Mean Field Research Articles

Mode Analysis of Spin Field of Thermal Atomic Ensembles

Abstract The spin dynamics in a thermal atomic vapor cell have been investigated thoroughly over the past decades and have proven successful in quantum metrology and memory owing to their long coherent time and manipulation convenience. The existing mean field analysis of spin dynamics among the whole cell is sometimes inaccurate due to the non-uniform of the ensemble and spatial coupling of multi-physical fields interacting with the ensembles. Here we perform mode analysis onto the quasi-continuous spin field including atomic thermal motion to derive Bloch mode equations and obtain corresponding analytical solutions in diffusion regime. We show that the widely used mean field dynamics of thermal gas is a particular case in our solution corresponding to the uniform spatial mode. This mode analysis approach offers a precise method for analyzing the dynamics of the spin ensemble in greater details from a field perspective, enabling the effective determination of spatially non-uniform multi-physical field coupling with the spin ensembles, which cannot be accurately analyzed by the mean field method. Furthermore, this work paves a way to address noises and relaxation mechanisms associated with non-uniform fields and interatomic interactions, which are limiting the further improvement of ultrasensitive spin-based sensors.

Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems

It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators, the dynamics can be understood in terms of lower dimensional equations. This is the case, for instance, of memristive circuits. Memristive systems are important classes of devices with wide-ranging applications in electronic circuits, artificial neural networks, and memory storage. We show that such mean-field theories can emerge from averages over the group of orthogonal matrices, interpreted as cycle-preserving transformations applied to the projector operator describing Kirchhoff’s laws. Our results provide insights into the fundamental principles underlying the behavior of resistive and memristive circuits and highlight the importance of conservation laws for their mean-field theories. In addition, we argue that our results shed light on the nature of the critical avalanches observed in quasi-two-dimensional nanowires as boundary phenomena.

Linkage among the neutron-skin thickness of 208Pb and nuclear symmetry energy using heavy particle radioactivity

The nuclear symmetry energy (NSE) is a linchpin in deciphering the behavior of matter in a wider domain extending from the characteristics of exotic nuclei to those of neutron stars in the cosmos. Therefore, it is crucial to utilize potential probes to constrain the NSE and its slope parameter L(ρ 0). In this work, we put forth the heavy particle radioactivity (HPR) as a probable bridge among the slope of NSE (L(ρ 0)) and neutron-skin thickness of 208Pb (R skin 208), which serves to put constrain on the L(ρ 0) value. The NSE and its slope parameter are determined from the single nucleon potential of asymmetric nuclear matter exploiting the analytical relationship between these quantities. The isovector/symmetry potential component of the single nucleon potential is derived through HPR for varying R skin 208 by employing the heavy particle/cluster densities and core densities from the relativistic mean field model in conjunction with M3Y nucleon–nucleon interaction. It facilitates in constraining the L(ρ 0) value and neutron skin of finite nuclei using HPR as a linkage, where heavy cluster and core densities of standard Fermi form are considered. The constrained value of L(ρ o ) is 45 ± 8 MeV, which aligns with other estimations derived from nuclear mass measurements, dipole polarizability measurements, and astrophysical data.

The Morse Property of Limit Functions Appearing in Mean Field Equations on Surfaces with Boundary

In this paper, we study the Morse property for functions related to limit functions of mean field equations on a smooth, compact surface Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma $$\\end{document} with boundary ∂Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Sigma $$\\end{document}. Given a Riemannian metric g on Σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma $$\\end{document} we consider functions of the formwhere σi≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _i \ e 0$$\\end{document} for i=1,…,m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i=1,\\ldots ,m$$\\end{document}, Gg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G^g$$\\end{document} is the Green function of the Laplace-Beltrami operator on (Σ,g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Sigma ,g)$$\\end{document} with Neumann boundary conditions, Rg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^g$$\\end{document} is the corresponding Robin function, and h∈C2(Σm,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h \\in {{\\mathcal {C}}}^{2}(\\Sigma ^m,\\mathbb {R})$$\\end{document} is arbitrary. We prove that for any Riemannian metric g, there exists a metric g~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{g}$$\\end{document} which is arbitrarily close to g and in the conformal class of g such that fg~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{\\widetilde{g}}$$\\end{document} is a Morse function. Furthermore we show that, if all σi>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _i>0$$\\end{document}, then the set of Riemannian metrics for which fg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_g$$\\end{document} is a Morse function is open and dense in the set of all Riemannian metrics.

