In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
In this paper,we consider the adiabatic limit of Fu–Yau equations on a product of two Calabi–Yau manifolds.We prove that the adiabatic limit of Fu–Yau equations are quasilinear equations.
We provide an analytical construction of the gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition.This result is a necessary ingredient in studies of the relation betw...We provide an analytical construction of the gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition.This result is a necessary ingredient in studies of the relation between gauged sigma model and nonlinear sigma model,such as the closed or open quantum Kirwan map.展开更多
The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computatio...The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computation of the ground state of the Gross-Pitaevskii equation(GPE).Numerical results for the linear and nonlinear Schr odinger equation and for the ground state solution of the GPE are also presented and validated against analytical results or other classical schemes such as Crank-Nicholson.展开更多
基金supported by National Natural Science Foundation of USA(Grant No.DMS0705284)National Natural Science Foundation of China(Grant No.10801027)
文摘In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
基金Supported by the project"Analysis and Geometry on Bundle"of Ministry of Science and Technology of the People’s Republic of China(Grant No.SQ2020YFA070080)NSF in China(Grant Nos.11625106,11571332and 11721101)。
文摘In this paper,we consider the adiabatic limit of Fu–Yau equations on a product of two Calabi–Yau manifolds.We prove that the adiabatic limit of Fu–Yau equations are quasilinear equations.
文摘We provide an analytical construction of the gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition.This result is a necessary ingredient in studies of the relation between gauged sigma model and nonlinear sigma model,such as the closed or open quantum Kirwan map.
文摘The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computation of the ground state of the Gross-Pitaevskii equation(GPE).Numerical results for the linear and nonlinear Schr odinger equation and for the ground state solution of the GPE are also presented and validated against analytical results or other classical schemes such as Crank-Nicholson.
