Maximal and atomic Hardy spaces Hp and H A, 0 < p ≤ 1, are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is shown that Hp = H A with equivalent norms.

An exploratory study of the low-lying eigenvalues of the Wilson-Dirac operator and their corresponding eigen-vectors is presented. Results for the eigenvalues from quenched and unquenched simulations are discussed. The eigenvectors are studied with respect to their localization properties in the quenched approximation for the cases of SU(2) and SU(3).

We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, shows no critical slowing down for this problem.

In this paper the localization properties of the spectral expansions of distributions related to the self adjoint extension of the Schrodinger operator are investigated. Spectral decompositions of the distributions and some classes of distributions are defined. Estimations for Riesz means of the spectral decompositions of the distributions in the norm of the Sobolev classes with negative order ...

A particle with finite initial velocity in a disordered potential comes back and on average stops at the original location. This phenomenon, dubbed ``quantum boomerang effect'' (QBE), has been recently observed an experiment simulating quantum kicked-rotor model [Sajjad et al., Phys. Rev. X 12, 011035 (2022)]. We provide analytical arguments that support presence of QBE wide class systems. Suff...

Background: Heat stress in the steel industry is considered as a serious threat to the health and safety of workers. A wide spectrum of complications and diseases from mild disorders such as burning sensation to fatal conditions such as thermal shock may occur due to uncontrolled thermal stress. In this study, heat stress assessment was performed according to the wet-bulb globe temperature (WBG...

Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests quantum simulations. Here we experimentally investigate emergent Z2 invariance a 1D superconducting circuit with 10 transmon qubits. By precisely adjusting staggered longitudinal transverse fields to each qubit, construct an effective Hamiltonia...

Chiral symmetry provides the protection for a large class of topological edge states. It exists in non-Hermitian systems as well, and same anticommutation relation between Hamiltonian linear chiral operator, i.e., ${H,\mathrm{\ensuremath{\Pi}}}=0$, now warrants symmetric spectrum about origin complex energy plane. Utilizing two general approaches to identify generate symmetry, we first show tha...