Sentence examples for a quantum metric from inspiring English sources

We also introduce a notion of regularity for quantum metrics on G, and show how to construct a quantum metric from any ergodic action of G, starting from a regular quantum metric on G. Furthermore, we introduce a quantum Gromov Hausdorff distance between ergodic actions of G when G is separable and show that it induces the above topology.

So this one is somewhat of a "quantum metric" whose state changes depending on how you look at it.

We show that when G is a Lie group and G/Γ is connected, given any norm on the Lie algebra of G, the seminorm on C∗ ˆG/Γ,ρ) induced by the derivation map of the canonical G-action defines a compact quantum metric.

Mario is the Founder | CEO @ Quantum Metric, a digital experience analytics company that processes petabytes of digital traffic monthly.

We show that distoq is Lipschitz equivalent to Rieffel's distance distq, and give criteria for when a parameterized family of compact quantum metric spaces is continuous with respect to distoq.

We introduce a new distance distoq between compact quantum metric spaces.

We develop a matricial version of Rieffel's Gromov Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C∗-algebras.

Moreover, we also establish that if the length function l is allowed to vary, we can collapse quantum metric spaces to various quotient quantum metric spaces.

Several applications are given, including Wiener/Rademacher chaos estimation and new examples of Rieffelʼs compact quantum metric spaces.

Fundamentally, the topological physics arises from the geometric properties of quantum wavefunctions (e.g., Berry curvature, Berry connection, quantum metric, etc)., which have remained difficult to detect experimentally.

Furthermore, it is shown that this compact quantum metric space depends on ρ continuously, with respect to quantum Gromov Hausdorff distances.