydisk D^n,which extend the distortion theorems of Liu and Minda to higher dimensions.As an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in D^n.In particular,our results reduce to the classical results of Ahlfors and Landau when n=1.
