Abstract Ball’s complex plank theorem states that if $$v_1,\dots ,v_n$$ v 1 , ⋯ n are unit vectors in $${\mathbb {C}}^d$$ C d , and $$t_1,\...

The nitrogen-vacancy (NV) center has enabled widespread study of nanoscale nuclear magnetic resonance (NMR) spectroscopy at low fields. NMR high fields significantly improves the technique's spectral resolution, enabling clear identification closely related chemical species. However, NV-detected is typically performed using AC sensing through electron spin echo envelope modulation (ESEEM), a hy...

A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its $1/T_1$ relaxation rate due magnetic noise created by electric current fluctuations in material. We analyze this technique as wireless probe superconductivity atomically thin two dimensional materials. At temperatures $T \lesssim T_c$, dominant is transverse arising from quasiparticle excitatio...

We consider $$u(t,x)=(u_1(t,x),\cdots ,u_d(t,x))$$ the solution to a system of non-linear stochastic heat equations in spatial dimension one driven by d-dimensional space-time white noise. prove that, when $$d\le 3$$ , local time $$L(\xi ,t)$$ $$\{u(t,x)\,,\;t\in [0,T]\}$$ exists and $$L(\cdot ,t) $$ belongs a.s. Sobolev space H^{\alpha }({\mathbb {R}}^d)$$ for $$\alpha <\frac{4-d}{2}$$ $$d\ge ...

We investigate the magnetic ground state of Sm$_3$BWO$_9$ with distorted kagome lattice. A phase transition is identified at $T_N=0.75$ K from temperature dependence specific heat. From $^{11}$B nuclear resonance (NMR) measurements, an incommensurate order shown by double-horn type spectra under a $c$-axis field. While, absence line splitting observed for field oriented within $ab$-plane, indic...

Abstract Let $\ell $ and p be (not necessarily distinct) prime numbers F a global function field of characteristic with constants $\kappa . Assume that there exists $P_\infty which has degree $1$ let $\mathcal {O}_F$ the subring consisting functions no poles away from $f(X)$ polynomial in X coefficients We study solutions to Diophantine equations form $Y^{n}=f(X)$ lie and, particular, show if m...

We demonstrate rapid, high-fidelity state preparation and measurement in exchange-only Si/SiGe triple-quantum-dot qubits. Fast integration ($980$ ns) initialization ($\approx 300$ operations are performed with all-electrical, baseband control. emphasize a leakage-sensitive joint metric, developed the context of qubits but applicable more broadly, report an infidelity $2.5\pm0.5\times 10^{-3}$. ...

High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent use coupler elements tunably control interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling frequency crowding issues. Nonetheless, gate errors still limit capability near-term applications. reason, part, is exist...

To elucidate the origin of re-enhanced high-$T_c$ phase in heavily electron-doped Fe-pnictides, systematic $^{75}$As NMR studies are performed on LaFe$Pn$O$_{0.75}$H$_{0.25}$ by controlling pnictogen height ($h_{Pn}$) from Fe plane through substitution at $Pn$(=As) site with Sb or P. The measurements nuclear spin relaxation rate (1/$T_1$) and Knight shift ($K$) reveal that moderate fluctuations...

Inelastic-neutron-scattering measurements were performed on a single crystal of the heavy-fermion paramagnet UTe$_2$ above its superconducting temperature. We confirm presence antiferromagnetic fluctuations with incommensurate wavevector $\mathbf{k}_1=(0,0.57,0)$. A quasielastic signal is found, whose momentum-transfer dependence compatible magnetic moments $\mu\parallel\mathbf{a}$, sine-wave m...