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Yixiao Qiao

Publications and source records attributed to Yixiao Qiao.

At least 19 recordsLinked to original sources
arXiv2026

Relative topological entropy and relative mean dimension of induced factors

We study the relation of relative topological entropy and relative mean dimension between a factor map and its induced factor map for amenable group actions. On the one hand, we prove that a factor map has zero relative topological entropy if and only if so does the induced factor map. On the other hand, we prove that a factor map has positive relative topological entropy if and only if the induced factor map has infinite relative mean dimension.

math.DS↗
arXiv2026

Topological entropy, mean dimension, and weakly equivalent flows

In this paper, we mainly revisit a nice theory for topological entropy of weakly equivalent flows, which was originally investigated by Ohno in 1980. We will develop a new approach, being more straightforward and elementary than the measure-theoretic one provided by Ohno, to the theory for weak equivalence of flows, and as a novelty, we study both topological entropy and mean dimension with a highly unified process in relation to such objects. In particular, for weakly equivalent flows without fixed points we recover Ohno's theorem for topological entropy relation with a substantially different method, and moreover, carry out an analogue within the framework of mean dimension; while for weakly equivalent flows with fixed points, our technique refines the procedure suggested in Ohno's construction, and strengthens Ohno's example with a view towards topological complexity of dynamical systems. Essentially, our method is topological. For this purpose, we first introduce a modification to the definition of topological entropy, by relating a spanning set inside the state space to a finite set outside, which comes to be a tiny but key difference, via a map, and further, show that it leads eventually to the same value as the topological entropy. Although to an intermediate extent, the modified quantity generally does not coincide with the one appearing in the classical definition, it has some basic combinatorial feature, which not only applies flexibly to topological entropy, but also adapts directly to the mean dimension context. Using this alternative, we are allowed to re-establish and enrich Ohno's theory.

math.DS↗
arXiv2025

Infinite topological entropy, positive mean dimension, and factors of subshifts

We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical systems, the subshifts of block type in the Hilbert cube. This in particular leads to a large class of concrete (and new) examples of dynamical systems having this property.

math.DS↗
arXiv2024

Anomalous switching pattern in the ferrimagnetic memory cell

Replacing the ferromagnet with ferrimagnet (FiM) in the magnetic tunnel junction (MTJ) allows faster magnetization switching in picoseconds. The operation of a memory cell that consists of the MTJ and a transistor requires reversable magnetization switching. When a constant voltage is applied, we find that the spin-transfer torque can only switch the FiM-MTJ from parallel to antiparallel state. This stems from the small switching window of FiM and the dynamic resistance variation during the magnetization switching. We find the resulting current variation can be suppressed by reducing the magnetoresistance ratio. Furthermore, we demonstrate that the switching window can be expanded by adjusting the amount of Gd in FiM. We predict that the polarity of both switching current (Jc,switch) and oscillation current (Jc,osc) reverses at the angular momentum compensation point but not the magnetization compensation point. This anomalous dynamic behavior is attributed to the different physical nature of magnetization switching and oscillation in FiM, which must be considered when designing FiM-based MRAM.

cond-mat.mes-hall↗
arXiv2024

Orthogonal Spin-Orbit Torque-Induced Deterministic Switching in NiO

The electrical switching of antiferromagnet (AFM) is very important for the development of ultrafast magnetic random-access memory (MRAM). This task becomes more difficult in antiferromagnetic oxide NiO which has complex anisotropy. We show that by utilizing two spin-orbit torques (SOT) from orthogonal currents, one can deterministically switch the magnetic moments of NiO in two electrical distinguishable states that can be read out using the spin Hall magnetoresistance. This deterministic switching relies on the symmetry of SOT on different sublattices, where the sign reversal of magnetic moments leads to constructive torques in the beginning and balanced torques in the end. In addition, we show that the easy-plane anisotropy plays a key role in the switching, which has been ignored in some previous works. The uniform magnetic dynamics in this work provides a clear physical picture in understanding the SOT switching of NiO. Furthermore, the electrical writing and reading function in our device advances the development of AFM-MRAM.

