Mean-field Effects Research Articles

Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach

Exploring the impact of dimensionality on the quantum dynamics of interacting bosons in traps including particle correlations is an interesting but challenging task. Due to the different participating length scales, the modelling of the short-range interactions in three dimensions plays a special role. We review different approaches for the latter and elaborate that for multi-configurational computational strategies, finite-range potentials are adequate resulting in the need for large grids to resolve the relevant length scales. This results in computational challenges, which include the exponential scaling of complexity with the number of atoms. We show that the recently developed ab initio multi-layer multi-configurational time-dependent Hartee method for bosons (ML–MCTDHB) (2013 J. Chem. Phys. 139 134103) can face both numerical challenges and present an efficient numerical implementation of ML–MCTDHB in three spatial dimensions, particularly suited to describe the quantum dynamics for elongated traps. The beneficial scaling of our approach is demonstrated by studying the tunnelling dynamics of bosonic ensembles in a double well. Comparing three-dimensional with quasi-one dimensional simulations, we find dimensionality-induced effects in the density. Furthermore, we study the crossover from weak transversal confinement, where a mean-field description of the system is sufficient, towards tight transversal confinement, where particle correlations and beyond mean-field effects are pronounced.

Social Optima in Mean Field Linear-Quadratic-Gaussian Models with Markov Jump Parameters

This paper investigates social optima of mean field linear-quadratic-Gaussian (LQG) control models with Markov jump parameters. The common objective of the agents is to minimize a social cost---the cost average of the whole society. In the cost functions there are coupled mean field terms. First, we consider the centralized case and get a parameterized equation of mean field effect. Then, we design a set of distributed strategies by solving a limiting optimal control problem in an augmented state space subject to the consistency requirement for mean field approximation. It is shown that the set of distributed strategies is asymptotically team-optimal, and the asymptotically optimal social cost value can be obtained explicitly. The optimal social average cost is compared with the optimal individual cost in mean field games by virtue of the explicit expressions, and the difference is further illustrated by a numerical example.

Ultracold metastable helium: Ramsey fringes and atom interferometry

We report on interference studies in the internal and external degrees of freedom of metastable triplet helium atoms trapped near quantum degeneracy in a \( 1.5\kern0.166667em \upmu \mathrm{m} \) optical dipole trap. Applying a single \( \pi /2 \) rf pulse we demonstrate that 50% of the atoms initially in the \( m=+1 \) state can be transferred to the magnetic field insensitive \( m=0 \) state. Two \( \pi /2 \) pulses with varying time delay allow a Ramsey-type measurement of the Zeeman shift for a high precision measurement of the \( {2}^3{S}_1 \)–\( {2}^1{S}_0 \) transition frequency. We show that this method also allows strong suppression of mean-field effects on the measurement of the Zeeman shift, which is necessary to reach the accuracy goal of 0.1 kHz on the absolute transition frequencies. Theoretically the feasibility of using metastable triplet helium atoms in the \( m=0 \) state for atom interferometry is studied demonstrating favorable conditions, compared to the alkali atoms that are used traditionally, for a non-QED determination of the fine structure constant.

Fate of Alpha Dynamos at Large Rm.

At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha dynamos as the magnetic Reynolds number Rm is increased. Using Floquet theory, we are able to precisely quantify mean-field effects like the alpha and beta effect (i)by rigorously distinguishing dynamo modes that involve large-scale components from the ones that only involve small scales, and by (ii)providing a way to investigate arbitrary large-scale separations with minimal computational cost. We apply this framework to helical and nonhelical flows as well as to random flows with short correlation time. Our results determine that the alpha description is valid for Rm smaller than a critical value Rm_{c} at which small-scale dynamo instability starts. When Rm is above Rm_{c}, the dynamo ceases to follow the mean-field description and the growth rate of the large-scale modes becomes independent of the scale separation, while the energy in the large-scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus, alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean-field modeling are proposed.

