Mean-field Level Research Articles

Fission of 180\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{180}$$\\end{document}Hg and 264\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{264}$$\\end{document}Fm: a comparative study

180\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{180}$$\\end{document}Hg is experimentally found to fission asymmetrically. This result was not expected as a naive fragment shell effects study would support the symmetric mode to be the most probable. In the present study we investigate both symmetric and asymmetric 180\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{180}$$\\end{document}Hg fission modes at the mean field level using various multipole moment constraints. Potential energy surfaces are analysed in terms of shell effects that shape their topographies and connections to fragment shell effects are made. The non-occurrence of low energy symmetric fission is interpreted in terms of 90\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{90}$$\\end{document}Zr fragment properties. Throughout this study a comparison with 264\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{264}$$\\end{document}Fm and its symmetric doubly magic 132\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{132}$$\\end{document}Sn fission fragments is done.

Strong Pairing Originated from an Emergent Z_{2} Berry Phase in La_{3}Ni_{2}O_{7}.

The recent discovery of high-temperature superconductivity in La_{3}Ni_{2}O_{7} offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that the electrons in d_{z^{2}} orbitals nearly form local moments, we examine the effect of the Hubbard interaction U on the binding strength of Cooper pairs based on a single-orbital bilayer model with intralayer hopping t_{∥} and interlayer superexchange J_{⊥}. By extensive density matrix renormalization group calculations, we observe a remarkable enhancement in binding energy as much as 10-20 times larger with U/t_{∥} increasing from 0 to 12 at J_{⊥}/t_{∥}∼1. We demonstrate that such a substantial enhancement stems from a kinetic-energy-driven mechanism. Specifically, a Z_{2} Berry phase will emerge at large U due to the Hilbert space restriction (Mottness), which strongly suppresses the mobility of single particle propagation as compared to U=0. However, the kinetic energy of the electrons (holes) can be greatly restored by forming an interlayer spin-singlet pairing, which naturally results in a superconducting state even for relatively small J_{⊥}. An effective hard-core bosonic model is further proposed to estimate the superconducting transition temperature at the mean-field level.

Fluctuation-induced first order transition to collective motion

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

Polarization-induced stress in the noisy voter model

A new model for the dynamics of opinion formation is proposed and analyzed at the mean-field level. It can be regarded as a generalization of the noisy voter model in which agents update their binary states by copying others and by an intrinsic mechanism affected by the degree of polarization in the system. It also takes into account whether the agents enhance or reduce their intrinsic mechanism upon increasing polarization. Four phases or shapes of the steady-state probability of a fraction of agents in a given state are found (unimodal, bimodal, W and M). In the unimodal (resp. bimodal) phase, the copying (resp. intrinsic) mechanism is globally dominant, while in the W (resp. M) phase the copying (resp. intrinsic) mechanism is the relevant one close to the consensus states while it reduces its influence as approaching coexistence. In the thermodynamic limit, the bimodal and W phases disappear, while the unimodal and M phases prevail. The theoretical results, obtained analytically from the master equation, and the numerical simulations are in good agreement.

Chiral spin liquid phase in an optical lattice at mean-field level

Chiral spin liquid phase in an optical lattice at mean-field level

A mean-field model of gamma-frequency oscillations in networks of excitatory and inhibitory neurons.

Gamma oscillations are widely seen in the cerebral cortex in different states of the wake-sleep cycle and are thought to play a role in sensory processing and cognition. Here, we study the emergence of gamma oscillations at two levels, in networks of spiking neurons, and a mean-field model. At the network level, we consider two different mechanisms to generate gamma oscillations and show that they are best seen if one takes into account the synaptic delay between neurons. At the mean-field level, we show that, by introducing delays, the mean-field can also produce gamma oscillations. The mean-field matches the mean activity of excitatory and inhibitory populations of the spiking network, as well as their oscillation frequencies, for both mechanisms. This mean-field model of gamma oscillations should be a useful tool to investigate large-scale interactions through gamma oscillations in the brain.

Production of positronium chloride: A study of the charge exchange reaction between Ps and Cl.