Magnetic topological phases in the double exchange model with spin-orbit coupling

Abstract The double exchange model with the spin-orbit coupling is studied by the dynamical mean field theory. It reveals a competition between the magnetic, charge orderings and the non-trivial topology of the ground state. The spin exchange tends to maintain the magnetic ordering, and at the same time it tries to suppress the charge ordering. The spin-orbit coupling maintains nontrivial topology of the ground state, whereas the magnetic ordering tries to destroy it. As a result, a rich phase diagram is obtained. The competition leads to a half topological ground state, where spin-up electrons form a nontrivial topological state, while spin-down electrons are in the topological trivial insulating state.

Cluster decay dynamics of actinides yielding non-Pb-daughter within relativistic mean field formalism

Cluster decay dynamics of actinides yielding non-Pb-daughter within relativistic mean field formalism

Multi-timescale neuromodulation strategy for closed-loop deep brain stimulation in Parkinson’s disease

Objective. Beta triggered closed–loop deep brain stimulation (DBS) shows great potential for improving the efficacy while reducing side effect for Parkinson’s disease. However, there remain great challenges due to the dynamics and stochasticity of neural activities. In this study, we aimed to tune the amplitude of beta oscillations with different time scales taking into account influence of inherent variations in the basal ganglia–thalamus–cortical circuit. Approach. A dynamic basal ganglia–thalamus–cortical mean–field model was established to emulate the medication rhythm. Then, a dynamic target model was designed to embody the multi-timescale dynamic of beta power with milliseconds, seconds and minutes. Moreover, we proposed a closed-loop DBS strategy based on a proportional–integral–differential (PID) controller with the dynamic control target. In addition, the bounds of stimulation amplitude increments and different parameters of the dynamic target were considered to meet the clinical constraints. The performance of the proposed closed-loop strategy, including beta power modulation accuracy, mean stimulation amplitude, and stimulation variation were calculated to determine the PID parameters and evaluate neuromodulation performance in the computational dynamic mean–field model. Main results. The Results show that the dynamic basal ganglia–thalamus–cortical mean–field model simulated the medication rhythm with the fasted and the slowest rate. The dynamic control target reflected the temporal variation in beta power from milliseconds to minutes. With the proposed closed-loop strategy, the beta power tracked the dynamic target with a smoother stimulation sequence compared with closed-loop DBS with the constant target. Furthermore, the beta power could be modulated to track the control target under different long-term targets, modulation strengths, and bounds of the stimulation increment. Significance. This work provides a new method of closed–loop DBS for multi-timescale beta power modulation with clinical constraints.

Hartree–Fock Mean Field Calculations with Random Phase Approximation for 140Ce Nuclei Structure

Hartree–Fock Mean Field Calculations with Random Phase Approximation for 140Ce Nuclei Structure

Comprehensive investigation of half Heusler alloy: Unveiling structural, electronic, magnetic, mechanical, thermodynamic, and transport properties

This study employs density functional theory (DFT) using Wien2k to comprehensively analyze the essential properties of two half-Heusler alloys, KCrSi and KCrGe. Our findings demonstrate that the ferromagnetic Type 2 configuration exhibits superior stability over non-magnetic and antiferromagnetic states for all KCrZ (Z = Si, Ge) alloys. These alloys exhibit complete spin polarization and half-metallic character, with calculated magnetic moments of 3 μB for both KCrSi and KCrGe. The Curie temperature (TC) is determined using the mean field approximation. Mechanical stability is assessed through second-order elastic constants (SOECs), and electronic properties are analyzed using local spin density approximation (LSDA), Perdew-Burke Generalized Gradient Approximation (PBE-GGA), and Tran-Blaha modified Becke-Johnson (TB-mBJ) schemes, confirming the retention of the half-metallic nature. The negative enthalpy of formation (ΔH) suggests material stability. The use of semi-classical Boltzmann theory, incorporated through the sophisticated scheme of BoltzTraP, explores transport coefficients. High pressures and temperature discrepancies in thermodynamics are considered by implementing the quasi-harmonic Debye approximation to illustrate stability. Finally, optical properties are summarized to assess the applicability of this alloy for optoelectronic applications. The overall characteristics of these particular alloys suggest potential applications in sustainable thermoelectric and optoelectronic features.

Region‐dependent meteorological conditions of thunderstorm based on clustering analysis of stability and precipitable water indices

