【摘 要】
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In this talk,I will introduce the Wigner transport equation(WTE),which can be regarded as a quantum correction of the Boltzmann equation.The WTE has found m
【出 处】
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Workshop on Mathematical and Computational Methods for Trans
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In this talk,I will introduce the Wigner transport equation(WTE),which can be regarded as a quantum correction of the Boltzmann equation.The WTE has found many applications in many fields,such as nanoscale semiconductor device simulations and quantum optics.But the well-posedness of the stationary Wigner equation with inflow boundary conditions is still an open problem.I will introduce the recent progress on mathematical analysis and numerical simulation of the WTE.My talk will focus on the following three works cooperated with Ruo Li and Zhangpeng Sun at Peking University.First,we proved that the solution of the WTE with inflow boundary conditions is symmetric if the potential is symmetric even if the inflow conditions are asymmetric.Second,we proposed a semi-discretion method and showed that the solution of the semi-discrete WTE goes to the continuous WTE under some conditions as the mesh size of the velocity goes to zero.Third,we proved that the solution of the WTE of a close quantum system must be an even function of velocity.
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