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Qin Deng

Publications and source records attributed to Qin Deng.

9 recordsLinked to original sources
arXiv2026

Phase calibration of quantum oscillations in the magnetostrictive coefficient using the topological antiferromagnet YbMnBi$_2$

The Berry phase accumulated along a cyclotron orbit encodes important information about electronic band topology and is commonly inferred from the phase of quantum oscillations. Measurements of the ac magnetostrictive coefficient have recently emerged as a sensitive thermodynamic probe of quantum oscillations, but the phase offset has not been experimentally calibrated. Here, using the topological antiferromagnet YbMnBi$_2$, we calibrate this offset by directly comparing quantum oscillations in magnetization with those in the ac magnetostrictive coefficient. Measurements of both responses on the same single crystal reveal a single fundamental frequency of approximately 160 T in fields up to 14 T, enabling a direct phase comparison free from ambiguities associated with multiple frequencies. We observe an approximately $\pi/2$ relative phase shift between the two oscillatory responses, consistent with the Maxwell relation linking the magnetostrictive coefficient to the stress derivative of magnetization. Our results establish the appropriate phase needed to extract cyclotron-orbit phase information from quantum oscillations in the ac magnetostrictive coefficient.

cond-mat.str-el↗
arXiv2025

Topology of non-collapsed three-dimensional RCD spaces

We show that non-collapsed $\text{RCD}(K,3)$ spaces without boundary are orbifolds whose topological singularities are locally finite and locally homeomorphic to cones over $\mathbb{RP}^2$, and that the topology of such spaces is stable under non-collapsed Gromov-Hausdorff convergence. We study the notion of non-orientability on these spaces as a key part of our analysis and show that the property of non-orientability (on uniformly sized balls) is stable under non-collapsed Gromov-Hausdorff convergence. Finally, we show that any non-orientable non-collapsed $\text{RCD}(K,3)$ space without boundary admits a ramified double cover which is itself an orientable non-collapsed $\text{RCD}(K,3)$ space without boundary, and that such ramified double cover is stable under non-collapsed Gromov-Hausdorff convergence.

math.DG↗
arXiv2023

Margulis Lemma on $\text{RCD}(K,N)$ spaces

We extend the Margulis Lemma for manifolds with lower Ricci curvature bounds to the $\text{RCD}(K,N)$ setting. As one of our main tools, we obtain improved regularity estimates for Regular Langrangian flows on these spaces.

math.DG↗
arXiv2022

Unique Continuation Problem on RCD Spaces. I

In this note we establish the weak unique continuation theorem for caloric functions on compact $RCD(K,2)$ spaces and show that there exists an $RCD(K,4)$ space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point. We also establish frequency estimates for eigenfunctions and caloric functions on the metric horn. In particular, this gives a strong unique continuation type result on the metric horn for harmonic functions with a high rate of decay at the horn tip, where it is known that the standard strong unique continuation property fails.

math.DG↗
arXiv2022

Failure of strong unique continuation for harmonic functions on RCD Spaces

Unique continuation of harmonic functions on $RCD$ space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on $RCD(K,2)$ spaces and give a counterexample for strong unique continuation in the setting of $ RCD(K,N)$ space for any $N\geq 4$ and any $K\in \mathbb{R}$.

math.DG↗
arXiv2021

Improved regularity estimates for Lagrangian flows on $\text{RCD}(K,N)$ spaces

This paper gives a contribution to the study of regularity of Lagrangian flows on non-smooth spaces with lower Ricci curvature bounds. The main novelties with respect to the existing literature are the better behaviour with respect to time and the local nature of the regularity estimates. These are obtained by sharpening previous results of the first and third authors, in combination with some tools recently developed by the second author (adapting to the synthetic framework ideas introduced in [Colding-Naber 12]. The estimates are suitable for applications to the fine study of $\text{RCD}$ spaces and play a central role in the construction of a parallel transport in this setting.

math.MG↗
arXiv2020

H\"older continuity of tangent cones in RCD(K,N) spaces and applications to non-branching

In this paper we prove that a metric measure space $(X,d,m)$ satisfying the finite Riemannian curvature-dimension condition ${\sf RCD}(K,N)$ is non-branching and that tangent cones from the same sequence of rescalings are H\"older continuous along the interior of every geodesic in $X$. More precisely, we show that the geometry of balls of small radius centred in the interior of any geodesic changes in at most a H\"older continuous way along the geodesic in pointed Gromov-Hausdorff distance. This improves a result in the Ricci limit setting by Colding-Naber where the existence of at least one geodesic with such properties between any two points is shown. As in the Ricci limit case, this implies that the regular set of an ${\sf RCD}(K,N)$ space has $m$-a.e. constant dimension, a result already established by Bru\`e-Semola, and is $m$-a.e convex. It also implies that the top dimension regular set is weakly convex and, therefore, connected. In proving the main theorems, we develop in the ${\sf RCD}(K,N)$ setting the expected second order interpolation formula for the distance function along the Regular Lagrangian flow of some vector field using its covariant derivative.

math.DG↗