National Center for Theoretical Sciences

Lacunary δ‐Discretized Spherical Maximal Operators

ABSTRACT We study the lacunary analog of the ‐discretized spherical maximal operators introduced by Hickman and Jančar, for , and establish the boundedness on for all , along with the endpoint weak‐type estimate . We also prove the corresponding boundedness for the multi‐paramete...

Evidence for Exceptional Points as Topological Defects

Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the existing literature focuses on eigenstate sub...

A Sensitive Nonclassicality Certification Functional for Continuous-Variable Systems

If the \ps-based Glauber-Sudarshan distribution, $P_{\state}$, has negative values the quantum state,~$\state$, it describes is nonclassical. Due to $P$'s singular behaviour this simple criterion is impractical to use. Recent work [Bohmann and Agudelo, Phys. Rev. Lett. 124, 13360...

Solving the Gross-Pitaevskii equation with quantic tensor trains: Ground states and nonlinear dynamics

We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. For sufficiently regular functions, the QTT approach enables exponential...