AbstractThunderstorms contribute to a large number of destructive weather events. However, due to the availability of comprehensive thunderstorm datasets, current researches on thresholds of stability indices during thunderstorms have always been limited within a specific local area during a relatively short time span. This study uses observations of thunderstorms data and ERA5 reanalysis data in summer (June–August) at 0600 and 1200 UTC from 1995 to 2019 to investigate the region‐dependent thresholds of four indices for indicating the occurrence of thunderstorm. The indices include the K index (K), the Showalter index (SI), convective available potential energy (CAPE), and precipitable water (PW). By applying the K‐means clustering method on the composite mean fields of four indices on thunderstorm days, China is objectively divided into three regions based on three stability indices (K, SI, and CAPE) and two regions based on PW index. Region‐dependent thresholds have been established for each index related to thunderstorms. When these thresholds are applied, accuracy rate of detecting thunderstorms exceeds 60% at 85% of the stations over China. The remarkable regional difference in the thresholds of the four indices are further attributed to the climatic backgrounds. Summer climatological means of surface potential temperature and surface relative humidity play a pivotal role in shaping the distinctive thresholds of K, CAPE, and PW across diverse regions, while surface potential temperature and topography are pivotal for the region‐dependent thresholds of SI. Based on the terrain characteristics and relevant summer climatology in each region, the thunderstorm thresholds can be potentially applied to regions with limited thunderstorm records but exhibiting similar climatic features beyond China. These findings would provide a reliable reference for thunderstorm monitoring by meteorological departments and related decision‐making services.

A mean field game approach to relative investment–consumption games with habit formation

A mean field game approach to relative investment–consumption games with habit formation

Exploring mean field spin models with multiple populations: A theoretical framework

This paper thoroughly investigates the analysis of a modified generalized mean-field Ising model. The thermodynamic limit of free energy is investigated, and both the upper and lower bounds are derived. The lower bound is derived using a standard entropic variational principle, whereas a decoupling method is employed to derive the upper bound. Although the two bounds differ in form, they exhibit the same local maxima. Finally, the impact of a slight external field on the magnetic order is analyzed.

Climatology and Variability of Sea Surface Temperature in the Azores Region and Its Relation to Climate Indices

Daily sea surface temperature (SST) data from the Advanced Very High Resolution Radiometer from 1982 to 2020 were used to study the spatiotemporal variability and climatology of SST in the Azores. In addition, the relationships between the SST anomaly (SSTA) and three climate index time series for the period 1982-2020 were investigated: the Oceanic Niño Index (ONI), the Southern Oscillation Index (SOI) and the North Atlantic Oscillation (NAO) index. The spatiotemporal variability and climatology of the SST were studied by analyzing annual, seasonal, and monthly mean SST time series and climate fields. Relationships between the SSTA and climate index time series were investigated using Pearson's correlation analysis and wavelet coherence analysis. The annual mean SST time series shows a positive linear trend of about 0.027°C per year over the period 1982-2020. The spatial variability of the linear trend shows that the positive trend is consistent throughout the study area, ranging from 0.024 to 0.034°C per year. The spatial variability is not uniform, and high values of the trend are observed in the upper northwestern part and southwestern half of the basin. Seasonal mean SST fields show a positive North-South latitudinal gradient, with higher temperatures in the south, especially in the southwestern basin. In addition, the seasonal mean SST fields show possible coastal upwelling signatures along the coast of the Azores islands in different seasons. The results of Pearson's correlation analysis between basin-averaged, de-trended monthly mean SSTA and climate indices show that SSTA shows a significant positive correlation with SOI and a negative correlation with ONI from 1982 to 2020. NAO shows positive correlation with SSTA for the December-January-February season. Wavelet coherence analysis confirms significant coherences between the Azores SSTA and the climate-ocean indices at certain time scales and periods.

A hierarchy of the optimal velocity model with optimal path for pedestrian evacuation: From microscopic to macroscopic models

We study the evacuation process of pedestrians by adopting an optimal velocity model. The Eikonal equation is coupled to the optimal velocity model for optimal path to guide the movement directions of pedestrians. It depends on pedestrian density. We derive the corresponding mean field equation, hydrodynamic and scalar models from the scaled microscopic optimal velocity model. Several numerical experiments are performed in a corridor with two exits. We show and compare results on the microscopic as well as on the hydrodynamic and scalar models. Results from microscopic model are closed to the hydrodynamic and scalar models when a large number of particles are considered in microscopic simulation. The computation time increases as number of particles in microscopic simulation increases. The computation times of the hydrodynamic and scalar models are less than the computation time of the microscopic model with large number of particles. Hence it is beneficial to apply the hydrodynamic and scalar models over the microscopic model when a large number of particles in microscopic system are considered.

On Lipschitz solutions of mean field games master equations

We develop a theory of existence and uniqueness of solutions of MFG master equations when the initial condition is Lipschitz continuous. Namely, we show that as long as the solution of the master equation is Lipschitz continuous in space, it is uniquely defined. Because we do not impose any structural assumptions, such as monotonicity for instance, there is a maximal time of existence for the notion of solution we provide. We analyze three cases: the case of a finite state space, the case of master equation set on a Hilbert space, and finally on the set of probability measures, all in cases involving common noises. In the last case, the Lipschitz continuity we refer to is on the gradient of the value function with respect to the state variable of the player.

