Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the mean...Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-d...For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used toform a complete set. Some techniques, such as calculus of variations, isoparametric transformation,patch approximation, operator-splitting, characteristic method, negative norm estimate, energymethod, the theory of prior estimates and techniques are used. For the nonrectangular regions case,optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thusthe well-known theoretical problem has been thoroughly and completely solved. These methods havebeen successfully used in multilayer oil resources migration-accumulation numerical simulation.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 11175113)
文摘Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
基金This research is supported by the Major State Basic Research of China, the National Foundation of China and the National Key-Problems-Tackling Program of China.
文摘For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used toform a complete set. Some techniques, such as calculus of variations, isoparametric transformation,patch approximation, operator-splitting, characteristic method, negative norm estimate, energymethod, the theory of prior estimates and techniques are used. For the nonrectangular regions case,optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thusthe well-known theoretical problem has been thoroughly and completely solved. These methods havebeen successfully used in multilayer oil resources migration-accumulation numerical simulation.
