arXiv subjects

Xiangjun Xing

Publications and source records attributed to Xiangjun Xing.

At least 37 records · Page 2Linked to original sources

arXiv2020

Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises

The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works for systems with or without detailed balance, and is substantially simpler than previous theories. Its relation with deterministic theory is clarified. The unitary limit and Hermitian limit of the theory are examined. Some implications on the choices of stochastic calculus are also discussed.

cond-mat.stat-mech↗

arXiv2020

Enhanced skyrmion motion via strip domain wall

When magnetic skyrmions move under spin orbit torque in magnetic nanowires, they experience a skyrmion Hall effect, which pushes them towards the nanowire edge where they risk being annihilated; this puts an upper limit on how fast they can be driven. However, the same magnetic multilayer harboring skyrmions can sustain a Néel-type strip domain wall along the nanowire length, potentially keeping the skyrmions separated from the edge. Here we study the interplay between current driven skyrmions and domain walls and find that they increase the annihilation current and allow the skyrmions to move faster. Based on the Thiele formalism, we confirm that the emergent longitudinal repulsive force and the modified energy landscape linked to the domain wall are responsible for the enhanced skyrmion motion. Furthermore, we identify that the longitudinal repulsive force emerges because of the broken axisymmetry in the local magnetization in front of the skyrmion. Our study uncovers key aspects in the interplay between two topological magnetic textures from different homotopy groups and may inspire new device concepts.

cond-mat.mes-hall↗

arXiv2019

Action Principle and Dynamic Ensemble Theory for Non-equilibrium Markov Chains

An overarching action principle, the principle of minimal free action, exists for ergodic Markov chain dynamics. Using this principle and the Detailed Fluctuation Theorem, we construct a dynamic ensemble theory for non-equilibrium steady states (NESS) of Markov chains, which is in full analogy with equilibrium canonical ensemble theory. Concepts such as energy, free energy, Boltzmann macro-sates, entropy, and thermodynamic limit all have their dynamic counterparts. For reversible Markov chains, minimization of Boltzmann free action yields thermal equilibrium states, and hence provide a dynamic justification of the principle of minimal free energy. For irreversible Markov chains, minimization of Boltzmann free action selects the stable NESS, and determines its macroscopic properties, including entropy production. A quadratic approximation of free action leads to linear-response theory with reciprocal relations built-in. Hence, in so much as non-equilibrium phenomena can be modeled as Markov processes, minimal free action serves as a basic principle for both equilibrium and non-equilibrium statistical physics.

cond-mat.stat-mech↗

arXiv2019

Skyrmion Tubes as Magnonic Waveguides

Various latest experiments have proven the theoretical prediction that domain walls in planar magnetic structures can channel spin waves as outstanding magnonic waveguides, establishing a superb platform for building magnonic devices. Recently, three-dimensional nanomagnetism has been boosted up and become a significant branch of magnetism, because three-dimensional magnetic structures expose a lot of emerging physics hidden behind planar ones and will inevitably provide broader room for device engineering. Skyrmions and antiSkyrmions, as natural three-dimensional magnetic configurations, are not considered yet in the context of spin-wave channeling and steering. Here, we show that skyrmion tubes can act as nonplanar magnonic waveguides if excited suitably. An isolated skyrmion tube in a magnetic nanoprism induces spatially separate internal and edge channels of spin waves; the internal channel has a narrower energy gap, compared to the edge channel, and accordingly can transmit signals at lower frequencies. Additionally, we verify that those spin-wave beams along magnetic nanoprism are restricted to the regions of potential wells. Transmission of spin-wave signals in such waveguides results from the coherent propagation of locally driven eigenmodes of skyrmions, i.e., the breathing and rotational modes. Finally, we find that spin waves along the internal channels are less susceptible to magnetic field than those along the edge channels. Our work will open a new arena for spin-wave manipulation and help bridge skyrmionics and magnonics.

cond-mat.mes-hall↗

arXiv2018

Depletion zones and crystallography on pinched spheres

Understanding the interplay between ordered structures and substrate curvature is an interesting problem with versatile applications, including functionalization of charged supramolecular surfaces and modern microfluidic technologies. In this work, we investigate the two-dimensional packing structures of charged particles confined on a pinched sphere. By continuously pinching the sphere, we observe cleavage of elongated scars into pleats, proliferation of disclinations, and subsequently, emergence of a depletion zone at the negatively curved waist that is completely void of particles. We systematically study the geometrics and energetics of the depletion zone, and reveal its physical origin as a finite size effect, due to the interplay between Coulomb repulsion and concave geometry of pinched sphere. These results further our understanding of crystallography on curved surfaces, and have implications in design and manipulation of charged, deformable interfaces in various applications.