Liquid quantum droplets of ultracold magnetic atoms

The simultaneous presence of two competing inter-particle interactions can lead to the emergence of new phenomena in a many-body system. Among others, such effects are expected in dipolar Bose–Einstein condensates, subject to dipole–dipole interaction and short-range repulsion. Magnetic quantum gases and in particular Dysprosium gases, offering a comparable short-range contact and a long-range dipolar interaction energy, remarkably exhibit such emergent phenomena. In addition an effective cancellation of mean-field effects of the two interactions results in a pronounced importance of quantum-mechanical beyond mean-field effects. For a weakly dominant dipolar interaction the striking consequence is the existence of a new state of matter equilibrated by the balance between weak mean-field attraction and beyond mean-field repulsion. Though exemplified here in the case of dipolar Bose gases, this state of matter should appear also with other microscopic interactions types, provided a competition results in an effective cancellation of the total mean-field. The macroscopic state takes the form of so-called quantum droplets. We present the effects of a long-range dipolar interaction between these droplets.

Does non-monotonic behavior of directed flow signal the onset of deconfinement?

We investigate the effects of nuclear mean-field as well as the formation and decay of nuclear clusters on the directed flow v1 in high energy nucleus-nucleus collisions from sNN=7.7 GeV to 27 GeV incident energies within a transport model. Specifically, we use the JAM transport model in which potentials are implemented based on the framework of the relativistic quantum molecular dynamics. Our approach reproduces the rapidity dependence of directed flow data up to sNN≈8 GeV showing the significant importance of mean-field. However, the slopes of dv1/dy at mid-rapidity are calculated to be positive at sNN11.7 and 19.6 GeV, and become negative above 27 GeV. Thus the result from the JAM hadronic transport model with nuclear mean-field approach is incompatible with the data. Therefore within our approach, we conclude that the excitation function of the directed flow cannot be explained by the hadronic degree of freedom alone.

Preequilibrium neutron emission in heavy ion reaction: Mean field effect and multiple emission

Effects of nuclear mean field and of multiple preequilibrium (PEQ) emission on double differential neutron multiplicity distribution from heavy ion reactions (12C+165Ho and 20Ne+165Ho) at 10–30 MeV/u have beeninvestigated in the framework of the semiclassical formalism for heavy ion reaction (henceforth termed “HION”)developed earlier. HION follows the equilibration of a target+projectile composite system through the kinematics of two-body scattering. In the present work nuclear density distribution in the composite system is estimated in the relativistic mean field (RMF) approach. The nucleon-nucleon collision rates and subsequently the nucleon emission probability are calculated from this density distribution. A second approach based on a semiphenomenological formalism is also used for nuclear density distribution. Energy-angle distribution of neutron multiplicities calculated with this modified HION model coupled with multiple PEQ emission could reproduce the measured data of earlier workers in the projectile energy range of 10–30 MeV/u.

Vibronic approach to the calculation of the decay rate of the photoexcited charge-transfer state of Guanine–Cytosine stacked dimer in water solution

We compute the rate of the charge recombination (CR) process from the minimum of the charge transfer (CT) Guanine–Cytosine stacked dimer in water solution to the ground electronic state (GS). We adopt the quantum non-adiabatic theory of electron transfer reactions, where key ingredients to determine the CR rate are the electronic coupling and the so-called Franck–Condon density of states (FCWD). In order to compute the FCWD, we exploited recent developments in the field of the time-independent and time-dependent simulations of vibronic spectra of large systems, based on model harmonic potential energy surfaces (PESs). Both mean-field solvent effects on the PESs and the solvent reorganization effects on the CR rate were described by implicit polarizable continuum model. We show that an improper treatment of the contributions of the inter-base modes to the FCWD results in artefacts which can change the estimate of the CR rates by orders of magnitude and we devise a computational protocol in internal coordinates able to determine “effective normal modes” that separate the stiff (intra-base) modes and the inter-base ones. The results for the CR rate are qualitatively consistent with available experimental data. By computing the CR rate for four different stacking geometries, we show that all the parameters ruling the CR rate, namely the CT character of the excited state (ES), the equilibrium position of stiff modes (and therefore the FCWD), the electronic coupling and the energy gap between the GS and ES are all strongly dependent on the fluctuation of the dimer structure along the inter-base modes. On this ground, we discuss some possible future theoretical developments to achieve a non-phenomenological fully first-principle estimate of the CR rate that can be directly compared with experiment.

