arXiv subjects

Zhuang Xu

Publications and source records attributed to Zhuang Xu.

16 recordsLinked to original sources

arXiv2026

The Global Diffusion Limit for the Space Dependent Variable-Order Time-Fractional Diffusion Equation

The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous time random walks with exponential and heavy-tailed waiting time distributions. The space-dependent variable-order time-fractional diffusion equation is a generalization of the time-fractional diffusion equation with a fractional exponent that varies over space, modelling systems with spatial heterogeneity. However, there has been limited work on defining a global diffusion limit and an underlying random walk for this macroscopic governing equation, which is needed to make meaningful interpretations of the parameters for applications. Here, we introduce continuous time and discrete time random walk models that limit to the variable-order fractional diffusion equation via a global diffusion limit and space- and time-continuum limits. From this, we show how the master equation of the discrete time random walk can be used to provide a numerical method for solving the variable-order fractional diffusion equation. The results in this work provide underlying random walks and an improved understanding of the diffusion limit for the variable-order fractional diffusion equation, which is critical for the development, calibration and validation of models for diffusion in spatially inhomogeneous media with traps and obstacles.

cond-mat.stat-mech↗

arXiv2026

Physical design of cold neutron direct geometry inelastic spectrometer at China Spallation Neutron Source

The Cold-Neutron Inelastic Spectrometer (CNIS) is a direct-geometry, time-of-flight instrument designed for China Spallation Neutron Source (CSNS) and optimized to probe low-energy lattice and magnetic excitations. The instrument integrates a long flight path with bent supermirror guides and an elliptical-focusing geometry to suppress high-energy background while improving cold-neutron delivery to the sample. A flexible multi-disk chopper suite provides pulse shaping, band selection and monochromatization, enabling multi-$E_\textrm{i}$ operation. Modular features, including an interchangeable high-focusing guide insert, radial collimation and a vacuum ``airbox'' for simplified sample-environment integration, enhance signal-to-noise and operational versatility. Through combined flight-path and chopper optimization, CNIS achieves excellent routine-mode energy resolution and can reach approximately $\sim 1\%$ in a dedicated high-resolution configuration. CNIS is planned to commence user operation in 2029, offering a highly flexible platform for cold-neutron inelastic scattering studies.

physics.app-ph↗

arXiv2025

Enhanced anomalous Hall effect in the topological Kagome metal Cs(V$_{1-x}$Mn$_x$)$_3$Sb$_5$

As a fundamental physical phenomenon, achieving and controlling a large anomalous Hall effect (AHE) is crucial for advancing the understanding of topological physics and for developing applied technologies in spintronics. The recently discovered topological Kagome metal $A$V$_3$Sb$_5$ ($A =$ K, Rb, Cs)exhibits a significant AHE along with charge density wave (CDW) and superconductivity, providing an ideal platform to study the interactions between nontrivial band topology, CDW, and superconductivity. In this study, we systematically investigated the evolution of CDW, superconductivity, and AHE in electron (Mn)-doped Cs(V$_{1-x}$Mn$_x$)$_3$Sb$_5$ single crystals. The experimental results show that electron doping rapidly suppresses superconductivity, while the CDW order remains relatively robust. Meanwhile, a significantly enhanced AHE, with a maximum anomalous Hall conductivity (AHC) of ~25331 \Ohm ^{-1}\cm^{-1} and an anomalous Hall angle of 6.66% occurs at a relatively low doping level of $x = 0.03$. Based on the Tian-Ye-Jin (TYJ) scaling model, such a significant enhancement AHC is mainly dominated by the skew scattering. We speculated enhanced skew scattering between electrons and Mn originating from the strengthened spin-orbital coupling. Our finding provides important guidance for the design and development of transverse transport properties in topological Kagome materials.

cond-mat.str-el↗

arXiv2025

A compounded random walk for space-fractional diffusion on finite domains

We formulate a compounded random walk that is physically well defined on both finite and infinite domains, and samples space-dependent forces throughout jumps. The governing evolution equation for the walk limits to a space-fractional Fokker-Planck equation valid on bounded domains, and recovers the well known superdiffusive space-fractional diffusion equation on infinite domains. We describe methods for numerical approximation and Monte Carlo simulations and demonstrate excellent correspondence with analytical solutions. This compounded random walk, and its associated fractional Fokker-Planck equation, provides a major advance for modeling space-fractional diffusion through potential fields and on finite domains.

cond-mat.stat-mech↗

arXiv2024

Delay Infectivity and Delay Recovery SIR model

We have derived the governing equations for an SIR model with delay terms in both the infectivity and recovery of the disease. The equations are derived by modelling the dynamics as a continuous time random walk, where individuals move between the classic SIR compartments. With an appropriate choice of distributions for the infectivity and recovery processes delay terms are introduced into the governing equations in a manner that ensures the physicality of the model. This provides novel insight into the underlying dynamics of an SIR model with time delays. The SIR model with delay infectivity and recovery allows for a more diverse range of dynamical behaviours. The model accounts for an incubation effect without the need to introduce new compartments.

