arXiv subjects

Zhiwei Sun

Publications and source records attributed to Zhiwei Sun.

At least 19 recordsLinked to original sources

arXiv2026

A convergent Scharfetter-Gummel scheme for a three-species drift-diffusion model for memristors

A structure-preserving fully implicit Scharfetter-Gummel finite-volume scheme for a three-species drift-diffusion model for semiconductors is proposed and analyzed. The equations describe the evolution of the electron, hole, and oxygen vacancy densities in a (bounded) memristor device, coupled to the Poisson equation for the electric potential, with mixed-type boundary conditions. Recasting the Scharfetter-Gummel fluxes in an upwind form, a hidden Fisher information component is revealed. Owing to the degeneracy of the Bernoulli function appearing in the fluxes, additional edgewise coercivity estimates are required, leading to refined local and global dissipation estimates. Using these ideas, the existence of a discrete finite-volume solution, a discrete free energy inequality, and the convergence of the numerical scheme are established. Numerical simulations in two space dimensions confirm the structure-preserving properties of the scheme and illustrate the filament formation in a memristor device.

math.NA↗

arXiv2026

A Bernoulli Phase-Fitted finite difference method with wavenumber-explicit analysis for the Helmholtz problem

A new Bernoulli phase-fitted finite difference method for the Helmholtz equation is introduced, obtained by applying a complexified Scharfetter--Gummel flux to the one-way factors of the operator. The rigorous analysis is developed for the one-dimensional Helmholtz problem with impedance boundary conditions. For the homogeneous problem, the scheme reproduces sampled plane-waves exactly, both in the interior and at the discrete impedance boundary closures. For the inhomogeneous problem, we prove wavenumber-explicit stability, consistency, and second-order convergence estimates for all nondegenerate mesh wavenumbers $kh\notin\pi\mathbb Z$. Under the fixed-resolution condition $kh\le s_0<\pi$ and $kL\ge\pi$, the estimates yield a pollution-free convergence theory. Numerical experiments confirm the plane-wave exactness and the predicted convergence behavior, and show favorable fixed-resolution performance compared with standard and dispersion-corrected finite difference methods.

math.NA↗

arXiv2026

A generalized Scharfetter-Gummel scheme for nonlocal cross-diffusion systems

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical scheme is based on a generalized Scharfetter-Gummel discretization of the nonlocal flux term. For merely integrable kernel functions, the scheme preserves the positivity, total mass, and entropy structure. The existence of a discrete solution and its convergence to a solution to the continuous problem, as the mesh size tends to zero, are shown. A key difficulty is the degeneracy of the generalized Bernoulli function in the Scharfetter-Gummel approximation. This issue is overcome by proving a uniform estimate for the discrete Fisher information, which requires both the Boltzmann and Rao entropy inequalities. Numerical simulations illustrate the features of the scheme in one and two space dimensions.

math.NA↗

arXiv2025

Quantitative Derivation of the Two-Component Gross--Pitaevskii Equation in the Hard-Core Limit with Uniform-in-Time Convergence Rate

We derive the time-dependent two-component Gross--Pitaevskii (GP) equation as an effective description of the dynamics of a dilute two-component Bose gas near its ground state, which exhibits a two-component Bose-Einstein condensate, in the GP limit. Our main result establishes a uniform-in-time bound on the convergence rate between the many-body dynamics and the effective description, explicitly quantified in terms of the particle number $N$, and also implies a uniform-in-time bound for the one-component case. This improves upon the works of Michelangeli and Olgliati [77, 89] by providing a sharper, $N$-dependent, time-independent convergence rate. Our approach further extends the framework of Benedikter, de Oliveira, and Schlein [10] to the multi-component Bose gas in the hard-core limit setting. More specifically, we develop the necessary Bogoliubov theory to analyze the dynamics of multi-component Bose gases in the GP regime.

math-ph↗

arXiv2024

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations

This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM with two types of loss functions, referred to as first-order and second-order least squares systems. By providing boundedness and coercivity analysis, we leverage C\'{e}a's Lemma to decompose the total error into the approximation, generalization, and optimization errors. Utilizing the Barron space theory and Rademacher complexity, an a priori error is derived regarding the training samples and network size that are exempt from the curse of dimensionality. Our results reveal that MIM significantly reduces the regularity requirements for activation functions compared to the deep Ritz method, implying the effectiveness of MIM in solving high-order equations.

math.NA↗

arXiv2024

Two-scale Analysis for Multiscale Landau-Lifshitz-Gilbert Equation: Theory and Numerical Methods