cond-mat.mes-hall↗
arXiv2024

Spin-Orbit Torque Driven Chiral Domain Wall Motion in Mn3Sn

Noncollinear chiral antiferromagnets, such as Mn3X (X = Sn, Ge), have garnered significant interest in spintronics due to their topologically protected Weyl nodes and large momentum-space Berry curvatures. In this study, we report rapid chirality domain-wall (CDW) motion in Mn3Sn, driven by spin-orbit torque at over 545.3 m.s^-1 a remarkably low current density of 9 10^10 A.m^-2. The results demonstrate that the chirality of the domain wall and the direction of the current collectively determine the displacement direction of the CDW. Theoretically, we provide ananalysis of the effective field experienced by the octupole moment, uncovering the underlying motion mechanism based on the unique profile of the chiral spin structure. Notably, CDWs with opposite chirality can form within the same Dzyaloshinskii-Moriya interaction sample, and the Neel-like CDW type is dictated by the orientation of the kagome plane rather than the negligible magnetostatic energy associated with the small magnetization (approximately 3.957 10^-3). Additionally, the CDW, with a considerable width of 770 nm, is segmented into three 60 portions due to the six-fold anisotropy in Mn3Sn. These emphasize that CDW motion in Mn3Sn cannot be quantitatively studied using ferromagnetic frameworks. We also demonstrate that a small external field can effectively regulate CDW velocity. Our comprehensive results and theoretical analysis provide crucial guidelines for integrating antiferromagnet CDWs into functional spintronic devices.

cond-mat.mes-hall↗
arXiv2024

Sofic mean dimension of typical actions and a comparison theorem

We refine two results in the paper entitled "Sofic mean dimension" by Hanfeng Li, improving two inequalities with two equalities, respectively, for sofic mean dimension of typical actions. On the one hand, we study sofic mean dimension of full shifts, for which, Li provided an upper bound which however is not optimal. We prove a more delicate estimate from above, which is optimal for sofic mean dimension of full shifts over arbitrary alphabets (i.e. compact metrizable spaces). Our refinement, together with the techniques (in relation to an estimate from below) in the paper entitled "Mean dimension of full shifts" by Masaki Tsukamoto, eventually allows us to get the exact value of sofic mean dimension of full shifts over any finite dimensional compact metrizable spaces. On the other hand, we investigate finite group actions. In contrast to the case that the acting group is infinite (and amenable), Li showed that if a finite group acts continuously on a finite dimensional compact metrizable space, then sofic mean dimension may be different from (strictly less than) the classical (i.e. amenable) mean dimension (an explicitly known value in this case). We strengthen this result by proving a sharp lower bound, which, combining with the upper bound, gives the exact value of sofic mean dimension for all the actions of finite groups on finite dimensional compact metrizable spaces. Furthermore, this equality leads to a satisfactory comparison theorem for those actions, deciding when sofic mean dimension would coincide with classical mean dimension. Moreover, our two results, in particular, verify for a typical class of sofic group actions that sofic mean dimension does not depend on sofic approximation sequences.

math.DS↗
arXiv2024

Sofic approximation sequences and sofic mean dimension

The main purpose of this paper is to strengthen our understanding of sofic mean dimension of two typical classes of sofic group actions. First, we study finite group actions. We prove that sofic mean dimension of any amenable group action does not depend on the choice of sofic approximation sequences. Previously, this result was known only if the acting group is an infinite amenable group. Moreover, we investigate the full shifts, for all sofic groups and all alphabets. We show that sofic mean dimension of any full shift depends purely on its alphabet. Our method is a refinement of the classical technique in relation to the estimates from above and below, respectively, for mean dimension of some typical actions. The key point of our results is that they apply to all compact metrizable spaces without any restriction (in particular, the alphabet concerned in a full shift and the space involved in a finite group action are not required to be finite-dimensional). Furthermore, we improve the quantitative knowledge of sofic mean dimension, restricted to finite-dimensional compact metrizable spaces, for those two typical classes of sofic group actions. As a direct consequence of the main ingredient of our proof, we obtain the exact value of sofic mean dimension of all the actions of finite groups on finite-dimensional compact metrizable spaces. Previously, only an upper bound for these actions was given. Besides, we also get the exact value of sofic mean dimension of full shifts when the alphabet is finite-dimensional.

