论文标题
较低的半经典演化
Semiclassical Evolution With Low Regularity
论文作者
论文摘要
我们证明了Schr \''Odinger-von neumann进化的半经典估计值，其平方根具有较低的规律性，或者在较长范围衰减的Hermite函数之间具有低规律性的wigner函数，其平方根具有较低的规律性。估计值以不同的弱拓扑结构结算，并适用于初始密度运算符，其平方根具有Wigner函数$ 7 $ $乘以尺寸，独立于尺寸。它们还适用于$ n $ $ n $的$ n $车身量子动力学。在附录中，我们最终估算出出现在Calderon-Vaillancourt定理上常数的范围中的依赖性。
We prove semiclassical estimates for the Schr\''odinger-von Neumann evolution with $C^{1,1}$ potentials and density matrices whose square root have either Wigner functions with low regularity independent of the dimension, or matrix elements between Hermite functions having long range decay. The estimates are settled in different weak topologies and apply to initial density operators whose square root have Wigner functions $7$ times differentiable, independently of the dimension. They also apply to the $N$ body quantum dynamics uniformly in $N$. In a appendix, we finally estimate the dependence in the dimension of the constant appearing on the Calderon-Vaillancourt Theorem.
