The authors investigate the global existence and semiclassical limit of weak solutions to a sixth-order parabolic system,which is a quantum-corrected macroscopic model derived recently to simulate the quantum effects ...The authors investigate the global existence and semiclassical limit of weak solutions to a sixth-order parabolic system,which is a quantum-corrected macroscopic model derived recently to simulate the quantum effects in miniaturized semiconductor devices.展开更多
In this paper,we use the Wigner meaure approach to study the semiclassical limit of nonlinear Schroedinger equation in small time.We prove that:the linits of the quantum density:ρ^ε=:|ψ^ε|^2,and the quantum moment...In this paper,we use the Wigner meaure approach to study the semiclassical limit of nonlinear Schroedinger equation in small time.We prove that:the linits of the quantum density:ρ^ε=:|ψ^ε|^2,and the quantum momentum:J^ε=:εIm(-↑ψ^ε↓△ψ^ε）satisfy the compressible Euler equations before the formation of singularities in the limit system.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10871112, 10771008)the Research Fund for the Doctoral Program of Higher Education of China (No. 20090005120009)+1 种基金 the Fundamental Research Funds for the Central Universities (No. BUPT2009RC0702)the Talents Scheme Funds of BUPT
文摘The authors investigate the global existence and semiclassical limit of weak solutions to a sixth-order parabolic system,which is a quantum-corrected macroscopic model derived recently to simulate the quantum effects in miniaturized semiconductor devices.
文摘In this paper,we use the Wigner meaure approach to study the semiclassical limit of nonlinear Schroedinger equation in small time.We prove that:the linits of the quantum density:ρ^ε=:|ψ^ε|^2,and the quantum momentum:J^ε=:εIm(-↑ψ^ε↓△ψ^ε）satisfy the compressible Euler equations before the formation of singularities in the limit system.
