We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths quantum scalar fields at different temperature $T_1$ and $T_2$ bilinear couplings between them. particularly focus on entanglement or inseparability property states. The critical temperatures respective oscillators, $T_{1c}$ $T_{2c}$, higher than which disappears, can be determined. It is foun...

Let $C$ be a smooth curve over an algebraically closed field $\mathbf{k}$, and let $E$ locally free sheaf of rank $r$. We compute, for every $d>0$, the generating function motives $[\mathrm{Quot}_C(E,\boldsymbol{n} )] \in K_0(\mathrm{Var}_{\mathbf{k}})$, varying $\boldsymbol{n} = (0\leq n_1\leq\cdots\leq n_d)$, where $\mathrm{Quot}_C(E,\boldsymbol{n} )$ is nested Quot scheme points, parametrisi...

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...

Neutral atom arrays are a rapidly developing platform for quantum science. In this work, we demonstrate universal set of gate operations on new type neutral qubit: nuclear spin in an alkaline earth-like (AEA), $^{171}$Yb. We present techniques cooling, trapping and imaging using newly discovered magic wavelength at $\lambda = 486.78$ nm. implement qubit initialization, readout, single-qubit gat...

Neutral atom arrays are a rapidly developing platform for quantum science. In this work, we demonstrate universal set of gate operations on new type neutral qubit: nuclear spin in an alkaline earth-like (AEA), $^{171}$Yb. We present techniques cooling, trapping and imaging using newly discovered magic wavelength at $\lambda = 486.78$ nm. implement qubit initialization, readout, single-qubit gat...

This paper solves the two-sided version and provides a counterexample to general of 2003 conjecture by Hadwin Larson. Consider evaluations linear matrix pencils $L=T_0+x_1T_1+\cdots+x_mT_m$ on tuples as $L(X_1,\dots,X_m)=I\otimes T_0+X_1\otimes T_1+\cdots+X_m\otimes T_m$. It is shown that ranks constitute collection separating invariants for simultaneous similarity tuples. That is, $m$-tuples $...