This paper discusses the theory and numerical method of two-scale analysis for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic materials. The novelty of this work can be summarized in three aspects: Firstly, the more realistic and complex model is considered, including the effects of the exchange field, anisotropy field, stray field, and external magnetic field. The explicit convergence orders in the $H^1$ norm between the classical solution and the two-scale solution are obtained. Secondly, we propose a robust numerical framework, which is employed in several comprehensive experiments to validate the convergence results for the Periodic and Neumann problems. Thirdly, we design an improved implicit numerical scheme to reduce the required number of iterations and relaxes the constraints on the time step size, which can significantly improve computational efficiency. Specifically, the projection and the expansion methods are given to overcome the inherent non-consistency in the initial data between the multiscale problem and homogenized problem.

math.NA↗

arXiv2023

Derivation of Vlasov equations for multi-species fermions

We explore a system of two-species fermions with $N$ particles. Through this exploration, we establish a two-species Husimi measure and construct a two-species Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy with error terms. We provide proofs of the smallness of these errors in the semiclassical and mean-field limits, fixing $\hbar = N^{-1/3}$. After that, we rigorously establish the uniqueness of this hierarchy. This allows us to conclude that the two-species Husimi measure from the solution of the $N$-particle Schr\"odinger equation approximates the solution of the Vlasov equation for two-species systems.

math-ph↗

arXiv2023

Electromagnetics with time-varied vacuum permittivity and permeability

Maxwell equations provide a complete description of the electromagnetic (EM) phenomena, which have been one of the key fundamental-theories of modern physics, such as electromagnetism, optics, quantum theories, etc. The vacuum permittivity and permeability (P&P) in the constitutive relation were regarded as constant, resulting into that the vacuum lightspeed is constant with time. However, neither the Maxwell equations nor any experiments demonstrated that the P&P must be invariable with time. Here, the P&P are assumed as time-varied, achieving a mathematical result exhibits that the P&P are increased with time exponentially. Then, the Maxwell equations of static and covariant EM fields are presented, which include the different constitutive relations. The EM characters in the time-varied case are investigated that, the lightspeed, level EM intensity, and magnetic effect of charge-motion decreases with time. The EM energy transforms into a new energy form caused by the P&P variation, and a new momentum-tensor form caused by propagation is found as well. At last, the Maxwell equations based on the observation results at our time are presented. Meanwhile, since the level EM intensity decreases with time, the energy per frequency is time-decreased, resulting into that the Planck constant decreases exponentially, and correspondingly, the Rydberg constant increases with time. A red-shift of absorption spectrum is predicted based on this finding, which is coincident with the Hubble observation results.

physics.class-ph↗

arXiv2023

Continuum Limit of Spin Dynamics on Hexagonal Lattice

This study investigates the atomistic spin system in $\rm CrCl_{3}$, which exhibits topologically nontrivial meron structures within its layered hexagonal lattice framework. We analyze the complete model of discrete spin dynamics on a two-dimensional hexagonal lattice and demonstrate its convergence to the continuum Landau-Lifshitz-Gilbert equation in the weak sense. The primary challenge lies in defining appropriate difference quotient and interpolation operators for the hexagonal lattice since the loss of symmetry. To address these, we utilized a one-step difference quotient for the 2nd nearest neighbors and introduced novel multi-step difference quotients for the 1st and 3rd nearest neighbors, enabling the integration by parts formula. Additionally, we generalized Ladysenskaya's interpolation operator for hexagonal lattices and provided an alternative strategy for the convergence procedure by applying an isometric mapping property. This work provides necessary tools for analyzing weak convergence in other atomistic nonlinear problems on hexagonal lattices towards the continuum limit.

math-ph↗

arXiv2023

Error Analysis of Mixed Residual Methods for Elliptic Equations

We present a rigorous theoretical analysis of the convergence rate of the deep mixed residual method (MIM) when applied to a linear elliptic equation with various types of boundary conditions. The MIM method has been proposed as a more effective numerical approximation method compared to the deep Galerkin method (DGM) and deep Ritz method (DRM) in various cases. Our analysis shows that MIM outperforms DRM and deep Galerkin method for weak solution (DGMW) in the Dirichlet case due to its ability to enforce the boundary condition. However, for the Neumann and Robin cases, MIM demonstrates similar performance to the other methods. Our results provides valuable insights into the strengths of MIM and its comparative performance in solving linear elliptic equations with different boundary conditions.

math.NA↗

arXiv2022

Homogenization of the Landau-Lifshitz-Gilbert equation with natural boundary condition

The full Landau-Lifshitz-Gilbert equation with periodic material coefficients and natural boundary condition is employed to model the magnetization dynamics in composite ferromagnets. In this work, we establish the convergence between the homogenized solution and the original solution via a Lax equivalence theorem kind of argument. There are a few technical difficulties, including: 1) it is proven the classic choice of corrector to homogenization cannot provide the convergence result in the $H^1$ norm; 2) a boundary layer is induced due to the natural boundary condition; 3) the presence of stray field give rise to a multiscale potential problem. To keep the convergence rates near the boundary, we introduce the Neumann corrector with a high-order modification. Estimates on singular integral for disturbed functions and boundary layer are deduced, to conduct consistency analysis of stray field. Furthermore, inspired by length conservation of magnetization, we choose proper correctors in specific geometric space. These, together with a uniform $W^{1,6}$ estimate on original solution, provide the convergence rates in the $H^1$ sense.