Multi-scale modeling of elasto-plastic response of SnAgCu lead-free solder alloys at different ageing conditions: Effect of microstructure evolution, particle size effects and interfacial failure

In microelectronics applications, SnAgCu lead-free solder joints play the important role of ensuring both the mechanical and electrical integrity of the components. In such applications, the SnAgCu joints are subjected to elevated homologous temperatures for an extended period of time causing significant microstructural changes and leading to reliability issues. In this study, the link between the change in microstructures and deformation behavior of SnAgCu solder during ageing is explained by developing a hybrid multi-scale microstructure-based modeling approach. Herein, the SnAgCu solder alloy is seen as a three phase metal matrix composite in which Ag3Sn and Cu6Sn5 hard intermetallics play the role of reinforcements and Sn the role of a ductile matrix. The hardening of the Sn matrix due to fine intermetallics in the eutectic mixture is modeled by incorporating the mean field effects of geometrically necessary dislocations. Subsequently, a two level homogenization procedure based on micromechanical finite element (FE) models is used to capture the interactions between the different phases. For this purpose, tomographic images of microstructures obtained by Focused Ion Beam (FIB) and synchrotron X-Ray in different ageing conditions are directly used to generate statistically representative volume elements (RVE) using 3D FE models. The constitutive behavior of the solder is determined by sequentially performing two scales of numerical homogenization at the eutectic level and then at the dendrite level. For simplification, the anisotropy of Sn as well as the potential recovery processes have been neglected in the modeling. The observed decrease in the yield strength of solder due to ageing is well captured by the adopted modeling strategy and allows explaining the different ageing mechanisms. Finally, the effects of potential debonding at the intermetallic particle-matrix interface as well as particle fracture on the overall strength of solder are discussed based on simplified unit cell FE models and experimental observations.

Engineering dark solitary waves in ring-trap Bose–Einstein condensates

We demonstrate the feasibility of generation of quasi-stable counter-propagating solitonic structures in an atomic Bose–Einstein condensate confined in a realistic toroidal geometry, and identify optimal parameter regimes for their experimental observation. Using density engineering we numerically identify distinct regimes of motion of the emerging macroscopic excitations, including both solitonic motion along the azimuthal ring direction, such that structures remain visible after multiple collisions even in the presence of thermal fluctuations, and snaking instabilities leading to the decay of the excitations into vortical structures. Our analysis, which considers both mean field effects and fluctuations, is based on the ring trap geometry of Murray et al (2013 Phys. Rev. A 88 053615).

Global performance of multireference density functional theory for low-lying states insd-shell nuclei

We present a comprehensive study of low-lying states in even-even Ne, Mg, Si, S, Ar isotopes with the multireference density functional theory (MR-DFT) based on a relativistic point-coupling energy density functional (EDF). Beyond mean-field (BMF) effects are taken into account by configuration mixing of both particle-number and angular-momentum projected axially deformed states with generator coordinate method (GCM). Global performance of the MR-DFT for the properties of both ground state and of the first $2^+, 4^+$ states is examined, in comparison with previous studies based on nonrelativistic EDFs and available data. Our results indicate that an EDF parameterized at the BMF level is demanded to achieve a quantitative description.

Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture.

According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, g_{12}^{2}>g_{11}g_{22}. We show that instead of collapsing such a mixture gets into a dilute liquidlike droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The droplet thus automatically evaporates itself to zero temperature, the property potentially interesting by itself and from the viewpoint of sympathetic cooling of other systems.

