arXiv subjects

Zhidong Zhang

Publications and source records attributed to Zhidong Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Room temperature giant magnetoresistance detection of spin hall nano-oscillator dynamics in synthetic antiferromagnetic Spin-Valve

Conventional spin Hall nano-oscillators (SHNOs) face fundamental power limitations due to the low anisotropic magnetoresistance (AMR < 0.3%) of ferromagnetic layers. To address this, we developed a synthetic antiferromagnetic spin-valve (SAF-SV) heterostructure [Ta/NiFe/Ru/NiFe/Cu/NiFe/Hf/Pt] that enables efficient giant magnetoresistance (GMR)-based detection of SHNO dynamics at room temperature. The NiFe/Ru/NiFe SAF reference layer, operating in the spin-flop state, couples with the NiFe free layer through a Cu spacer to achieve a remarkable GMR ratio of 0.568% - exhibiting complete independence of magnetic field/current orientation. Spin-torque ferromagnetic resonance (ST-FMR) verifies that the ferromagnetic resonance linewidth of the free layer can be effectively modulated by dc current through the Pt heavy metal layer, while maintaining decoupled dynamics from the SAF layer. Thermal management via high-thermal-conductivity SiC substrates and AlN capping layers successfully mitigates current-shunting-induced Joule heating. Notably, stable auto-oscillation peaks are observed at 0.82 mA bias current, with oscillation frequency tunable by external magnetic field and potential dual-mode behavior at low fields. This work establishes a new paradigm for room-temperature, high-power spintronic oscillators, offering significant potential for neuromorphic computing and coherent RF communication applications.

cond-mat.mes-hall↗

arXiv2025

Relationship between spin-glass three-dimensional (3D) Ising model and traveling salesman problems

In this work, the relationship between a spin-glass three-dimensional (3D) Ising model with the lattice size N = mnl and the traveling salesman problem (TSP) in a 3D lattice is studied. In particular, the mathematical structures of the two systems are investigated in details. In both the hard problems, the nontrivial topological structures, the non-planarity graphs, the nonlocalities and/or the long-range spin entanglements exist, while randomness presents, which make the computation very complicated. It is found that an absolute minimum core (AMC) model exists not only in the spin-glass 3D Ising model but also in the 3D TSP for determining the lower bound of their computational complexities, which can be mapped each other. It is verified that the spin-glass AMC model equals to the difference between a two-level (l = 2) grid spin-glass 3D Ising model and a spin-glass 2D Ising model, which is NP-complete. Furthermore, according to the mapping between the spin-glass 3D Ising model and the TSP, it is proven that the AMC model for the TSP identifies to the difference between a two-level (l = 2) grid TSP model and a 2D TSP model, which is NP-complete also. The AMC models in both models are proven to be at the border between the NP-complete problems and the NP-intermediate problems. Because the lower bound of the computational complexity of the spin-glass 3D Ising model is the computational complexity by brute force search of the AMC model, the lower bound of the computational complexity of the TSP in a 3D lattice is the computational complexity by brute force search of the AMC model for the TSP. All of them are in subexponential and superpolynomial. The present work provides some implications on numerical algorithms for the NP-complete problems, for instance, one cannot develop a polynomial algorithm, but may develop a subexponential algorithm for the 3D spin-glass problem or TSP.

physics.gen-ph↗

arXiv2025

Lower bound of computational complexity of knapsack problems

The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum processes in computer science. In this work, I determined the lower bound of the computational complexity of knapsack problems. I investigated the origin of nontrivial topological structures in these hard problems. It was uncovered that the nontrivial topological structures arise from the contradictory between the three-dimensional character of the lattice and the two-dimensional character of the transfer matrices used in the quantum statistics mechanism. I illustrated a phase diagram for the non-deterministic polynomial (NP) vs polynomial (P) problems, in which a NP-intermediate (NPI) area exists between the NP-complete problems and the P-problems, while the absolute minimum core model is at the border between the NPI and the NP-complete problems. The absolute minimum core model of the knapsack problem cannot collapse directly into the P-problem. Under the guide of the results, one may develop the best algorithms for solving various optimum problems in the shortest time, being in subexponential and superpolynomial. This work illuminates the road on various fields of science ranging from physics to biology to finances, and to information technologies.

