The mass shifts for two-fermion bound and scattering P-wave states subject to the long-range interactions due QED in non-relativistic regime are derived. Introducing a short range force coupling spinless fermions one unit of angular momentum framework pionless EFT, we first calculate both perturbatively non-perturbatively Coulomb corrections fermion-fermion continuum infinite volume context. Mo...

We study the Hankel determinant generated by Laguerre weight with jump discontinuities at $t_k, k=1,\cdots,m$. By employing ladder operator approach to establish Riccati equations, we show that $\sigma_n(t_1,\cdots,t_m)$, logarithmic derivative of $n$-dimensional determinant, satisfies a generalization $\sigma$-from Painlev\'{e} V equation. Through investigating Riemann-Hilbert problem for asso...

Using $^{31}$P nuclear magnetic resonance (NMR) we investigate the recently discovered presaturation phase in highly frustrated two-dimensional spin system SrZnVO(PO$_4$)$_2$ [F. Landolt et al., Phys. Rev. B 104, 224435 (2021)]. Our data provide two pieces of evidence against presumed spin-nematic character this phase: i) NMR spectra reveal that it hosts a dipolar order and ii) 1/$T_1$ relaxati...

Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce ...

An element of a finitely generated non-Abelian free group F (X) is said to be filling if that element has positive translation length in every very small minimal isometric action of F (X) on an R-tree. We give a proof that the set of filling elements of F (X) is exponentially F (X)-generic in the sense of Arzhantseva and Ol’shanskĭı. We also provide an algebraic sufficient condition for an elem...