cond-mat.soft↗

arXiv2017

Definitions and Evolutions of Statistical Entropy for Hamiltonian Systems

Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I revisit the seminal ideas about non-equilibrium statistical entropy due to Boltzmann and due to Gibbs, and synthesize them into a coherent and precise framework. Using this framework, I clarify the anthropomorphic principle of entropy, and analyze the evolution of entropy for classical Hamiltonian systems under different experimental setups. I find that evolution of Boltzmann entropy obeys a Stochastic H-Theorem, which relates probability of Boltzmann entropy increasing to that of decreasing. By contrast, the coarse-grained Gibbs entropy is monotonically increasing, if the microscopic dynamics is locally mixing, and the initial state is a Boltzmann state. These results clarify the precise meaning of the second law of thermodynamics for classical systems, and demonstrate that it is the initial condition as a Boltzmann state that is ultimately responsible for the arrow of time.

cond-mat.stat-mech↗

arXiv2017

A GPU-based Large-scale Monte Carlo Simulation Method for Systems with Long-range Interactions

In this work we present an efficient implementation of Canonical Monte Carlo simulation for Coulomb many body systems on graphics processing units (GPU). Our method takes advantage of the GPU Single Instruction, Multiple Data (SIMD) architectures. It adopts the sequential updating scheme of Metropolis algorithm, and makes no approximation in the computation of energy. It reaches a remarkable 440-fold speedup, compared with the serial implementation on CPU. We use this method to simulate primitive model electrolytes. We measure very precisely all ion-ion pair correlation functions at high concentrations, and extract renormalized Debye length, renormalized valences of constituent ions, and renormalized dielectric constants. These results demonstrate unequivocally physics beyond the classical Poisson-Boltzmann theory.

physics.comp-ph↗

arXiv2017

Paving Spin-Wave Fibers in Magnonic Nanocircuits Using Spin-Orbit Torque

Recent studies have revealed that domain walls in magnetic nanostructures can serve as compact, energy-efficient spin-wave waveguides for building magnonic devices that are considered promising candidates for overcoming the challenges and bottlenecks of today's CMOS technologies. However, imprinting long strip-domain walls into magnetic nanowires remains a challenge, especially in curved geometries. Here, through micromagnetic simulations, we present a method for writing strip-domain walls into curved magnetic nanowires using spin-orbit torque. We employ Y-shaped magnetic nanostructures as well as an S-shaped magnetic nanowire to demonstrate the injection process. In addition, we verify that the Y-shaped nanostructures that incorporate strip-domain walls can function as superior spin-wave multiplexers, and that spin-wave propagation along each conduit can be controllably manipulated. This spin-wave multiplexer based on strip-domain walls is expected to become a key signal-processing component in magnon spintronics.

cond-mat.mes-hall↗

arXiv2016

Current-Controlled Skyrmionic Diode

In order to address many of the challenges and bottlenecks currently experienced by traditional charge based technologies, various alternatives are being actively explored to provide potential solutions of device miniaturization and scaling in the more-than-MOORE era. Amongst these alternatives, spintronics physics and devices have recently attracted a rapidly increasing interest by exploiting the additional degree of electron's spins. For example, magnetic domain-wall racetrack-memory and logic devices have been realized via manipulating domain-wall motion. As compared to domain-wall based devices, magnetic skyrmions have the advantages of ultra-small size (typically 5-100 nm in diameter), facile current-driven motion, topological stability and peculiar emergent electrodynamics, promising for next-generation electronics applications in the more-than-Moore regime. In this work, a magnetic meron diode, which behaves like a PN-junction diode, is demonstrated for the first time, by tailoring the current-controlled unidirectional motion of edge-merons (i.e., fractional skyrmions) in a nanotrack with interfacial Dzyaloshinskii-Moriya interaction. The working principles of the meron diode, theoretically expected from the Thiele equation for topological magnetic objects, are further verified by micromagnetic simulations. The present study reveals topology-independent transport property of magnetic objects, and is expected to open the vista toward integrated composite circuitry, with unified data storage and processing, based on a single magnetic chip, as the meron diode can be used either, as a building block, to develop complex logic components or, as a signal controller, to interconnect skyrmion, domain-wall, and even spin-wave devices.