We present cross sections for the formation of positronium chloride (PsCl) in its ground state from the charge exchange between positronium (Ps) and chloride (Cl-) in the range of 10 meV-100eV Ps energy. We have used theoretical models based on the first Born approximation in its three-body formulation. We simulated the collisions between Ps and Cl- using abinitio binding energies and positronic wave functions at both the mean-field and correlated levels extrapolated to the complete basis set limit. The accuracy of these abinitio data was benchmarked on the PsF system with the existing highly accurate results, including the very recent quantum Monte Carlo results. We have investigated Ps excited states up to n = 4. The results suggest that the channel Ps(n = 2) is of particular interest for the production of PsCl in the ground state and shows that an accurate treatment of correlation effects (i.e., electron-electron and electron-positron correlations) leads to a significant change in the magnitude of the PsCl production cross section with respect to the mean-field level.

Transport through a correlated polar side-coupled quantum dot transistor in the presence of a magnetic field and dissipation

Non-equilibrium magneto-transport properties of a quantum dot dimer transistor are studied in the presence of electron–electron and electron–phonon interactions and the interaction of the dimer phonons with the substrate phonon bath that gives rise to dissipation. The entire system is modeled by the Anderson–Holstein–Caldeira–Leggett Hamiltonian where the Caldeira–Leggett term takes care of the damping. The electron–phonon interaction is dealt with the Lang–Firsov transformation and the electron–electron interaction is treated at the mean-field level. The transport problem is studied using the Keldysh non-equilibrium Green function theory and the effects of electron–electron interaction, external magnetic field, electron–phonon interaction and damping on spectral function, tunneling current and differential conductance of the dimer transistor are calculated.

Effect of counterions on the structure and dynamics of water near a negatively charged surfactant: a theoretical vibrational sum frequency generation study.

Charged aqueous interfaces are of paramount importance in electrochemical, biological and environmental sciences. The properties of aqueous interfaces with ionic surfactants can be influenced by the presence of counterions. Earlier experiments involving vibrational sum frequency generation (VSFG) spectroscopy of aqueous interfaces with negatively charged sodium dodecyl sulfate (Na+DS- or SDS) surfactants revealed that the hydrogen bonding strength of the interfacial water molecules follows a certain order when salts of monovalent and divalent cations are added. It is known that cations do not directly participate in hydrogen bonding with water molecules, rather they only influence the hydrogen bonded network through their electrostatic fields. In the current work, we have simulated the aqueous interfacial systems of sodium dodecyl sulfate in the presence of chloride salts of mono and divalent countercations. The electronic polarization effects on the ions are considered at a mean-field level within the electronic continuum correction model. Our calculations of the VSFG spectra show a blue shift in the presence of added countercations whose origin is traced to different relative contributions of water molecules from the solvation shells of the surfactant headgroups and the remaining water molecules in the presence of countercations. Furthermore, the cations shield the electric fields of the surfactant headgroups, which in turn influences the contributions of water molecules to the total VSFG spectrum. This shielding effect becomes more significant when divalent countercations are present. The dynamics of water molecules is found to be slower at the interface in comparison to the bulk. The interfacial depth dependence of various dynamical quantities shows that the interface is structurally and dynamically more heterogeneous at the microscopic level.

Adsorption on nanoparticles with surface defects: mean field and energy level approaches.

In this work two theoretical approximations, the so-called theoretical approach of energy levels and an extension of the modified mean field approach (TAEL and MMFA, respectively) are applied to the study of surface decoration of modified nanostructures like crystalline nanoparticles. The surface of the nanoparticles is modified by the irreversible random deposition of defects consisting in isolated atoms. Such deposition is carried out until a certain surface density is reached, leaving the rest of the sites available for a second species to adsorb. Through the formulation of the integral equation, the theoretical approaches permit obtaining the adsorption isotherms and the compressibility of the adlayer. The main difference between the two approaches is the degree of details considered in their mathematical formulations: TAEL takes in account all the energy levels meanwhile MMFA only an average. The degree of precision and usefulness of both theories were evaluated in comparison with Monte Carlo simulations in the grand canonical assembly. Several cases were studied: attractive and repulsive lateral interactions and different fraction of defects. The effects of the nanoscale were considered for different types and sizes of nanoparticles. By calculating an integral error, we are able to affirm that TAEL reproduces all the properties of the analyzed quantities from the reference simulated curves. On the other hand, the MMFA performance is good only for a certain limited range of the parameters, however the strength is in the mathematical simplicity compared to TAEL.

Renormalized one-loop theory of correlations in disperse polymer blends.