math.DS↗
arXiv2024

Spin-Transfer-Torque Induced Spatially Nonuniform Switching in Ferrimagnets

Ferrimagnet (FiM), (FeCo)1-xGdx, attracts research attention due to its ultrafast magnetic dynamics and finite net magnetization. Incorporating FiM into the magnetic tunnel junction will be beneficial to further improve the writing speed of magnetic random access memory (MRAM). It is commonly assumed that the FeCo and Gd atoms are switched together due to the strong exchange coupling, which remains valid even if one performs the two-sublattice macrospin simulation. Interestingly, using the atomistic model developed by our group, it is clearly seen that different atoms are not switched together. In addition, our study reveals that the nature of switching is spatially nonuniform even in the small sample with the dimension of 20 nm-20 nm. Furthermore, the characteristics of nonuniformity are completely different for samples with different Gd composition (x). When x is close to the magnetization compensation point, successful switching cannot be obtained, but is accompanied by the stable oscillation. The atom type that dominates the oscillation is different from that predicted by the two-sublattice macrospin model. In addition, the size of singular region is a non-monotonic function of current density. All these results can only be understood by considering the spatial nonuniform magnetization dynamics.

cond-mat.mes-hall↗
arXiv2023

The Hilbert cube contains a minimal subshift of full mean dimension

We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in relation to mean dimension. Our result finally leads to a full understanding of a pair of exact ranges of all the possible values of mean dimension, within which there will always be a minimal dynamical system that can/cannot be embedded in the shift action on the Hilbert cube.

math.DS↗
arXiv2023

Deterministic Spin-Orbit Torque Switching of Mn3Sn with the Interplay between Spin Polarization and Kagome Plane

Previous studies have demonstrated spin-orbit torque (SOT) switching of Mn3Sn where the spin polarization lies in the kagome plane (configuration I). However, the critical current density ($ J_{crit}$) is unrealistically large ($ J_{crit}$=$ 10^{14}$ A/$ m^2$) and independent on the external field ($ H_{ext}$). The stabilized magnetic state also depends on the initial state. These features conflict with the ferromagnet (FM) switching scheme as claimed in those studies, and thus call for other explanations. Alternatively, the system with the spin polarization perpendicular to the kagome plane (configuration II) is more like the FM based system since the spin polarization is orthogonal to all magnetic moments. In this work, we show SOT switching of Mn3Sn in configuration II. Similar to the FM, Jcrit and Hext are in the order of $ 10^{10}$ A/$ m^2$ and hundreds of Oersted, respectively. The switching result is also independent of the initial state. Interestingly, the unique spin structure of Mn3Sn also leads to distinct features from FM systems. We demonstrate that Jcrit increases linearly with Hext, and extrapolation gives ultralow $ J_{crit}$ for the field-free switching system. In addition, the switching polarity is opposite to the FM. We also provide the switching phase diagram as a guideline for experimental demonstration. Our work provides comprehensive understanding for the switching mechanism in both configurations. The switching protocol proposed in this work is more advantageous in realistic spintronic applications. We also clearly reveal the fundamental difference between FM and noncollinear antiferromagnetic switching.

cond-mat.mes-hall↗
arXiv2022

Mean dimension of product spaces: a fundamental formula

Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was studied with deep applications around 2000 by Elon Lindenstrauss and Benjamin Weiss within the framework of amenable group actions. Let a countable discrete amenable group $G$ act continuously on compact metrizable spaces $X$ and $Y$. Consider the product action of $G$ on the product space $X\times Y$. The product inequality for mean dimension is well known: $\mathrm{mdim}(X\times Y,G)\le\mathrm{mdim}(X,G)+\mathrm{mdim}(Y,G)$, while it was unknown for a long time if the product inequality could be an equality. In 2019, Masaki Tsukamoto constructed the first example of two different continuous actions of $G$ on compact metrizable spaces $X$ and $Y$, respectively, such that the product inequality becomes strict. However, there is still one longstanding problem which remains open in this direction, asking if there exists a continuous action of $G$ on some compact metrizable space $X$ such that $\mathrm{mdim}(X\times X,G)<2\cdot\mathrm{mdim}(X,G)$. We solve this problem. Somewhat surprisingly, we prove, in contrast to (topological) dimension theory, a rather satisfactory theorem: If an infinite (countable discrete) amenable group $G$ acts continuously on a compact metrizable space $X$, then we have $\mathrm{mdim}(X^n,G)=n\cdot\mathrm{mdim}(X,G)$, for any positive integer $n$. Our product formula for mean dimension, together with the example and inequality (stated previously), eventually allows mean dimension of product actions to be fully understood.

