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Two applications of the ■■-Hodge Theory

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Chinese Annals of Mathematics,Series B 2024年第1期45卷 137-150页

作者： Dingchang WEI Shengmao ZHU center of mathematical sciences Zhejiang UniversityHangzhou 310027China Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina

Using Hodge theory and Banach fixed point theorem,Liu and Zhu developed a global method to deal with various problems in deformation *** this note,the authors generalize Liu-Zhu's method to treat two deformation problems for non-Kahler *** apply the ■■-Hodge theory to construct a deformation formula for(p,q)-forms of compact complex manifold under deformations,which can be used to study the Hodge number of complex manifold under *** the second part of this note,by using the ■■-Hodge theory,they provide a simple proof of the unobstructed deformation theorem for the non-Kahler Calabi-Yau ■■-manifolds.

关键词： Complex structures Deformations (p,q)-Forms Non-Kahler Calabi-Yaumanifolds

Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants

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Science China(Physics,Mechanics & Astronomy) 2024年第9期Mechanics & Astronomy) .卷 47-54页

作者： Xiao-Bin Liang Bo Li Shao-Ming Fei School of Mathematics and Computer Science Shangrao Normal University Quantum Information Research center Shangrao Normal University School of mathematical sciences Capital Normal University

Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables. Here, we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties. For any quantum state, we establish optimal sets of three observables for both product and summation forms of uncertainty relations, and analytically derive the corresponding tightest uncertainty constants. We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form. Furthermore, the existence of the tightest constants excludes the validity of standard real quantum mechanics, underscoring the essential role of complex numbers in this field. Additionally, our findings resolve the conjecture posed in [Phys. Rev. Lett. 118, 180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.

关键词： uncertainty relation the tightest uncertainty constants optimal observable sets

Cosmological interpretation for the stochastic signal in pulsar timing arrays

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Science China(Physics,Mechanics & Astronomy) 2024年第4期67卷 43-50页

作者： Yu-Mei Wu Zu-Cheng Chen Qing-Guo Huang School of Fundamental Physics and mathematical sciences Hangzhou Institute for Advanced StudyUniversity of Chinese Academy of SciencesHangzhou 310024China School of Physical sciences University of Chinese Academy of SciencesBeijing 100049China Department of Astronomy Beijing Normal UniversityBeijing 100875China Advanced Institute of Natural sciences Beijing Normal UniversityZhuhai 519087China Department of Physics and Synergistic Innovation center for Quantum Effects and applications Hunan Normal UniversityChangsha 410081China CAS Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China

The pulsar timing array(PTA)collaborations have recently reported compelling evidence for a stochastic signal consistent with a gravitational-wave *** this paper,we combine the latest data sets from NANOGrav,PPTA,and EPTA to explore cosmological interpretations for the PTA signal from first-order phase transitions,domain walls,and cosmic strings,*** find that the domain wall model is strongly disfavored with the Bayes factors compared with the first-order phase transitions and cosmic strings being 1/90 and 1/189,respectively,breaking the degeneracy among these models in individual data *** also find that:(1)a strong phase transition at temperatures below the electroweak scale is favored,and the bubble collisions make the dominant contribution to the energy density spectrum;(2)a small reconnection probability p<1.55×10^(-1)allowed by strings in(super)string theory is favored at the 95%confidence level,and ground-based detectors can further constrain the parameter space.

关键词： puslar timing arrays gravitational-wave background first-order phase transitions domain walls cosmic strings

BaTiO_(3)/p-GaN/Au self-driven UV photodetector with bipolar photocurrent controlled by ferroelectric polarization

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Chinese Physics B 2024年第4期33卷 202-207页

作者：韩无双刘可为杨佳霖朱勇学程祯陈星李炳辉刘雷申德振 State Key Laboratory of Luminescence and applications Changchun Institute of OpticsFine Mechanics and PhysicsChinese Academy of SciencesChangchun 130033China center of Materials Science and Optoelectronics Engineering University of Chinese Academy of SciencesBeijing 100049China

Ferroelectric materials are promising candidates for ultraviolet photodetectors due to their ferroelectric *** this work,a BaTiO_(3)/p-GaN/Au hybrid heterojunction-Schottky self-driven ultraviolet photodetector was fabricated with excellent bipolar photoresponse *** 0 V bias,the direction of the photocurrent can be switched by flipping the depolarization field of BaTiO_(3),which allows the performance of photodetectors to be controlled by the ferroelectric ***,a relatively large responsivity and a fast response speed can be also *** particular,when the depolarization field of BaTiO_(3) is in the same direction of the built-in electric field of the Au/p-GaN Schottky junction(up polarized state),the photodetector exhibits a high responsivity of 18 mA/W at 360 nm,and a fast response speed of<40 ms at 0 *** findings pave a new way for the preparation of high-performance photodetectors with bipolar photocurrents.

关键词： ferroelectric effect bipolar self-driven photodetector

Weak Graph Map Homotopy and Its applications

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 235-252页

作者： Conglei ZHANG Yanying WANG Zhiguo ZHANG Yan ZHAO School of mathematical sciences Hebei Normal UniversityShijiazhuang 050024China Department of Basic Science Shanxi Agricultural UniversityJinzhang 030801ShanxiChina center for Topology and Geometry based Technology School of Mathematical SciencesHebei Normal UniversityShijiazhuang 050024China School of mathematical sciences Hebei Normal UniversityTaiyuan 030031China School of Mathematics and Computer Science Shanxi Normal UniversityShijiazhuang 050024China School of Mathematics and Science Hebei GEO UniversityShijiazhuang 050031China

The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and *** prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in *** difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial *** discuss its advantages over the graph homotopy *** its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple ***,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.