math.AP↗

arXiv2019

Spin waves in ferromagnetic thin films

A spin wave is the disturbance of intrinsic spin order in magnetic materials. In this paper, a spin wave in the Landau-Lifshitz-Gilbert equation is obtained based on the assumption that the spin wave maintains its shape while it propagates at a constant velocity. Our main findings include: (1) in the absence of Gilbert damping, the spin wave propagates at a constant velocity with the increment proportional to the strength of the magnetic field; (2) in the absence of magnetic field, at a given time the spin wave converges exponentially fast to its initial profile as the damping parameter goes to zero and in the long time the relaxation dynamics of the spin wave converges exponentially fast to the easy-axis direction with the exponent proportional to the damping parameter; (3) in the presence of both Gilbert damping and magnetic field, the spin wave converges to the easy-axis direction exponentially fast at a small timescale while propagates at a constant velocity beyond that. These provides a comprehensive understanding of spin waves in ferromagnetic materials.

cond-mat.mes-hall↗

arXiv2019

Multi-party quantum summation based on quantum teleportation

We present a secure multi-party quantum summation protocol based on quantum teleportation, in which a malicious, but non-collusive, third party (TP) helps compute the summation. In our protocol, TP is in charge of entanglement distribution and Bell states are shared between participants. Users encode the qubits in their hand according to their private bits and perform Bell-state measurements. After obtaining participants' measurement results, TP can figure out the summation. The participants do not need to send their encoded states to others, and the protocol is therefore congenitally free from Trojan horse attacks. In addition, our protocol can be made secure against loss errors, because the entanglement distribution occurs only once at the beginning of our protocol. We show that our protocol is secure against attacks by the participants as well as the outsiders.

quant-ph↗

arXiv2016

Multiparty quantum key agreement protocol secure against collusion attacks

The fairness of a secure multi-party quantum key agreement (MQKA) protocol requires that all involved parties are entirely peer entities and can equally influence the outcome of the protocol to establish a shared key wherein no one can decide the shared key alone. However, it is found that parts of the existing MQKA protocols are sensitive to collusion attacks, i.e., some of the dishonest participants can collaborate to predetermine the final key without being detected. In this paper, a multi-party QKA protocol resisting collusion attacks is proposed. Different from previous QKA protocol resisting $N-1$ coconspirators or resisting $1$ coconspirators, we investigate the general circle-type MQKA protocol which can be secure against $t$ dishonest participants' cooperation. Here, $t < N$. We hope the results of the presented paper will be helpful for further research on fair MQKA protocols.

cs.CR↗

arXiv2015

Three-party quantum private comparison of equality based on genuinely maximally entangled six-qubit states

We propose a new three-party quantum private comparison protocol using genuinely maximally entangled six-qubit states. In our protocol, three participants can determine whether their private information are equal or not without an external third party who helps compute the comparison result. At the same time the participants can preserve the privacy of their inputs, respectively. Our protocol does not need any unitary operations to encode information due to the excellent properties of genuinely maximally entangled six-qubit states. Additionally, the protocol uses one-step quantum transmission and it is congenitally free from Trojan horse attacks. We have also shown that our protocol is secure against outside and participant attacks in this paper.

quant-ph↗

arXiv2012

Cryptanalysis of the efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement

We analyze the security of the efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. It is shown that the compromised third party (TP) can obtain the final comparison result without introducing any detectable errors in the standard semi-honest model. The attack strategy is discussed in detail and an improvement of this protocol is demonstrated. The idea of our attack might be instructive for the cryptanalysis of quantum cryptographic schemes.

quant-ph↗

arXiv2011

Improving the security of arbitrated quantum signature protocols

Arbitrated quantum signatures (AQS), for signing quantum message, have been proposed. It was claimed that the AQS schemes could guarantee unconditional security. However, in this paper, we show that all the presented AQS protocols are insecure if quantum one-time pad encryption is used where the signer Alice can always successfully acquire Bob's secret key and disavow any of her signatures. The detailed attack strategies and security analysis are described. Furthermore, the original version of the protocols is revised and accordingly the security of the AQS protocols are improved. And meanwhile we present a method to against Alice's disavowal proposed by Gao et al. (arXiv:1106.4398v1).

quant-ph↗

arXiv2011

Quantum key distribution with limited classical Bob

Two QKD protocols with limited classical Bob who performs only limited classical operations (preparing a (fresh) qubit in the classical basis and send it or doing nothing) are presented and are proved completely robust. As limited classical Bob can deterministically choose the bits, we use the feature to construct a quantum secure direct communication protocol, which is the direct communication of secret messages without first producing a shared secret key.

quant-ph↗