physics.gen-ph↗

arXiv2025

Computational complexity of spin-glass three-dimensional (3D) Ising model

In this work, the computational complexity of a spin-glass three-dimensional (3D) Ising model (for the lattice size N = lmn, where l, m, n are the numbers of lattice points along three crystallographic directions) is studied. We prove that an absolute minimum core (AMC) model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane, has its computational complexity O(2^mn). Any algorithms to make the model smaller (or simpler) than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model. Therefore, the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2^mn) by any algorithms, which is in subexponential time, superpolynomial.

physics.gen-ph↗

arXiv2025

Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem

The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z2 lattice gauge model shows that it can be mapped to a K-SAT problem for K > = 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3.

physics.gen-ph↗

arXiv2025

Topological Quantum Statistical Mechanics and Topological Quantum Field Theories

In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan-von Neumann-Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan-von Neumann-Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry.

cond-mat.stat-mech↗

arXiv2025

Quantitative estimates for a nonlinear inverse source problem in a coupled diffusion equations with uncertain measurements

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show two Lipschitz-type stability results in $L^2$ and $(H^1(\cdot))^*$ norms, respectively. However, in practice, we could only observe the measurements at discrete sensors, which contain the noise. Hence, this work further investigates the recovery of the unknown source from the discrete noisy measurements. We propose a stable inversion scheme and provide probabilistic convergence estimates between the reconstructions and exact solution in two cases: convergence respect to expectation and convergence with an exponential tail. We provide several numerical experiments to illustrate and complement our theoretical analysis.

math.NA↗

arXiv2025

Large area curved silicon modules for future trackers

For many years there has been an aspiration within the community to develop curved silicon detectors for particle physics applications. We present the results from 10 x 10cm low mass support modules as a part of the "ZeroMass" project that aims to minimise the material budget for tracking and vertexing systems for future colliders. We use 50 μm thick DC coupled strip sensors from Micron Semiconductor Ltd., with a carbon composite support frame. Our current module demonstrators use a radius of curvature of 15cm, typical of that used for the outer parts of large pixel systems, or the inner part of strip trackers and the outer part of large radii vertex detectors. The material budget obtained varies from an $X_0$ of 0.05\% in the active area to 0.62\% in the support structure, with an average of 0.28\%. There is further scope for material budget reduction in applying the concept and methods to large instruments for future detector systems, which we also discuss.

physics.ins-det↗

arXiv2025

Determine the point source of the heat equation with sparse boundary measurements

In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is considered. We propose a numerical method to reconstruct the location of a Dirac point source by reformulating the inverse problem as a least-squares optimization problem, which is efficiently solved using a gradient descent algorithm. Numerical experiments confirm the accuracy of the proposed method and demonstrate its robustness to noise.

math.NA↗

arXiv2025

Exact solution of two-dimensional (2D) Ising model with a transverse field: a low-dimensional quantum spin system

The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic 2D Ising model with a transverse field and the ferromagnetic three-dimensional (3D) Ising model. The results obtained in this work can be extended to be suitable for the antiferromagnetic 2D Ising model with a transverse field in the cases without frustration.

cond-mat.stat-mech↗

arXiv2024

Topological Feature Search Method for Multichannel EEG: Application in ADHD classification

