Dimensional Spin Research Articles

Time fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its Lie symmetries, exact solutions and conservation laws

Abstract In this paper, Lie symmetry analysis method is applied to (2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation. We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding (2+1)-dimensional fractional partial differential equations with Riemann-Liouville fractional derivative to (1+1)-dimensional counterparts with Erd'{e}lyi-Kober fractional derivative. Then we obtain the power series solutions of the reduced equations, prove their convergence and analyze their dynamic behavior graphically. In addition, the conservation laws for all the obtained Lie symmetries are constructed by the new conservation theorem and the generalization of Noether operators.

Double-pole anti-dark solitons for a Lakshmanan-Porsezian-Daniel equation in an optical fiber or a ferromagnetic spin chain

Under investigated in this paper is a Lakshmanan-Porsezian-Daniel equation that describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction or the propagation of the ultrashort pulses in a long-distance and high-speed optical fiber transmission system. Under certain parameter conditions, we simultaneously take the multi-pole phenomena and breather-to-soliton transitions into account, then utilize the second-order generalized Darboux transformation to derive the double-pole anti-dark solitons and graphically illustrate them. Asymptotic analysis is conducted to examine the interaction properties of double-pole anti-dark solitons, including their characteristic lines, amplitudes, phase shifts, slopes and position differences. Unlike the double-pole anti-dark solitons found in the Hirota equation, the ones in this study exhibit a distinct feature: Different soliton components share the same amplitude.

Evaluation of radiation induced brain injury in nasopharyngeal carcinoma patients based on multi-parameter quantitative MRI: A prospective longitudinal study

PurposeThree dimensional pulsed continuous arterial spin labeling (3D-pCASL) and incoherent movement within voxels (IVIM) imaging was combined to assess dynamic microscopic structure changes of the hippocampus and temporal lobe white matter (TLWM) of nasopharyngeal carcinoma (NPC) patients post intensity-modulated radiation therapy (IMRT). MethodsForty-six patients who were first diagnosed with NPC and underwent IMRT were prospectively enrolled. 3D-CASL and IVIM were performed pre-RT, within 1 week (1 W) post-RT, 3 months (3 M) post-RT, 6 months (6 M) post-RT, and 18 months (18 M) post-RT. Twenty-seven patients completed follow-ups for all time periods, and their data were analyzed. The cerebral flow (CBF) derived from ASL, and apparent diffusion coefficient (ADC), pure diffusion coefficient (D), pseudo-diffusion coefficient (D*), and perfusion fraction (F) derived from IVIM of hippocampus and TLWM were analyzed. The quantitative parameters were measured before RT as the baseline, and the corresponding parameter values and change rates at each time point post-RT were compared using the non-parametric Wilcoxon rank sum test. ResultsAt 1 W post-RT, CBF showed a significant increase and peaked in both the hippocampus and TLWM (p < 0.05) with change rate of 30.3 % and 24.1 %. In the hippocampus, both D and D* were significantly increased from pre-RT to 6 M post-RT with change rate of 6.66 % and 34.7 %, while D*-values remained significantly higher than pre-RT at 12 months post-RT with change rate of 41.2 %. In the TLWM, the F firstly increased and then decreased, and was significantly decreased from pre-RT to 6 M post-RT with change rate of 20.2 %. Conclusion3D-PCASL and IVIM can indirectly reflecting the developmental pattern and molecular mechanism of RT induced brain injury.

Nonequilibrium spin transport in integrable and nonintegrable classical spin chains.

Anomalous transport in low dimensional spin chains is an intriguing topic that can offer key insights into the interplay of integrability and symmetry in many-body dynamics. Recent studies have shown that spin-spin correlations in spin chains, where integrability is either perfectly preserved or broken by symmetry-preserving interactions, fall in the Kardar-Parisi-Zhang (KPZ) universality class. Similarly, energy transport can show ballistic or diffusive-like behavior. Although such behavior has been studied under equilibrium conditions, no results on nonequilibrium spin transport in classical spin chains has been reported so far. In this work, we investigate both spin and energy transport in classical spin chains (integrable and nonintegrable) when coupled to two reservoirs at two different temperatures/magnetizations. In both the integrable case and the broken-integrability (but spin-symmetry preserving) case, we report anomalous scaling of spin current with system size (J^{s}∝L^{-μ}), with an exponent value that, within error bars, is close to the KPZ universality class value μ≈2/3. On the other hand, it is noteworthy that theenergy current remains ballistic (J^{e}∝L^{-η} with η≈0) in the purely integrable casewhile there is departure from ballistic behavior (η>0) when integrability is brokenregardless of spin-symmetry. We also present results on other interesting observables in the nonequilibrium steady state such as the spatial profiles of magnetization and energy, and spin-spin correlations.