关键词： Weak graph map homotopy Trivial vertex Strong deformation retract Mapping class group MP-Homotopy group

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

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Acta Mathematica Scientia 2024年第4期44卷 1415-1440页

作者： Fan YANG Congming LI School of mathematical sciences CMA-ShanghaiShanghai Jiao Tong UniversityShanghai 200240China

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these *** this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

关键词： analysis of parabolic and elliptic types weak-strong uniqueness active liquid crystals weak solution energy equality

General formalism for dirty extreme-mass-ratio inspirals

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Science China(Physics,Mechanics & Astronomy) 2024年第7期67卷 22-29页

作者： Ye Jiang Wen-Biao Han Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China School of Astronomy and Space Science University of Chinese Academy of SciencesBeijing 100049China School of Fundamental Physics and mathematical sciences Hangzhou Institute for Advanced StudyUniversity of Chinese Academy of SciencesHangzhou 310024China Shanghai Frontiers Science center for Gravitational Wave Detection Shanghai 200240China

Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals(EMRIs).There is still a challenge to efficiently describe various“dirty”impacts on the inspirals,such as dark matter,gas,dipole radiation,and electromagnetic *** this study,we find the inherent linearity of the asymptotic solution of the inhomogeneous Teukolsky *** the basis of this property,we completely decouple the factors of the perturber and the background spacetime in the energy fluxes and *** the new decoupling form,the waveforms of EMRIs with non-geodesic motion in Kerr spacetime can be conveniently *** will help to resolve the environment(including gas,field,dark matter,electromagnetic interaction)around supermassive black holes and test general relativity.

关键词： gravitational wave Teukolsky equation extreme-mass-ratio inspirals

Nonvolatile and reconfigurable two-terminal electro-optic duplex memristor based on Ⅲ-nitride semiconductors

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Light(Science & applications) 2024年第4期13卷 706-716页

作者： Zhiwei Xie Ke Jiang Shanli Zhang Jianwei Ben Mingrui Liu Shunpeng Lv Yang Chen Yuping Jia Xiaojuan Sun Dabing Li State Key Laboratory of Luminescence and applications Changchun Institute of OpticsFine Mechanics and PhysicsChinese Academy of SciencesDongnanhu Road No.3888Changchun 130033China center of Materials Science and Optoelectronics Engineering University of Chinese Academy of SciencesYuquan Road No.19100049 BeijingChina

With the fast development of artificial intelligence(AI),Internet of things(IOT),etc,there is an urgent need for the technology that can efficiently recognize,store and process a staggering amount of *** AlScN material has unique advantages including immense remnant polarization,superior temperature stability and good latticematch to other III-nitrides,making it easy to integrate with the existing advanced III-nitrides material and device ***,due to the large band-gap,strong coercive field,and low photo-generated carrier generation and separation efficiency,it is difficult for AlScN itself to accumulate enough photo-generated carriers at the surface/interface to induce polarization inversion,limiting its application in in-memory sensing and *** this work,an electro-optic duplex memristor on a GaN/AlScN hetero-structure based Schottky diode has been *** twoterminal memristor shows good electrical and opto-electrical nonvolatility and *** both electrical and opto-electrical modes,the current on/off ratio can reach the magnitude of 104,and the resistance states can be effectively reset,written and long-termly *** on this device,the“IMP”truth table and the logic“False”can be successfully reproduced,indicating the huge potential of the device in the field of in-memory sensing and computing.

关键词： polarization duplex limiting

Quafu-RL:The cloud quantum computers based quantum reinforcement learning

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Chinese Physics B 2024年第5期33卷 29-34页

作者：靳羽欣许宏泽王正安庄伟峰黄凯旋时运豪马卫国李天铭陈驰通许凯冯玉龙刘培陈墨李尚书杨智鹏钱辰马运恒肖骁钱鹏顾炎武柴绪丹普亚南张翼鹏魏世杰曾进峰李行龙桂鲁金贻荣于海峰范桁刘东胡孟军 Beijing Academy of Quantum Information sciences Beijing 100193China State Key Laboratory of Low Dimensional Quantum Physics Department of PhysicsTsinghua UniversityBeijing 100084China Institute of Physics Chinese Academy of SciencesBeijing 100190China Frontier Science center for Quantum Information Beijing 100184China School of Physical sciences University of Chinese Academy of SciencesBeijing 100190China CAS center for Excellence in Topological Quantum Computation University of Chinese Academy of SciencesBeijing 100190China School of mathematical sciences Nankai UniversityTianjin 300071China

With the rapid advancement of quantum computing,hybrid quantum–classical machine learning has shown numerous potential applications at the current stage,with expectations of being achievable in the noisy intermediate-scale quantum(NISQ)*** reinforcement learning,as an indispensable study,has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical ***,despite the progress of quantum processors and the emergence of quantum computing clouds,implementing quantum reinforcement learning algorithms utilizing parameterized quantum circuits(PQCs)on NISQ devices remains *** this work,we take the first step towards executing benchmark quantum reinforcement problems on real devices equipped with at most 136 qubits on the BAQIS Quafu quantum computing *** experimental results demonstrate that the policy agents can successfully accomplish objectives under modified conditions in both the training and inference ***,we design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to quantum *** hope that the Quafu-RL can be a guiding example to show how to realize machine learning tasks by taking advantage of quantum computers on the quantum cloud platform.

关键词： quantum cloud platform quantum reinforcement learning evolutionary quantum architecture search