论文标题
部分可观测时空混沌系统的无模型预测
Pointillisme à la Signac and Construction of a Quantum Fiber Bundle Over Convex Bodies
论文作者
论文摘要
我们使用凸几何形状的极性二元性概念以及从符号几何形状的拉格朗日平面理论来构造椭圆形的纤维束，该纤维束可以看作是用于经典符号相空间的量子力学替代品。该纤维束的总空间由几何量子状态，Lagrangian平面通过其极性双重携带的凸形物体的产物组成，相对于第二个横向拉格朗日平面。.使用John Ellipsoid的理论，我们将这些几何学量子状态与以前的“量子blobs”相关联。量子斑点是与不确定性原理兼容相位空间的最小符号不变区域。我们表明，与单位相关的几何量子状态的一组等效类别与所有高斯波袋的集合一对一。
We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase space. The total space of this fiber bundle consists of geometric quantum states, products of convex bodies carried by Lagrangian planes by their polar duals with respect to a second transversal Lagrangian plane.. Using the theory of the John ellipsoid we relate these geometric quantum states to the notion of "quantum blobs" introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle. We show that the set of equivalence classes of unitarily related geometric quantum states is in a one-to-one correspondence with the set of all Gaussian wavepackets.
