In this paper, we give a new characterization for the boundedness and compactness of differences of generalized weighted composition operators from the Bloch space into weightedtype spaces. Moreover, we give some estimates for the essential norm of these operators. Mathematics subject classification (2010): 30D45, 47B38.

A Bloch point singularity can form a metastable state in a magnetic nanosphere. We classify possible types of Bloch points and analytically derive the shape of the magnetization distribution for different Bloch points. We show that an external gradient field can stabilize the Bloch point: The shape of the Bloch point becomes radially dependent. We compute the magnetization structure of the nano...

It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and semiclassical expansion $\hbar$ energies coincide. related to fact dynamics $x$-space $(gx)$-space corresponds same energy spectrum effective constant $\hbar g^2$. Two equations, which govern those two spaces, Riccati-Bl...

Quantum geometry is a key quantity that distinguishes electrons in crystal from those the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike Berry curvature, an intuitive understanding of metric lacking. Here, we show Bloch leads momentum-space gravity. In particular, by extending semiclassical formulatio...