Soliton dynamics in (2+1) dimensional Heisenberg spin chain with Dzyaloshinskii–Moriya interaction in nanowire systems

In this study, we delve into the theoretical framework of the (2+1)-dimensional Kadomtsev–Petviashvili equation coupled with Dzyaloshinskii–Moriya (DM) interaction, elucidated from the Landau-Lifshitz equation, a prominent model in the realm of ferromagnetic dynamics. Employing the binary Bell polynomial technique along with the Hirota bilinear form, we construct one- and two-soliton solutions for the considered physical system. Through the manipulation of parameters present in these solutions, we explore the various nonlinear dynamical phenomena characterizing ferromagnetic nano-wires with DM interaction. Our investigations elucidate that solitons can be effectively manipulated in the nanowire system through judicious selection of system parameters. Moreover, our findings illustrate that soliton profiles exhibit compression, amplification, shifting, and changes in orientation during evolution. These insights hold significant implications for experimentalists aiming to analyze the propagation of solitons in ferromagnetic nanowire systems.

Pioneering the plethora of soliton for the (3+1)-dimensional fractional heisenberg ferromagnetic spin chain equation

Abstract In this scholarly article, we investigate the complex structured (3+1)-dimensional Fractional Heisenberg Ferromagnetic Spin Chain equation (FHFSCE) with conformable fractional derivatives. We develop a diverse glut of soliton solutions using an improved version of the G ′ G -expansion method, namely the r + G ′ G -expansion method. The constraints for the existence of these solutions are painstakingly explained. Our findings are clearly communicated through a number of 3D and 2D graphical representations displaying periodic, multiple periodic, kink, and shock soliton solutions. These soliton solutions are expressed in several mathematical function forms, such as hyperbolic, trigonometric, and rational functions. Our findings support the suggested method’s efficacy as a powerful symbolic algorithm for discovering innovative soliton solutions within nonlinear evolution systems.

Magnetic phase transition and critical behavior in (Pr,Sm)[formula omitted]Fe[formula omitted] compounds: A comprehensive study using macroscopic and local experimental approaches

Achieving a comprehensive understanding of the properties and behaviors of magnetic phase transitions and critical behavior is a key objective of this study. A macroscopic approach utilizing magnetization measurement and a local approach utilizing 57Fe Mössbauer spectrometry were employed. The findings indicate that the critical exponents of Pr2Fe17 and (Pr,Sm)2Fe17 closely approximate those of the 3D-Ising model, as confirmed by the scaling analysis of our critical exponents. Moreover, we observed that isotherms collapse into two distinct and independent universal branches above and below the Curie temperature when utilizing the critical exponents we obtained. Our results indicate that the exponents determined using both conventional methods and Mössbauer spectrometry closely match those of the 3D-Ising model for spins coupled in three dimensions (lattice dimensionality d=3, spin dimensionality n=1) with attractive interactions between spins (J(r)) at the boundary of short-range and long-range decay as J(r)∝r−(3+σ).

Dynamical analysis and the soliton solutions of (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative

This paper investigates the soliton solutions and dynamical analysis of (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative, which is transformed into the ordinary differential equation. By using the second-order complete discriminant system, the soliton solutions are presented. By utilizing the theory of planar dynamical system, the phase portraits of the dynamical system and its disturbance system are drawn. Moreover, three-dimensional, two-dimensional, and contour plots of soliton solutions for (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative have also been plotted.

Analytical solutions and soliton behaviors in the space fractional Heisenberg ferromagnetic spin chain equation

This study investigates soliton solutions to the (2 + 1)-dimensional space fractional Heisenberg ferromagnetic spin chain equation incorporating beta fractional derivatives that explain the nonlinear propagation of spin wave in the ferromagnetic material with magnetic interactions including the both classical and semi-classical frameworks. This model has applications in spintronics, plasma physics, magnet theory, and condensed matter physics. Employing the two-potential extended Kudryashov and (G′/G, 1/G)-expansion methods, we derive some original and generic solutions composed of trigonometric functions, hyperbolic functions, and their rational forms. For particular values of the parameters, these solutions offer V-shaped, bell-shaped, kink, periodic, flat kink, and singular periodic solitons. The physical behavior of these solitons is demonstrated through three-dimensional, contour, and two-dimensional plots. The results are important in the study of phase transitions in ferromagnetic materials, lattice vibrations in condensed matter, and the propagation of shock waves in plasma. This study also demonstrates the potential and reliability of the employed strategies.

A continuous-wave and pulsed X-band electron spin resonance spectrometer operating in ultra-high vacuum for the study of low dimensional spin ensembles.

