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We study zero entropy automorphisms of a compact K\"ahler manifold $X$. Our goal is to bring to light some new structures of the action on the cohomology of $X$, in terms of the so-called dynamical filtrations on $H^{1,1}(X, {\mathbb R})$. Based on these filtrations, we obtain the first general upper bound on the polynomial growth of the iterations $(g^m)^* \, {\circlearrowleft} \, H^2(X, {\mathbb C})$ where $g$ is a zero entropy automorphism, in terms of ${\rm dim} \, X$ only. We also give an upper bound for the (essential) derived length $\ell_{\rm ess}(G, X)$ for every zero entropy subgroup $G$, again in terms of the dimension of $X$ only. We propose a conjectural upper bound for the essential nilpotency class $c_{\rm ess}(G,X)$ of a zero entropy subgroup $G$. Finally, we construct examples showing that our upper bound of the polynomial growth (as well as the conjectural upper bound of $c_{\rm ess}(G,X)$) are optimal., Comment: Geometric and Functional Analysis (2022), to appear; Title shortened a bit; Part of the content is moved to another paper in progress

Resonances in ultracold collisions involving heavy molecules are difficult to understand, and have proven challenging to detect. Here we report the observation of magnetically tunable Feshbach resonances in ultracold collisions between $^{23}$Na$^{40}$K molecules in the rovibrational ground state and $^{40}$K atoms. We prepare the atoms and molecules in various hyperfine levels of their ground states and observe the loss of molecules as a function of the magnetic field. The atom-molecule Feshbach resonances are identified by observing an enhancement of the loss rate coefficients. We have observed three resonances at approximately 101 G in various atom-molecule scattering channels, with the widths being a few hundred milliGauss. The observed atom-molecule Feshbach resonances at ultralow temperatures probe the three-body potential energy surface with an unprecedented resolution. Our work will help to improve the understanding of complicated ultracold collisions, and open up the possibility of creating ultracold triatomic molecules., Comment: 7 pages, 5 figures

Let $X$ be a normal projective variety admitting a polarized or int-amplified endomorphism $f$. We list up characteristic properties of such an endomorphism and classify such a variety from the aspects of its singularity, anti-canonical divisor and Kodaira dimension. Then we run the equivariant minimal model program with respect to not just the single $f$ but also the monoid $SEnd(X)$ of all surjective endomorphisms of $X$, up to finite-index. Several applications are given. We also give both algebraic and geometric characterizations of toric varieties via polarized endomorphisms., Comment: Acta Mathematica Vietnamica (to appear); minor changes. arXiv admin note: text overlap with arXiv:1806.05828

Let $X$ be a projective variety admitting a polarized (or more generally, int-amplified) endomorphism. We show: there are only finitely many contractible extremal rays; and when $X$ is $\mathbb{Q}$-factorial normal, every minimal model program is equivariant relative to the monoid $SEnd(X)$ of all surjective endomorphisms, up to finite index. Further, when $X$ is rationally connected and smooth, we show: there is a finite-index submonoid $G$ of $SEnd(X)$ such that $G$ acts via pullback as diagonal (and hence commutative) matrices on the Neron-Severi group; the full automorphisms group $Aut(X)$ has finitely many connected components; and every amplified endomorphism is int-amplified., Comment: Mathematical Research Letters (to appear); minor changes

Magnetic materials that possess large bulk perpendicular magnetic anisotropy (PMA) are essential for the development of magnetic tunnel junctions (MTJs) used in future spintronic memory and logic devices. The addition of an antiferromagnetic layer to these MTJs was recently predicted to facilitate ultra-fast magnetization switching. Here, we report a demonstration of a bulk perpendicular synthetic antiferromagnetic (P-SAFM) structure comprised of a (001) textured FePd/Ru/FePd trilayer with a face-centered-cubic (fcc) phase Ru spacer. The L10 FePd P-SAFM structure shows a large bulk PMA (~10.2 Merg/cc) and strong antiferromagnetic coupling (~2.60 erg/cm2). Full perpendicular magnetic tunnel junctions (P-MTJs) with a L10 FePd P-SAFM layer are then fabricated. Tunneling magnetoresistance ratios of up to ~25% (~60%) are observed at room temperature (5K) after post-annealing at 350 C. Exhibiting high thermal stabilities and large Ku, the bulk P-MTJs with an L10 FePd P-SAFM layer could pave a way for next-generation ultrahigh-density and ultra-low-energy spintronic applications., Comment: 8 pages, 4 figures

The study on deflagration-to-detonation transition (DDT) is very important because this mechanism has relevance to safety issues in industries, where combustible premixed gases are in general use. However, the quantitative prediction of DDT is one of the major unsolved problems in combustion and detonation theory to date. In this paper, the DDT process is studied theoretically and the critical condition is given by a concise theoretical expression. The results show that a deflagration wave propagating with about 60% Chapman-Jouguet (C-J) detonation velocity is a critical condition. This velocity is the maximum propagating velocity of a deflagration wave and almost equal to the sound speed of combustion products. When this critical conation is reached, a C-J detonation is triggered immediately. This is the quantitative criteria of the DDT process.

From very recent studies, the area spectral efficiency (ASE) performance of downlink (DL) cellular networks will continuously decrease and finally to zero with the network densification in a fully loaded ultra-dense network (UDN) when the absolute height difference between a base station (BS) antenna and a user equipment (UE) antenna is larger than zero, which is referred as the ASE Crash. We revisit this issue by considering the impact of the BS antenna downtilt on the downlink network capacity. In general, there exists a height difference between a BS and a UE in practical networks. It is common to utilize antenna downtilt to adjust the direction of the vertical antenna pattern, and thus increase received signal power or reduce inter-cell interference power to improve network performance. This paper focuses on investigating the relationship between the base station antenna downtilt and the downlink network capacity in terms of the coverage probability and the ASE. The analytical results of the coverage probability and the ASE are derived, and we find that there exists an optimal antenna downtilt to achieve the maximal coverage probability for each base station density. Moreover, we derive numerically solvable expressions for the optimal antenna downtilt, which is a function of the base station density. Our theoretical and numerical results show that after applying the optimal antenna downtilt, the network performance can be improved significantly. Specifically, with the optimal antenna downtilt, the ASE crash can be delayed by nearly one order of magnitude in terms of the base station density.

Let $X$ be a projective variety over an algebraically closed field $k$ of arbitrary characteristic $p \ge 0$. A surjective endomorphism $f$ of $X$ is $q$-polarized if $f^\ast H \sim qH$ for some ample Cartier divisor $H$ and integer $q > 1$. Suppose $f$ is separable and $X$ is $\mathbb{Q}$-Gorenstein and normal. We show that the anti-canonical divisor $-K_X$ is numerically equivalent to an effective $\mathbb{Q}$-Cartier divisor, strengthening slightly the conclusion of Boucksom, de Fernex and Favre (Theorem C) and also covering singular varieties over an algebraically closed field of arbitrary characteristic. Suppose $f$ is separable and $X$ is normal. We show that the Albanese morphism of $X$ is an algebraic fibre space and $f$ induces polarized endomorphisms on the Albanese and also the Picard variety of $X$, and $K_X$ being pseudo-effective and $\mathbb{Q}$-Cartier means being a torsion $\mathbb{Q}$-divisor. Let $f^{Gal}:\overline{X}\to X$ be the Galois closure of $f$. We show that if $p>5$ and co-prime to $deg\, f^{Gal}$ then one can run the minimal model program (MMP) $f$-equivariantly, after replacing $f$ by a positive power, for a mildly singular threefold $X$ and reach a variety $Y$ with torsion canonical divisor (and also with $Y$ being a quasi-\'etale quotient of an abelian variety when $\dim(Y)\le 2$). Along the way, we show that a power of $f$ acts as a scalar multiplication on the Neron-Severi group of $X$ (modulo torsion) when $X$ is a smooth and rationally chain connected projective variety of dimension at most three., Comment: Minor revision, 33 pages, Mathematische Annalen (to appear)

In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete interference information about two colors. The conceptual model provides an intuitional picture of the in-phase and out-of-phase photon correlations and a complete quantum understanding about the which-path information of two colored photons., Comment: 13 pages, 6 figures

We perform Feshbach spectroscopy in an ultracold mixture of $^{23}$Na and $^{40}$K with different spin-state combinations. We have observed 24 new interspecies Feshbach resonances at magnetic field up to 350 G. A full coupled-channel calculation is performed to assign these resonances. Among them, 12 resonances are identified as d-wave Feshbach resonances. These d-wave Feshbach resonances are about 5 G systematically smaller than the predications based on previous model potential. Taking into account these new experimental results, we improve the Born-Oppenheimer potentials between Na and K, and achieve good agreement between the theory and experiment for all the observed Feshbach resonances., Comment: 6 pages, 4 figures, 2 tables

Chemical reactions at ultracold temperature provide an ideal platform to study chemical reactivity at the fundamental level, and to understand how chemical reactions are governed by quantum mechanics. Recent years have witnessed the remarkable progress in studying ultracold chemistry with ultracold molecules. However, these works were limited to exothermic reactions. The direct observation of state-to-state ultracold endothermic reaction remains elusive. Here we report on the investigation of endothermic and nearly thermoneutral atom-exchange reactions in an ultracold atom-dimer mixture. By developing an indirect reactant-preparation method based on a molecular bound-bound transition, we are able to directly observe a universal endothermic reaction with tunable energy threshold and study the state-to-state reaction dynamics. The reaction rate coefficients show a strikingly threshold phenomenon. The influence of the reverse reaction on the reaction dynamics is observed for the endothermic and nearly thermoneutral reactions. We carry out zero-range quantum mechanical scattering calculations to obtain the reaction rate coefficients, and the three-body parameter is determined by comparison with the experiments. The observed endothermic and nearly thermoneutral reaction may be employed to implement collisional Sisyphus cooling of molecules, study the chemical reactions in degenerate quantum gases and conduct quantum simulation of Kondo effect with ultracold atoms., Comment: 5+5 pages, 4+6 figures

Let $X$ be a normal projective variety and $f:X\to X$ a non-isomorphic polarized endomorphism. We give two characterizations for $X$ to be a toric variety. First we show that if $X$ is $\mathbb{Q}$-factorial and $G$-almost homogeneous for some linear algebraic group $G$ such that $f$ is $G$-equivariant, then $X$ is a toric variety. Next we give a geometric characterization: if $X$ is of Fano type and smooth in codimension 2 and if there is an $f^{-1}$-invariant reduced divisor $D$ such that $f|_{X\backslash D}$ is quasi-\'etale and $K_X+D$ is $\mathbb{Q}$-Cartier, then $X$ admits a quasi-\'etale cover $\widetilde{X}$ such that $\widetilde{X}$ is a toric variety and $f$ lifts to $\widetilde{X}$. In particular, if $X$ is further assumed to be smooth, then $X$ is a toric variety., Comment: Mathematische Zeitschrift (to appear); minor changes