math.DS↗

arXiv2024

Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations

Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a separation of variables approach. Examples are provided showing oscillatory and translatory behaviours that are fundamentally different to standard propagating wave solutions.

math.AP↗

arXiv2024

Finite Time Blowup of Integer- and Fractional-Order Time-Delayed Diffusion Equations

In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using Fourier transform methods in conjunction with the known properties of delay functions. It is observed that the solutions do not exhibit infinite speed of propagation for smooth initial conditions that are bounded and positive. Sufficient conditions on the initial condition are also established such that the finite time blowup of the solutions can be explicitly calculated. Examples are provided that highlight the contrasting behaviours of these exact solutions with the known dynamics of solutions to the standard diffusion equation.

math.AP↗

arXiv2024

A Stochastic Simulation Method for Fractional Order Compartment Models

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing integer-order derivatives with fractional order derivatives. In these models, inherent stochasticity becomes important, particularly when dealing with the dynamics of small populations far from the continuum limit of large particle numbers. The necessity for stochastic simulations arises from deviations of the mean states from those obtained from the governing equations in these scenarios. To address this, we introduce an exact stochastic simulation algorithm designed for fractional order compartment models, based on a semi-Markov process. We have considered a fractional order resusceptibility SIS model and a fractional order recovery SIR model as illustrative examples, highlighting significant disparities between deterministic and stochastic dynamics when the total population is small. Beyond its modeling applications, the algorithm presented serves as a versatile tool for solving fractional order differential equations via Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2024

Delay compartment models from a stochastic process

Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent an incubation period. In this work, we derive a compartment model with delay terms from an underlying non-Markov stochastic process. Delay terms arise when waiting times are drawn from a delay exponential distribution. This stochastic process approach allows us to preserve the physicality of the model, gaining understanding into the conditions under which delay terms can arise. By providing the conditions under which the delay exponential function is a probability distribution, we establish a critical value for the delay terms. An exact stochastic simulation method is introduced for the generalized model, enabling us to utilize the simulation in scenarios where intrinsic stochasticity is significant, such as when the population size is small. We illustrate the applications of the model and validate our simulation algorithm on examples drawn from epidemiology and pharmacokinetics.

math.DS↗

arXiv2019

Strong local moment antiferromagnetic spin fluctuations in V-doped LiFeAs

We use neutron scattering to study vanadium (hole)-doped LiFe$_{1-x}$V$_x$As. In the undoped state, LiFeAs exhibits superconductivity at $T_c=18$ K and transverse incommensurate spin excitations similar to electron overdoped iron pnictides. Upon vanadium-doping to form LiFe$_{0.955}$V$_{0.045}$, the transverse incommensurate spin excitations in LiFeAs transform into longitudinally elongated in a similar fashion as that of potassium (hole) doped Ba$_{0.7}$K$_{0.3}$Fe$_2$As$_2$, but with dramatically enhanced magnetic scattering and elimination of superconductivity. This is different from the suppression of the overall magnetic excitations in hole doped BaFe$_2$As$_2$ and the enhancement of superconductivity near optimal hole doping. These results are consistent with density function theory plus dynamic mean field theory calculations, suggesting that vanadium-doping in LiFeAs may induce an enlarged effective magnetic moment $S_{eff}$ with a spin crossover ground state arising from the inter-orbital scattering of itinerant electrons.

cond-mat.supr-con↗

arXiv2019

Spin fluctuation anisotropy as a probe of orbital-selective hole-electron quasiparticle excitations in detwinned Ba(Fe1-xCox)2As2

We use inelastic neutron scattering to study spin excitation anisotropy in mechanically detwinned Ba(Fe1-xCox)2As2 with x = 0.048 and 0.054. Both samples exhibit a tetragonal-to-orthorhombic structural transition at Ts, a collinear static antiferromagnetic (AF) order at wave vector Q1 = QAF = (1, 0) below the Neel temperature TN, and superconductivity below Tc (Ts > TN > Tc). In the high temperature paramagnetic tetragonal phase (T > Ts), spin excitations centered at Q1 and Q2 = (0, 1) are gapless and have four-fold (C4) rotational symmetry. On cooling to below TN but above Tc, spin excitations become highly anisotropic, developing a gap at Q2 but still are gapless at Q1. Upon entering into the superconducting state, a neutron spin resonance appears at Q1 with no magnetic scattering at Q2. By comparing these results with those from angle resolved photoemission spectroscopy experiments, we conclude that the anisotropic shift of the dyz and dxz bands in detwinned Ba(Fe1-xCox)2As2 below Ts is associated with the spin excitation anisotropy, and the superconductivity-induced resonance arises from the electron-hole Fermi surface nesting of quasiparticles with the dyz orbital characters.