math.DS↗
arXiv2022

Mean dimension of Bernstein spaces and universal real flows

We study the action of translation on the spaces of uniformly bounded continuous functions on the real line which are uniformly band-limited in a compact interval. We prove that two intervals themselves will decide if two spaces are topologically conjugate, while the length of an interval tells the mean dimension of a space. We also investigate universal real flows. We construct a sequence of compact invariant subsets of a space consisting of uniformly bounded smooth one-Lipschitz functions on the real line, which have mean dimension equal to one, such that all real flows can be equivariantly embedded in the translation on their product space. Moreover, we show that the countable self-product of any among them does not satisfy such a universal property. This, on the one hand, presents a more reasonable choice of a universal real flow with a view towards mean dimension, and on the other hand, clarifies a seemingly plausible impression; meanwhile, it refines the previously known results in this direction. Our proof goes through an approach of harmonic analysis. Furthermore, both the universal space that we provide and an embedding mapping which we build for any real flow are explicit.

math.DS↗
arXiv2022

Directional mean dimension and continuum-wise expansive $\mathbb{Z}^k$-actions

We study directional mean dimension of $\mathbb{Z}^k$-actions (where $k$ is a positive integer). On the one hand, we show that there is a $\mathbb{Z}^2$-action whose directional mean dimension (considered as a $[0,+\infty]$-valued function on the torus) is not continuous. On the other hand, we prove that if a $\mathbb{Z}^k$-action is continuum-wise expansive, then the values of its $(k-1)$-dimensional directional mean dimension are bounded. This is a generalization (with a view towards Meyerovitch and Tsukamoto's theorem on mean dimension and expansive multiparameter actions) of a classical result due to Mañé: Any compact metrizable space admitting an expansive homeomorphism (with respect to a compatible metric) is finite-dimensional.

math.DS↗
arXiv2019

Topological entropy of nonautonomous dynamical systems

Let $\mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^\ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system $(X,\{f_n\}_{n=1}^{+\infty})$ vanishes, then so does that of its induced system $(\mathcal{M}(X),\{f_n\}_{n=1}^{+\infty})$; moreover, once the topological entropy of $(X,\{f_n\}_{n=1}^{+\infty})$ is positive, that of its induced system $(\mathcal{M}(X),\{f_n\}_{n=1}^{+\infty})$ jumps to infinity. In contrast to Bowen's inequality, we construct a nonautonomous dynamical system whose topological entropy is not preserved under a finite-to-one extension.

math.DS↗
arXiv2018

Zero-dimensional isomorphic dynamical models

By an \emph{assignment} we mean a mapping from a Choquet simplex $K$ to probability measure-preserving systems, obeying some natural restrictions. We prove that if $Φ$ is an aperiodic assignment on a Choquet simplex $K$ such that the set of extreme points $\mathsf{ex}K$ is a countable union $\bigcup_n E_n$, where each set $E_n$ is compact, zero-dimensional, and the restriction of $Φ$ to the Bauer simplex $K_n$ spanned by $E_n$ can be `embedded' in some topological dynamical system, then $Φ$ can be `realized' in a zero-dimensional system.

math.DS↗
arXiv2017

The embedding problem in topological dynamics and Takens' theorem

We prove that every $\mathbb{Z}^{k}$-action $(X,\mathbb{Z}^{k},T)$ of mean dimension less than $D/2$ admitting a factor $(Y,\mathbb{Z}^{k},S)$ of Rokhlin dimension not greater than $L$ embeds in $(([0,1]^{(L+1)D})^{\mathbb{Z}^{k}}\times Y,σ\times S)$, where $D\in\mathbb{N}$, $L\in\mathbb{N}\cup\{0\}$ and $σ$ is the shift on the Hilbert cube $([0,1]^{(L+1)D})^{\mathbb{Z}^{k}}$; in particular, when $(Y,\mathbb{Z}^{k},S)$ is an irrational $\mathbb{Z}^{k}$-rotation on the $k$-torus, $(X,\mathbb{Z}^{k},T)$ embeds in $(([0,1]^{2^kD+1})^{\mathbb{Z}^k},σ)$, which is compared to a previous result by the first named author, Lindenstrauss and Tsukamoto. Moreover, we give a complete and detailed proof of Takens' embedding theorem with a continuous observable for $\mathbb{Z}$-actions and deduce the analogous result for $\mathbb{Z}^{k}$-actions. Lastly, we show that the Lindenstrauss--Tsukamoto conjecture for $\mathbb{Z}$-actions holds generically, discuss an analogous conjecture for $\mathbb{Z}^{k}$-actions appearing in a forthcoming paper by the first two authors and Tsukamoto and verify it for $\mathbb{Z}^{k}$-actions on finite dimensional spaces.

math.DS↗