cond-mat.mes-hall↗

arXiv2016

Domain wall-gated skyrmion logic

Skyrmions and domain walls are typical spin textures of significant technological relevance to magnetic memory and logic applications, where they are used as carriers of information. The unique topology of skyrmions makes them to display distinct dynamical properties compared to domain walls. Some studies have demonstrated that the two topologically inequivalent magnetic objects could be interconverted by cleverly designed geometric structures. Here, we numerically address the skyrmion-domain wall collision in a magnetic racetrack by introducing relative motion between the two objects based on a specially designed junction. An electric current serves as the driving force that moves a skyrmion toward a trapped domain-wall pair. We observe different types of collision dynamics by changing the driving parameters. Most importantly, the domain wall modulation of skyrmion transport is realized in this system, allowing a set of domain wall-gated logical NOT, NAND, and NOR gates to be constructed. By providing a promising logic architecture that is fully compatible with racetrack memories, this work is expected to speed up the development of skyrmion-based magnetic computation.

cond-mat.mes-hall↗

arXiv2016

Charge Renormalization and Charge Oscillation in Asymmetric Primitive Model

The Debye charging method is generalized to study the linear response properties of the asymmetric primitive model for electrolytes. Analytic results are obtained for the effective charge distributions of constituent ions inside the electrolyte, from which all static linear response properties of system follow. It is found that, as the ion density increases, both the screening length and the dielectric constant receive substantial renormalization due to ionic correlations. Furthermore, the valence of larger ion is substantially renormalized upwards by ionic correlations, whilst that of smaller ions remains approximately the same. For sufficiently high density, the system exhibit charge oscillations. The threshold ion density for charge oscillation is much lower than the corresponding value for symmetric electrolytes. Our results agree well with large scale Monte Carlo simulations.

cond-mat.soft↗

arXiv2016

Particles inside Electrolytes with Ion-specific Interactions, Their Effective Charge Distributions and Effective Interactions

In this work, we explore the statistical physics of colloidal particles that interact with electrolytes via ion-specific interactions. Firstly we study particles interact weakly with electrolyte using linear response theory. We find that the mean potential around a particle is linearly determined by the {\em effective charge distribution} of the particle, which depends both on the bare charge distribution and on ion-specific interactions. We also discuss the effective interaction between two such particles and show that, in far field regime, it is bilinear in the effective charge distributions of two particles. We subsequently generalize the above results to the more complicated case where particles interact strongly with the electrolyte. Our results indicate that in order to understand the statistical physics of non-dilute electrolytes, both ion-specific interactions and ionic correlations have to be addressed in a single unified and consistent framework.

cond-mat.soft↗

arXiv2016

Charged Plate in Asymmetric Electrolytes: One-loop Renormalization of Surface Charge Density and Debye Length due to Ionic Correlations

The self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a $m:-n$ electrolyte. A perturbation series is developed in terms of $g = 4 πb/\ell_{\rm {\scriptscriptstyle DB}}$, where $b, \ell_{\rm{\scriptscriptstyle DB}}$ are Bjerrum length and {\em bare} Debye length respectively. To the zeroth order, we obtain nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes ($m \neq n$), the first order (one-loop) correction to mean potential contains a {\em secular term}, which indicates the breakdown of regular perturbation method. Using a renormalizaton group transformation (RG), we remove the secular term and obtain a globally well-behaved one-loop approximation with {\em a renormalized Debye length} and {\em a renormalized surface charge density}. Furthermore, we find that if the counter-ions are multivalent, the surface charge density is renormalized substantially {\em downwards}, and may undergo a change of sign, if the bare surface charge density is sufficiently large.

cond-mat.soft↗

arXiv2015

A Multi-scale Monte Carlo Method for Electrolytes

Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of which are unphysical from the view point of real systems. To cure these problems, we introduce a multi-scale Monte Carlo method, where ions inside a spherical cavity are simulated explicitly, whilst ions outside are treated implicitly using continuum theory. Using the method of Debye charging, we explicitly derive the effective interactions between ions inside the cavity, arising due to the fluctuations of ions outside. We find that these effective interactions consist of two types: 1) a constant cavity potential due to the asymmetry of the electrolyte, and 2) a reaction potential that depends on the positions of all ions inside. Combining the Grand Canonical Monte Carlo (GCMC) with a recently developed fast algorithm based of image charge method, we perform a multi-scale Monte Carlo simulation of symmetric electrolytes, and compare it with other simulation methods, including PBC+GCMC method, as well as large scale Monte Carlo simulation. We demonstrate that our multi-scale MC method is capable of capturing the correct physics of a large system using a small scale simulation.