Polymer blends are critical in many commercial products and industrial processes and their phase behavior is therefore of paramount importance. In most circumstances, such blends are formulated with samples of high dispersity, which have generally only been studied at the mean-field level. Here, we extend the renormalized one-loop theory of concentration fluctuations to account for blends of disperse polymers. Analyzing the short and long length-scale fluctuations in a consistent manner, various measures of polymer molecular weight and dispersity arise naturally in the free energy. Thermodynamic analysis in terms of moments of the molecular weight distribution(s) provides exact results for the inverse susceptibility and demonstrates that the theory is not formally renormalizable. However, physically motivated approximations allow for an "effective" renormalization, yielding (1) an effective interaction parameter, χe, which depends directly on the sample dispersities (i.e., Mw/Mn) and leaves the form of the mean-field spinodal unchanged, and (2) an apparent interaction parameter χa that depends on higher-order dispersity indices, for instance Mz/Mw, and characterizes the true limits of blend stability accounting for long-range off-critical fluctuations. We demonstrate the importance of dispersity on several example systems, including both "toy" models that may be realized in computer simulation and more realistic industrially relevant blends. We find that the effects of long-range fluctuations are particularly prominent in blends where the component dispersities are mismatched, especially when there is a small quantity of the high-dispersity species. This can be understood as a consequence of the shift in the critical concentration(s) from the monodisperse value(s).

Replica symmetry broken states of some glass models.

We have studied in detail the M-p balanced spin-glass model, especially the case p=4. These types of model have relevance to structural glasses. The models possess two kinds of broken replica states; those with one-step replica symmetry breaking (1RSB) and those with full replica symmetry breaking (FRSB). To determine which arises requires studying the Landau expansion to quintic order. There are nine quintic-order coefficients, and five quartic-order coefficients, whose values we determine for this model. We show that it is only for 2≤M<2.4714⋯ that the transition at mean-field level is to a state with FRSB, while for larger M values there is either a continuous transition to a state with 1RSB (when M≤3) or a discontinuous transition for M>3. The Gardner transition from a 1RSB state at low temperatures to a state with FRSB also requires the Landau expansion to be taken to quintic order. Our result for the form of FRSB in the Gardner phase is similar to that found when 2≤M<2.4714⋯, but differs from that given in the early paper of Gross etal. [Phys. Rev. Lett. 55, 304 (1985)0031-900710.1103/PhysRevLett.55.304]. Finally we discuss the effects of fluctuations on our mean-field solutions using the scheme of Höller and Read [Phys. Rev. E 101, 042114 (2020)2470-004510.1103/PhysRevE.101.042114] and argue that such fluctuations will remove both the continuous 1RSB transition and discontinuous 1RSB transitions when 8>d≥6 leaving just the FRSB continuous transition. We suggest values for M and p which might be used in simulations to confirm whether fluctuation corrections do indeed remove the 1RSB transitions.

Universal correlations along the BEC-BCS crossover

Universality of the long-distance behavior across the Bardeen–Cooper–Schrieffer (BEC)-Bose–Einstein condensate (BCS) smooth transition for two-body density correlation functions and the Cooper-pair probability density is demonstrated in a balanced mixture of a two-component Fermi gas at T = 0. It is numerically shown at the mean-field level that these two-body quantities exhibit an exponential decay in terms of the chemical potential and the low-energy behavior of the gap. A general expression is found for the two-body distributions holding for different features of finite-range potentials, such as divergences at the origin, discontinuities at a finite radius, power-law decay, and exponential decay. The correlation length characterizing the long-distance behavior unravels the dependence on the energy needed to break pairs along the BEC-BCS crossover, a quantity meaningful to the stability of the many-body state.

Assessment of the partial saddle point approximation in field-theoretic polymer simulations.

Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a "signproblem" associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the signproblem. Although CL is exact in principle, it can be difficult to stabilize in strongly fluctuating systems. An alternate approach for blends or block copolymers with two segment species is to make a "partial saddle point approximation" (PSPA) in which the stiff pressure-like field is constrained to its mean-field value, eliminating the signproblem in the remaining field theory, allowing for traditional (real) sampling methods. The consequences of the PSPA are relatively unknown, and direct comparisons between the two methods are limited. Here, we quantitatively compare thermodynamic observables, order-disorder transitions, and periodic domain sizes predicted by the two approaches for a weakly compressible model of AB diblock copolymers. Using Gaussian fluctuation analysis, we validate our simulation observations, finding that the PSPA incorrectly captures trends in fluctuation corrections to certain thermodynamic observables, microdomain spacing, and location of order-disorder transitions. For incompressible models with contact interactions, we find similar discrepancies between the predictions of CL and PSPA, but these can be minimized by regularization procedures such as Morse calibration. These findings mandate caution in applying the PSPA to broader classes of soft-matter models and systems.

