We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists 0 < c ≤ 1 such that for every r > 0, there is R > 0 for which, if ν is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded ...

In the new agricultural scenarios, the interaction between autonomous tractors and a human operator is important when they jointly perform a task. Obtaining and exchanging accurate localization information between autonomous tractors and the human operator, working as a team, is a critical to maintaining safety, synchronization, and efficiency during the execution of a mission. An advanced loca...

We study the operator growth problem and its complexity in many-body localization (MBL) system from Lanczos algorithm perspective. Using Krylov basis, can be viewed as a single-particle hopping on semi-infinite chain with amplitudes given by coefficients. find that, MBL systems, coefficients scale \sim n/\ln(n) ...

In this paper we give a Specht-type characterization for unitary equivalence of operator tuples in the Cowen-Douglas class via their point-wise localizations.

We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator D such that the localization operator with symbol f coincides with the Toeplitz operator with symbol Df . An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Co...

The localization of vibrations is a widely observed, but little understood physical phenomenon. Roughly speaking, the effect of localization is a confinement of some eigenfunctions of an elliptic operator to a small portion of the original domain in the presence of irregularities of the boundary or of the coefficients of the underlying operator. Until recently, there have been essentially no ma...

A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation is derived in order for the localization of a particle to represent a space-time event. It is shown that there exists a conflict between this relation and t...