cond-mat.supr-con↗

arXiv2019

Flat band magnetism and helical magnetic order in Ni-doped SrCo$_2$As$_2$

A series of Sr(Co$_{1-x}$Ni$_x$)$_2$As$_2$ single crystals was synthesized allowing a comprehensive phase diagram with respect to field, temperature, and chemical substitution to be established. Our neutron diffraction experiments revealed a helimagnetic order with magnetic moments ferromagnetically (FM) aligned in the $ab$ plane and a helimagnetic wavevector of $q=(0,0,0.56)$ for $x$ = 0.1. The combination of neutron diffraction and angle-resolved photoemission spectroscopy (ARPES) measurements show that the tuning of a flat band with $d_{x^2-y^2}$ orbital character drives the helimagnetism and indicates the possibility of a quantum order-by-disorder mechanism.

cond-mat.str-el↗

arXiv2019

Coexistence of ferromagnetic and stripe antiferromagnetic spin fluctuations in SrCo$_2$As$_2$

We use inelastic neutron scattering to study energy and wave vector dependence of spin fluctuations in SrCo$_2$As$_2$, derived from SrFe$_{2-x}$Co$_x$As$_2$ iron pnictide superconductors. Our data reveals the coexistence of antiferromagnetic (AF) and ferromagnetic (FM) spin fluctuations at wave vectors $\textbf{Q}_{\rm AF}$=(1,0) and $\textbf{Q}_{\rm FM}$=(0,0)/(2,0), respectively. By comparing neutron scattering results with those of dynamic mean field theory calculation and angle-resolved photoemission spectroscopy experiments, we conclude that both AF and FM spin fluctuations in SrCo$_2$As$_2$ are closely associated with a flat band of the $e_g$ orbitals near the Fermi level, different from the $t_{2g}$ orbitals in superconducting SrFe$_{2-x}$Co$_x$As$_2$. Therefore, Co-substitution in SrFe$_{2-x}$Co$_x$As$_2$ induces a $t_{2g}$ to $e_g$ orbital switching, and is responsible for FM spin fluctuations detrimental to the singlet pairing superconductivity.

cond-mat.str-el↗

arXiv2018

Dynamic spin-lattice coupling and nematic fluctuations in NaFeAs

We use inelastic neutron scattering to study acoustic phonons and spin excitations in single crystals of NaFeAs, a parent compound of iron pnictide superconductors. NaFeAs exhibits a tetragonal-to-orthorhombic structural transition at $T_s\approx 58$ K and a collinear antiferromagnetic (AF) order at $T_N\approx 45$ K. While longitudinal and out-of-plane transverse acoustic phonons behave as expected, the in-plane transverse acoustic phonons reveal considerable softening on cooling to $T_s$, and then harden on approaching $T_N$ before saturating below $T_N$. In addition, we find that spin-spin correlation lengths of low-energy magnetic excitations within the FeAs layer and along the $c$-axis increase dramatically below $T_s$, and show weak anomaly across $T_N$. These results suggest that the electronic nematic phase present in the paramagnetic tetragonal phase is closely associated with dynamic spin-lattice coupling, possibly arising from the one-phonon-two-magnon mechanism.

cond-mat.str-el↗

arXiv2017

Unified phase diagram for iron-based superconductors

High-temperature superconductivity is closely adjacent to a long-range antiferromagnet, which is called a parent compound. In cuprates, all parent compounds are alike and carrier doping leads to superconductivity, so a unified phase diagram can be drawn. However, the properties of parent compounds for iron-based superconductors show significant diversity and both carrier and isovalent dopings can cause superconductivity, which casts doubt on the idea that there exists a unified phase diagram for them. Here we show that the ordered moments in a variety of iron pnictides are inversely proportional to the effective Curie constants of their nematic susceptibility. This unexpected scaling behavior suggests that the magnetic ground states of iron pnictides can be achieved by tuning the strength of nematic fluctuations. Therefore, a unified phase diagram can be established where superconductivity emerges from a hypothetical parent compound with a large ordered moment but weak nematic fluctuations, which suggests that iron-based superconductors are strongly correlated electron systems.

cond-mat.supr-con↗

arXiv2017

Phase diagram and neutron spin resonance of superconducting NaFe$_{1-x}$Cu$_x$As

We use transport and neutron scattering to study the electronic phase diagram and spin excitations of NaFe$_{1-x}$Cu$_x$As single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\approx2\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\approx 50\%$. Using transport measurements, we demonstrate that the resistivity in NaFe$_{1-x}$Cu$_x$As exhibits non-Fermi-liquid behavior near $x\approx1.8\%$. Our inelastic neutron scattering experiments reveal a single neutron spin resonance mode exhibiting weak dispersion along $c$-axis in NaFe$_{0.98}$Cu$_{0.02}$As. The resonance is high in energy relative to the superconducting transition temperature $T_{\rm c}$ but weak in intensity, likely resulting from impurity effects. These results are similar to other iron pnictides superconductors despite the superconducting phase in NaFe$_{1-x}$Cu$_x$As is continuously connected to an antiferromagnetically ordered insulating phase near $x\approx 50\%$ with significant electronic correlations. Therefore, electron correlations is an important ingredient of superconductivity in NaFe$_{1-x}$Cu$_x$As and other iron pnictides.

cond-mat.supr-con↗