Solitary Vortex Dynamics of 2D Bose-Einstein Condensates with Higher-Order Nonlinear Interactions

For study of Continuous matter waves in Bose-Einstein condensates in nonlinear and quantum atom optics, the two-dimensional Gross-Pitaevskii equation (GPE) is chosen as the reliable model for studying the dynamics of vortices in the framework of mean-field theory. In related problems in several recent studies showing that higher-order interrelationships are an indispensable component of the GPE even at the mean-field level, by numerically estimating the vortex dynamics variables. In this paper, derive the vortex soliton solutions using the variational method and investigate the effect of higher-order nonlinear corrections on the behavior of the vortex dynamics, which are shown to have an important impact on the vortex dynamics behavior.

Entropy of Charge Inversion in DNA including One-Loop Fluctuations.

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice gas model, each adsorption site is assumed to have either a vacancy or a positively charged dimer attached with the dimer oriented either parallel or perpendicular to the double-helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak-binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean-field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics.

The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural networks at a mean-field level, e.g., assuming large fully connected networks. Moreover, its stochastic counterpart allows one to study fluctuation-induced phenomena, such as avalanches. Here we revisit the stochastic Wilson-Cowan model paying special attention to the possible phase transitions between quiescent and active phases. We unveil eight possible types of such transitions, including continuous ones with scaling behavior belonging to known universality classes-such as directed percolation and tricritical directed percolation-as well as six distinct ones. In particular, we show that under some special circumstances, at a so-called "Hopf tricritical directed percolation" transition, rather unconventional behavior is observed, including the emergence of scaling breakdown. Other transitions are discontinuous and show different types of anomalies in scaling and/or exhibit mixed features of continuous and discontinuous transitions. These results broaden our knowledge of the possible types of critical behavior in networks of excitatory and inhibitory units and are, thus, of relevance to understanding avalanche dynamics in actual neuronal recordings. From a more general perspective, these results help extend the theory of nonequilibrium phase transitions into quiescent or absorbing states.

Beyond-Mean-Field with an Effective Hamiltonian Mapped from an Energy Density Functional

A method for beyond-mean-field calculations based on an energy density functional is described. The main idea is to map the energy surface for the nuclear quadrupole deformation, obtained from an energy density functional at the mean-field level, into an effective Hamiltonian expressed as a many-body operator. The advantage of this procedure is that one avoids the problems with density dependence which can arise in beyond-mean-field methods. The effective Hamiltonian is then used in a straightforward way in the generator-coordinate-method with the inclusion of projections onto good particle numbers and angular momentum. In the end, both spectra and wave functions are obtained. As an example of the method, calculations for the nucleus 62Zn is performed with three different parametrizations of the Skyrme functional. The results are compared with experiment.

Consensus based optimization with memory effects: Random selection and applications

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system. We discuss some implementation aspects which lead to increased efficiency while preserving the success rate in the optimization process. In particular, we show how employing a random selection strategy to discard particles during the computation improves the overall performance. Several benchmark problems and applications to image segmentation and Neural Networks training are used to validate and test the proposed method. A theoretical analysis allows to recover convergence guarantees under mild assumptions on the objective function. This is done by first approximating the evolution of the particles with a continuous-in-time dynamics, and then by taking the mean-field limit of such dynamics. Convergence to a global minimizer is finally proved at the mean-field level.

Confinement of Fractional Excitations in a Triangular Lattice Antiferromagnet.

High-resolution neutron and THz spectroscopies are used to study the magnetic excitation spectrum of Cs_{2}CoBr_{4}, a distorted-triangular-lattice antiferromagnet with nearly XY-type anisotropy. What was previously thought of as a broad excitation continuum [L. Facheris etal., Phys. Rev. Lett. 129, 087201 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.087201] is shown to be a series of dispersive bound states reminiscent of "Zeeman ladders" in quasi-one-dimensional Ising systems. At wave vectors where interchain interactions cancel at the mean field level, they can indeed be interpreted as bound finite-width kinks in individual chains. Elsewhere in the Brillouin zone their true two-dimensional structure and propagation are revealed.