cond-mat.soft↗

arXiv2014

The Correlation Potential of a Test Ion Near a Strongly Charged Plate

We analytically calculate the correlation potential of a test ion near a \emph{strongly} charged plate inside a dilute $m:-n$ electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear background potential, the latter having been obtained using the nonlinear Poisson-Boltzmann theory. We consider the general case where the dielectric constants of the plate and the electrolyte are distinct. The following generic results emerge from our analyses: (1) If the distance to the plate $Δz$ is much larger than a Gouy-Chapman length, the plate surface will behave effectively as an infinitely charged surface, and the dielectric constant of the plate effectively plays no role. (2) If $Δz$ is larger than a Gouy-Chapman length but shorter than a Debye length, the correlation potential can be interpreted in terms of an image charge that is three times larger than the source charge. This behavior is independent of the valences of the ions. (3) The Green's function vanishes inside the plate if the surface charge density is infinitely large; hence the electrostatic potential is constant there. In this respect, a strongly charged plate behaves like a conductor plate. (4) If $Δz$ is smaller than a Gouy-Chapman length, the correlation potential is dominated by the conventional image charge due to the dielectric discontinuity at the interface. (5) If $Δz$ is larger than a Debye length, the leading order behavior of the correlation potential will depend on the valences of the ions in the electrolyte. Furthermore, inside an \emph{asymmetric} electrolyte, the correlation potential is \emph{singly} screened, i.e., it undergoes exponential decay with a decay width equal to the Debye length.

cond-mat.soft↗

arXiv2013

Generalized Deam-Edwards Approach to the Statistical Mechanics of Randomly Crosslinked Systems

We address the statistical mechanics of randomly and permanently crosslinked networks. We develop a theoretical framework (vulcanization theory) which can be used to systematically analyze the correlation between the statistical properties of random networks and their histories of formation. Generalizing the original idea of Deam and Edwards, we consider an instantaneous crosslinking process, where all crosslinkers (modeled as Gaussian springs) are introduced randomly at once in an equilibrium liquid state, referred to as the preparation state. The probability that two functional sites are crosslinked by a spring exponentially decreases with their distance squared. After formally averaging over network connectivity, we obtained an effective theory with all degrees of freedom replicated 1 + n times. Two thermodynamic ensembles, the preparation ensemble and the measurement ensemble, naturally appear in this theory. The former describes the thermodynamic fluctuations in the state of preparation, while the latter describes the thermodynamic fluctuations in the state of measurement. We classify various correlation functions and discuss their physical significances. In particular, the memory correlation functions characterize how the properties of networks depend on their history of formation, and are the hallmark properties of all randomly crosslinked materials. We clarify the essential difference between our approach and that of Deam-Edwards, discuss the saddle-point order parameters and its physical significance. Finally we also discuss the connection between saddle-point approximation of vulcanization theory, and the classical theory of rubber elasticity as well as the neo-classical theory of nematic elastomers.

cond-mat.stat-mech↗

arXiv2013

Mellin Transform and Image Charge Method for Dielectric Sphere in an Electrolyte

We revisit the image charge method for the Green's function problem of the Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a source charge inside the sphere in terms of one dimensional distribution of image charges. The image charges are generically composed of a point image at the Kelvin point and a line image extending from the Kelvin point to infinity with an oscillatory line charge strength. We further develop an efficient and accurate algorithm for discretization of the line image using Padé approximation and finite fraction expansion. Finally we illustrate the power of our method by applying it in a multiscale reaction-field Monte Carlo simulation of monovalent electrolytes.

physics.comp-ph↗

arXiv2013

Statistical physics of isotropic-genesis nematic elastomers: I. Structure and correlations at high temperatures

Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly, permanently cross-linked in the high-temperature state so as to form an equilibrium random solid. Thus, instead of being free to diffuse throughout the entire volume, as they would be in the liquid state, the constituent LCPs in an IGNE are mobile only over a finite length-scale controlled by the density of cross-links. We address the effects that such network-induced localization have on the liquid-crystalline characteristics of an IGNE, as probed via measurements made at high temperatures. In contrast with the case of uncross-linked LCPs, for IGNEs these characteristics are determined not only by thermal fluctuations but also by the quenched disorder associated with the cross-link constraints. To study IGNEs, we consider a microscopic model of dimer nematogens in which the dimers interact via orientation-dependent excluded volume forces. The dimers are, furthermore, randomly, permanently cross-linked via short Hookean springs, the statistics of which we model by means of a Deam-Edwards type of distribution. We show that at length-scales larger than the size of the nematogens this approach leads to a recently proposed phenomenological Landau theory of IGNEs [Lu et al., Phys. Rev. Lett. 108, 257803 (2012)], and hence predicts a regime of short-ranged oscillatory spatial correlations in the nematic alignment, of both thermal and glassy types. In addition, we consider two alternative microscopic models of IGNEs: (i) a wormlike chain model of IGNEs that are formed via the cross-linking of side-chain LCPs; and (ii) a jointed chain model of IGNEs that are formed via the cross-linking of main-chain LCPs. At large length-scales, both of these models give rise to liquid-crystalline characteristics that are qualitatively in line with those predicted by the dimer-and-springs model.

cond-mat.soft↗