A unified quantification of synchrony in globally coupled populations with the Wiener order parameter.

We tackle the quantification of synchrony in globally coupled populations. Furthermore, we treat the problem of incomplete observations when the population mean field is unavailable, but only a small subset of units is observed. We introduce a new order parameter based on the integral of the squared autocorrelation function and demonstrate its efficiency for quantifying synchrony via monitoring general observables, regardless of whether the oscillations can be characterized in terms of the phases. Under condition of a significant irregularity in the dynamics of the coupled units, this order parameter provides a unified description of synchrony in populations of units of various complexities. The main examples include noise-induced oscillations, coupled strongly chaotic systems, and noisy periodic oscillations. Furthermore, we explore how this parameter works for the standard Kuramoto model of coupled regular-phase oscillators. The most significant advantage of our approach is its ability to infer and quantify synchrony from the observation of a small percentage of the units and even from a single unit, provided the observations are sufficiently long.

WCD Ideas: Teleconnections through weather rather than stationary waves

Abstract. Conventionally, teleconnections in the atmosphere are described by correlations between monthly mean fields. These correlations are supposedly caused by stationary Rossby waves. The main hypothesis explored in this idea is that teleconnections are instead established by chains of events on synoptic timescales, that is by weather. Instead I hypothesise that non-stationary Rossby waves play an important role in establishing teleconnections. If these hypotheses are correct, much of the vast literature on this topic misses an essential part of the atmospheric dynamics leading to teleconnections.

Statistical relations between spectropolarimetric observables and the polar strength of the stellar dipolar magnetic field

Global magnetic fields of early-type stars are commonly characterised by the mean longitudinal magnetic field $ z and the mean field modulus $ B derived from the circular polarisation and intensity spectra, respectively. Observational studies often report a root mean square (rms) of $ z and an average value of $ B In this work, I used numerical simulations to establish statistical relationships between these cumulative magnetic observables and the polar strength d $, of a dipolar magnetic field. I show that in the limit of many measurements randomly distributed in rotational phase, $ z rms d $ and $ B avg d $. The same values can be recovered with only three measurements, provided that the observations are distributed uniformly in the rotational phase. These conversion factors are suitable for ensemble analyses of large stellar samples, where each target is covered by a small number of magnetic measurements.

Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons.

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.

Origins of multi-sublattice magnetism and superexchange interactions in double–double perovskite CaMnCrSbO6

The multi-sublattice magnetism and electronic structure in double–double perovskite compound CaMnCrSbO6 is explored using density functional theory. The bulk magnetization and neutron diffraction suggest a ferrimagnetic order ( TC∼ 49 K) between between Mn2+ and Cr3+ spins. Due to the non-equivalent Mn atoms (labelled as Mn(1) and Mn(2) which have tetrahedral and planar oxygen coordinations, respectively) and the Cr atom in the centre of distorted oxygen octahedron in the unit cell, the exchange interactions are more complex than that expected from a two sublattice magnetic system. The separations between the on-site energies of the d-orbitals of Mn(1), Mn(2) and Cr obtained from Wannier function analysis are in agreement with their expected crystal field splitting. While the DOS obtained from non spin-polarized calculations show a metallic character, starting from Hubbard U = 0 eV the spin-polarized electronic structure calculations yield a ferrimagnetic insulating ground state. The band gap increases with Ueff (U − J), thereby showing a Mott–Hubbard nature of the system. The inclusion of anti-site disorder in the calculations show decrease in band-gap and also reduction in the total magnetic moment. Due to the ∼90∘ superexchange, nearest neighbour exchange constants obtained from DFT are an order of magnitude smaller than those reported for various magnetic perovskite and double-perovskite compounds. The Mn(1)–O–Mn(2) (out of plane and in-plane), Mn(1)–O–Cr and Mn(2)–O–Cr superexchange interactions are found to be anti-ferromagnetic, while the Cr–O–O–Cr super-superexchange is found to be ferromagnetic. The Mn(2)–O–Cr superexchange is weaker than the Mn(1)–O–Cr super-exchange, thus effectively resulting in ferrimagnetism. From a simple 3-site Hubbard model, we derived expressions for the antiferromagnetic superexchange strength JAFM and also for the weaker ferromagnetic JFM . The relative strengths of JAFM for the various superexchange interactions are in agreement with those obtained from DFT. The expression for Cr–O–O–Cr super-superexchange strength ( J~SS ), which has been derived considering a 4-site Hubbard model, predicts a ferromagnetic exchange in agreement with DFT. Finally, our mean field calculations reveal that assuming a set of four magnetic sub-lattices for Mn2+ spins and a single magnetic sublattice for Cr3+ spins yields a much improved T C , while a simple two magnetic sublattice model yields a much higher T C .