In recent years, the preliminary diagnosis of ADHD using EEG has attracted the attention from researchers. EEG, known for its expediency and efficiency, plays a pivotal role in the diagnosis and treatment of ADHD. However, the non-stationarity of EEG signals and inter-subject variability pose challenges to the diagnostic and classification processes. Topological Data Analysis offers a novel perspective for ADHD classification, diverging from traditional time-frequency domain features. However, conventional TDA models are restricted to single-channel time series and are susceptible to noise, leading to the loss of topological features in persistence diagrams.This paper presents an enhanced TDA approach applicable to multi-channel EEG in ADHD. Initially, optimal input parameters for multi-channel EEG are determined. Subsequently, each channel's EEG undergoes phase space reconstruction (PSR) followed by the utilization of k-Power Distance to Measure for approximating ideal point clouds. Then, multi-dimensional time series are re-embedded, and TDA is applied to obtain topological feature information. Gaussian function-based Multivariate Kernel Density Estimation is employed in the merger persistence diagram to filter out desired topological feature mappings. Finally, the persistence image method is employed to extract topological features, and the influence of various weighting functions on the results is discussed.The effectiveness of our method is evaluated using the IEEE ADHD dataset. Results demonstrate that the accuracy, sensitivity, and specificity reach 78.27%, 80.62%, and 75.63%, respectively. Compared to traditional TDA methods, our method was effectively improved and outperforms typical nonlinear descriptors. These findings indicate that our method exhibits higher precision and robustness.

cs.LG↗

arXiv2024

Towards improved understanding of spontaneous imbibition into dry porous media using pore-scale direct numerical simulations

Traditional approaches to mathematically describe spontaneous imbibition are usually based on either macro-scale models, such as Richards equation, or simplified pore-scale models, such as the bundle of capillary tubes (BCTM) or pore-network modeling (PNM). It is well known that such models cannot provide full microscopic details of the multiphase flow processes and that many pore-scale mechanisms still lack proper mathematical descriptions. To improve the predictive capabilities of traditional models, a fundamental understanding of pore-scale dynamics is needed. The focus of this paper is obtaining detailed insight and consistent explanation of particular processes during capillary-controlled water imbibition into dry porous media. We use two-dimensional model geometries and perform fully dynamic volume-of-fluid based direct numerical simulations of air-water multiphase flow at the pore-scale, to study processes that generally are not considered in traditional models. More specifically, we investigate differences between converging and diverging geometries, dynamic pressure and meniscus reconfiguration during pore-filling events, and the influence of inertia and pore size on imbibition dynamics and the occurrence of capillary barriers. Furthermore, we perform a detailed comparison between non-interacting and interacting BCTM and study the impact of the narrow contractions on imbibition dynamics and the trapping of the non-wetting phase. Obtained knowledge can be used to improve predictive models, which are broadly relevant considering the importance of spontaneous imbibition in many different natural and industrial processes.

physics.flu-dyn↗

arXiv2024

Conditional well-posedness and data-driven method for identifying the dynamic source in a coupled diffusion system from one single boundary measurement

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary measurement in finite time domain. We build the uniqueness theorem of this inverse problem. After that, we introduce a weighted norm and establish the conditional stability of Lipschitz type for the inverse problem by this weighted norm. The numerical inversions are considered under the framework of the deep neural networks (DNNs). We establish the generalization error estimates rigorously derived from Lipschitz conditional stability of inverse problem. Finally, we propose the reconstruction algorithms and give several numerical examples illustrating the performance of the proposed inversion schemes.

math.NA↗

arXiv2023

Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensors

This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.

math.NA↗

arXiv2023

Three-dimensional characterization of the steel-concrete interface by FIB-SEM nanotomography

