Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures.Here,we point out that discrete synthe...Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures.Here,we point out that discrete synthetic Poincaréhalf-planes and Poincarédisks,which are created by lattices in flat planes,support infinitely degenerate eigenstates for any nonzero eigenenergies.Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces.Furthermore,all eigenstates are exponentially localized in the hyperbolic coordinates,signifying the first example of quantum funneling effects in Hermitian systems.As such,any initial wave packet travels towards the edge of the Poincaréhalf-plane or its equivalent on the Poincarédisk,delivering an efficient scheme to harvest light and atoms in two dimensions.Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.展开更多
In recent years,an extensive study has focused on the effects of various factors associated with the membrane support layer such as the size of the pores,porosity,thickness,hydrophobicity,and hydrophilicity,through bo...In recent years,an extensive study has focused on the effects of various factors associated with the membrane support layer such as the size of the pores,porosity,thickness,hydrophobicity,and hydrophilicity,through both theoretical and empirical approaches.Along with numerical and analytical modeling,these variables are described by various two-and three-dimensional models,which have also developed for these parameters and variables.For engineering the selective layer,different categories of materials based on various morphologies,dimensions,or porosity were used as interlayers.Regarding the interlayers,there are relatively inconsistent reports in the literature and publications,primarily due to a lack of research and modeling.By modeling the influence of interlayers in thin film composite membranes,an innovative insight could be provided for optimizing other membrane processes.As a result,this research emphasizes the modeling and discussion of interlayers and their performance,particularly in the forward osmosis process,where scientific data and modeling are lacking.In addition to discussing the funnel and gutter effect carried out by the interlayers present in all membrane processes,modeling the impacts of the interlayer in the forward osmosis process will provide novel perspectives that could influence other processes.展开更多
基金supported by the National Natural Science Foundation of China(11804268)the National Key R&D Program of China(2018YFA0307601)。
文摘Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures.Here,we point out that discrete synthetic Poincaréhalf-planes and Poincarédisks,which are created by lattices in flat planes,support infinitely degenerate eigenstates for any nonzero eigenenergies.Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces.Furthermore,all eigenstates are exponentially localized in the hyperbolic coordinates,signifying the first example of quantum funneling effects in Hermitian systems.As such,any initial wave packet travels towards the edge of the Poincaréhalf-plane or its equivalent on the Poincarédisk,delivering an efficient scheme to harvest light and atoms in two dimensions.Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.
基金support of the Babol Noshirvani University of Technology(No.BNUT/389026/03)INSF(No.4039888).
文摘In recent years,an extensive study has focused on the effects of various factors associated with the membrane support layer such as the size of the pores,porosity,thickness,hydrophobicity,and hydrophilicity,through both theoretical and empirical approaches.Along with numerical and analytical modeling,these variables are described by various two-and three-dimensional models,which have also developed for these parameters and variables.For engineering the selective layer,different categories of materials based on various morphologies,dimensions,or porosity were used as interlayers.Regarding the interlayers,there are relatively inconsistent reports in the literature and publications,primarily due to a lack of research and modeling.By modeling the influence of interlayers in thin film composite membranes,an innovative insight could be provided for optimizing other membrane processes.As a result,this research emphasizes the modeling and discussion of interlayers and their performance,particularly in the forward osmosis process,where scientific data and modeling are lacking.In addition to discussing the funnel and gutter effect carried out by the interlayers present in all membrane processes,modeling the impacts of the interlayer in the forward osmosis process will provide novel perspectives that could influence other processes.