We report the development of a continuous-wave and pulsed X-band electron spin resonance (ESR) spectrometer for the study of spins on ordered surfaces down to cryogenic temperatures. The spectrometer operates in ultra-high vacuum and utilizes a half-wavelength microstrip line resonator realized using epitaxially grown copper films on single crystal Al2O3 substrates. The one-dimensional microstrip line resonator exhibits a quality factor of more than 200 at room temperature, close to the upper limit determined by radiation losses. The surface characterizations of the copper strip of the resonator by atomic force microscopy, low-energy electron diffraction, and scanning tunneling microscopy show that the surface is atomically clean, flat, and single crystalline. Measuring the ESR spectrum at 15K from a few nm thick molecular film of YPc2, we find a continuous-wave ESR sensitivity of 2.6 × 1011spins/G · Hz1/2, indicating that a signal-to-noise ratio of 3.9G · Hz1/2 is expected from a monolayer of YPc2 molecules. Advanced pulsed ESR experimental capabilities, including dynamical decoupling and electron-nuclear double resonance, are demonstrated using free radicals diluted in a glassy matrix.

Anderson localization and quenched induced dynamics of spin orbit coupled Bose–Einstein condensate in a random potential

We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.

Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

Magnetization reversal phenomenon of higher-order lump and mixed interaction structures on periodic background in the (2+1)-dimensional Heisenberg ferromagnet spin equation

This paper mainly researches a useful model that can describe the rapid magnetization reversal process, namely the (2+1)-dimensional Heisenberg ferromagnet spin equation. Based on its Lax pair, we construct the iterative generalized (r,N−r)-fold Darboux transformation (DT), and obtain new position-controllable higher-order lump, periodic wave and rich mixed lump–breather interaction structures on periodic background. In particular, with the increase of N in the iterative generalized (r,N−r)-fold DT, we find that the structure of the lump and periodic wave can flip over with respect to the background. Moreover, we also find a bright lump structure with two peaks and two valleys, which does not flip with the increase of N. We study the magnetization trajectory and magnetization on the Bloch sphere, from which we discover that the magnetization is distributed in an incomplete unit sphere for the flipped case, while the magnetization is distributed in a complete unit sphere for the non-flipped case. These magnetization reversal phenomena are expected to have potential applications in understanding the rapid magnetization reversal process.

Remarks on Effects of Projective Phase on Eigenstate Thermalization Hypothesis

Abstract The existence of p-form symmetry in a (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $\mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $\mathbb {Z}_N\times \mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $\mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $\mathbb {Z}_2$ lattice gauge theory.

Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

Exact solutions, symmetry groups and conservation laws for some (2+1)-dimensional nonlinear physical models

In this paper, the Bernoulli sub-equation function method is used to construct new exact travelling wave solutions for two important physical models: (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. These solutions provide valuable insights into the behavior of these models, described in terms of exponential and hyperbolic tangent (tanh) functions. The study also involves an exploration of the infinitesimal generators and symmetry groups through the Lie symmetry method. In addition, by using multiplier approach, the conservation laws are established for these models. Graphical simulation of some solutions in the form of two-dimensional and three-dimensional are plotted to understanding of the underlying physical phenomena and mathematical properties of the (2+1)-dimensional HNLS and HFSC equations. The solutions and graphing are performed using Maple software.

The Dabrowski-Sitarz-Zalecki type theorems for six dimensional manifolds with boundary

In this paper, we define the spectral Einstein functionals of spin manifolds with boundary, and we give a complete proof of the Dabrowski-Sitarz-Zalecki type theorem for six dimensional spin manifolds with boundary.

A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds

Earlier results show that the N=1/2 supersymmetric path integral Jg on a closed even dimensional Riemannian spin manifold (X,g) can be constructed in a mathematically rigorous way via Chen differential forms and techniques from noncommutative geometry, if one considers Jg as a current on the loop space LX, that is, as a linear form on differential forms on LX. This construction admits a Duistermaat-Heckman localization formula. In this note, fixing a topological spin structure on X, we prove that any smooth family g•=(gt)t∈[0,1] of Riemannian metrics on X canonically induces a Chern-Simons current Cg• which fits into a transgression formula for the supersymmetric path integral. In particular, this result entails that the supersymmetric path integral induces a differential topological invariant on X, which essentially stems from the Aˆ-genus of X.

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

Here, we consider the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is forced by the multiplicative Brownian motion in the Stratonovich sense. We utilize the (G′/G)-expansion method and the mapping method to attain the analytical solutions of the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic chain equation. Various types of analytical stochastic solutions, such as the hyperbolic, elliptic, and trigonometric functions, have been obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because the magnetic soliton has been categorized as one of the interesting groups of nonlinear excitations representing spin dynamics in the semiclassical continuum Heisenberg systems. Moreover, we employ MATLAB tools to plot 3D and 2D graphs for some obtained solutions to address the influence of Brownian motion on these solutions.

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation