Noah Tischler | Searcharxiv

arXiv2026

From Closed to Relative Higher-Genus Gromov-Witten Invariants via Resurgent Functions

Higher genus Gromov-Witten invariants of Calabi-Yau threefolds are encoded in a generating function which is an asymptotic series in a formal parameter $λ$. Using resurgence, analytic functions in this formal parameter were uncovered. In this paper we focus on the resolved conifold and study the enumerative meaning of the strong-coupling asymptotic expansion, in powers of $ 1/λ$, of the resurgent analytic functions. We show that this expansion contains both a closed curve-counting contribution in dual variables and a contribution governed by relative Gromov-Witten invariants, naturally interpreted in logarithmic geometry.

math.AG↗

arXiv2021

Electron-electron double resonance detected NMR spectroscopy using ensemble NV centers at 230 GHz and 8.3 Tesla

The nitrogen-vacancy (NV) center has enabled widespread study of nanoscale nuclear magnetic resonance (NMR) spectroscopy at low magnetic fields. NMR spectroscopy at high magnetic fields significantly improves the technique's spectral resolution, enabling clear identification of closely related chemical species. However, NV-detected NMR is typically performed using AC sensing through electron spin echo envelope modulation (ESEEM), a hyperfine spectroscopic technique that is not feasible at high magnetic fields. Within this paper, we have explored an NV-detected NMR technique for applications of high field NMR. We have demonstrated optically detected magnetic resonance (ODMR) with the NV Larmor frequency of 230 GHz at 8.3 Tesla, corresponding to a proton NMR frequency of 350 MHz. We also demonstrated the first measurement of electron-electron double resonance detected NMR (EDNMR) using the NV center and successfully detected $^{13}C$ nuclear bath spins. The described technique is limited by the longitudinal relaxation time ($T_1$), not the transverse relaxation time ($T_2$). Future applications of the method to perform nanoscale NMR of external spins at 8.3 T and even higher magnetic fields are also discussed.

cond-mat.mes-hall↗