Alexander Zorin | Searcharxiv

arXiv2024

On periodic approximate solutions of ordinary differential equations

The issue of inheriting periodicity of an exact solution of a dynamic system by a difference scheme is considered. It is shown that some difference schemes (midpoint scheme, Kahan scheme) in some special cases provide approximate solutions of differential equations, which are periodic sequences. Such solutions are called periodic. A purely algebraic method for finding such solutions is developed. It is shown that midpoint scheme inherits periodicity not only in case of linear oscillator, but also in case of nonlinear oscillator, integrable into elliptic functions.

math.CA↗

arXiv2013

Nb nano superconducting quantum interference devices with high spin sensitivity for operation in magnetic fields up to 0.5\,T

We investigate electric transport and noise properties of microstrip-type submicron direct current superconducting quantum interference devices (dc SQUIDs) based on Nb thin films and overdamped Josephson junctions with a HfTi barrier. The SQUIDs were designed for optimal spin sensitivity $S_μ^{1/2}$ upon operation in intermediate magnetic fields $B$ (tens of mT), applied perpendicular to the substrate plane. Our so far best SQUID can be continuously operated in fields up to $B\approx\pm50\,\rm{mT}$ with rms flux noise $S_{Φ,\rm w}^{1/2}\leq250\,\rm{nΦ_0/Hz^{1/2}}$ in the white noise regime and spin sensitivity $S_μ^{1/2}\leq29\,\rm{μ_B/Hz^{1/2}}$. Furthermore, we demonstrate operation in $B=0.5\,\rm{T}$ with high sensitivity in flux $S_{Φ,\rm w}^{1/2}\approx680\,\rm{nΦ_0/Hz^{1/2}}$ and in electron spin $S_μ^{1/2}\approx79\,\rm{μ_B/Hz^{1/2}}$. We discuss strategies to further improve the nanoSQUID performance.

cond-mat.supr-con↗