While it is widely accepted that the steel-concrete interface (SCI) plays an important role in governing the long-term durability of reinforced concrete structures, understanding about the primary features of the SCI that influence corrosion degradation mechanisms has remained elusive. This lack of knowledge can be attributed, on the one hand, to the complex heterogeneous nature of the SCI, and, on the other hand, the absence of experimental techniques suitable for studying the relevant features of the SCI. Here, we use focused ion beam - scanning electron microscopy (FIB-SEM) nanotomography to obtain high resolution 3D tomograms of the steel-concrete interfacial zone. Five tomograms, spanning volumes ranging from 8,000 to 200,000 cubic micrometer, were acquired for situations representative of both non-corroded and corroded SCIs. The achieved voxel size falls within the range of 30-50 nm, thus providing a resolution clearly surpassing the capabilities of computed X-ray tomography. This resolution enables the 3D characterization of the microstructure at the capillary scale, which is the scale at which relevant corrosion and related mass transport processes occur. Thus, FIB-SEM nanotomography is capable of yielding datasets of the SCI that serve as basis for the generation of digital twins of the interfacial microstructure, thereby enabling future studies about durability and corrosion of reinforced concrete at the pore scale.

cond-mat.mtrl-sci↗

arXiv2023

Fractional Quantum Zeno Effect Emerging from Non-Hermitian Physics

Exploring non-Hermitian phenomenology is an exciting frontier of modern physics. However, the demonstration of a non-Hermitian phenomenon that is quantum in nature has remained elusive. Here, we predict quantum non-Hermitian phenomena: the fractional quantum Zeno (FQZ) effect and FQZ-induced photon antibunching. We consider a quantum optics platform with reservoir engineering, where nonlinear emitters are coupled to a bath of decaying bosonic modes whose own decay rates form band structures. By engineering the dissipation band, the spontaneous emission of emitters can be suppressed by strong dissipation through an algebraic scaling with fractional exponents - the FQZ effect. This fractional scaling originates uniquely from the divergent dissipative density of states near the dissipation band edge, different from the traditional closed-bath context. We find FQZ-induced strong photon antibunching in the steady state of a driven emitter even for weak nonlinearities. Remarkably, we identify that the sub-Poissonian quantum statistics of photons, which has no classical analogs, stems here from the key role of non-Hermiticity. Our setup is experimentally feasible with the techniques used to design lattice models with dissipative couplings.

quant-ph↗

arXiv2023

Solving the inverse potential problem in the parabolic equation by the deep neural networks method

In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is parameterized by deep neural networks (DNNs) for the reconstruction scheme. First, the uniqueness of the inverse problem is proved under some regularities assumption on the input sources. Then we propose a new loss function with regularization terms depending on the derivatives of the residuals for partial differential equations (PDEs) and the measurements. These extra terms effectively induce higher regularity in solutions so that the ill-posedness of the inverse problem can be handled. Moreover, we establish the corresponding generalization error estimates rigorously. Our proofs exploit the conditional stability of the classical linear inverse source problems, and the mollification on the noisy measurement data which is set to reduce the perturbation errors. Finally, the numerical algorithm and some numerical results are provided.

math.NA↗

arXiv2023

Magnetic phase diagram and multiple field-induced states in the intermetallic triangular-lattice antiferromagnet NdAuAl$_4$Ge$_2$ with Ising-like spins

Geometrical frustration and the enhancement of strong quantum fluctuations in two-dimensional triangular antiferromagnets can lead to various intriguing phenomena. Here, we studied the spin-1/2 triangular lattice antiferromagnet NdAuAl$_4$Ge$_2$. Thermodynamic and transport properties, such as magnetization and specific heat together with the resistivity measurements were performed. In zero field, two successive phase transitions were observed at $T_{\rm N1}=1.75\pm 0.02$ K and $T_{\rm N2}=0.49\pm 0.02$ K, respectively. Under magnetic field, $\rm XXZ$-type anisotropy was revealed, with the moments pointing along the easy $c$ axis. For $B\parallel c$, multiple field-induced states were observed, and the magnetic phase diagram was established based on the specific heat and magnetization data. The temperature-dependent resistivity measurements indicate that NdAuAl$_4$Ge$_2$ is a good metal. It is very likely that both the long-range RKKY interactions and the geometrical frustration play an important roles in this case.

cond-mat.str-el↗