Non-resonant kaon pair production and medium effects in proton–nucleus collisions

We study the non-resonant (non-ϕ) production of pairs by protons of 2.83 GeV kinetic energy on C, Cu, Ag and Au targets within the collision model, based on the nuclear spectral function, for incoherent primary proton–nucleon and secondary pion–nucleon creation processes. The model takes into account the initial proton and final kaon absorption, target nucleon binding and Fermi motion as well as nuclear mean-field potential effects on these processes. We calculate the antikaon momentum dependences of the exclusive absolute and relative pair yields in the acceptance window of the ANKE magnetic spectrometer, used in a recent experiment performed at COoler SYnchrotron (COSY), within the different scenarios for the antikaon–nucleus optical potential. We demonstrate that the above observables are strongly sensitive to this potential. Therefore, they can be useful to help determine the optical potential from the direct comparison of the results of our calculations with the data from the respective ANKE-at-COSY experiment. We also show that the pion–nucleon production channels dominate in the low-momentum , production in the considered kinematics and, hence, they have to be accounted for in the analysis of these data.

Impact of Soil Variability on Irrigated and Rainfed Cotton

Cotton is a vital component of the economies of Mid-South states. Producers and landowners are looking for ways to reduce the variability of irrigated yields, and soil apparent electrical conductivity (ECa) is a readily obtained parameter that can indicate soil variability. A study was conducted in 2011 and 2012 at the Fisher Delta Research Center in Portageville, MO, with the objective to determine the impact of soil spatial variability on yield and irrigation water use efficiency for cotton. Observed ECa values were low, consistent with average sand contents that ranged from 59 to 82% in the upper 0.76 m of the soil profile. Spatial autocorrelation was present in the data and thus spatial analyses were used. In 2011, yields for two treatments were not significantly different from the mean field effect; however, the ECa effect was significant, indicating that soil variability impacted yield more than irrigation differences for the two treatments. In 2012, yields for four of the six treatments were significantly different from the mean field effect; however, the ECa effect was not significant. A quadratic equation was fit to the combined data from irrigated and rainfed plots in 2012. The resulting equation had a maximum of 3,372 kg ha-1 at 135 mm total irrigation and the median observed ECa value (3.0 mS m-1). Future efforts will include additional fields and environments, which should increase the understanding of the impact of soil variability and allow for improved selection of optimum management zones for site specific application of water and other inputs.

QUENCHING AND ANISOTROPY OF HYDROMAGNETIC TURBULENT TRANSPORT

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.

Structure of krypton isotopes calculated with symmetry-conserving configuration-mixing methods

Shape transitions and shape coexistence in the $^{70-98}$Kr region are studied in a unified view with state-of-the-art beyond self-consistent mean field methods based on the Gogny D1S interaction. Beyond mean field effects are taken into account through the exact angular momentum and particle number restoration and the possibility of axial and non-axial shape mixing. The results of the low-lying properties of these isotopes are in good agreement with the experimental data when the triaxial degree of freedom is included. Shape transitions from axial-oblate ($^{70-72}$Kr) to triaxial-prolate ($^{74-78}$Kr) and from spherical-triaxial ($^{86-92}$Kr) to axial-oblate ($^{94-98}$Kr) ground states are obtained. Additionally, low-lying $0^{+}$ excited states and quasi-gamma bands are found showing the richness of the collective structure in this region.

Partonic mean-field effects on matter and antimatter elliptic flows

Abstract Using a partonic transport model based on the Nambu–Jona-Lasinio model, we study the effect of scalar and vector mean fields on the elliptic flows of quarks and antiquarks in relativistic heavy ion collisions that lead to the production of a baryon-rich quark matter. Although the scalar mean field, which is attractive for both quarks and antiquarks, reduces both their elliptic flows, the vector mean field, which is repulsive for quarks and attractive for antiquarks, leads to a splitting of their elliptic flows, and this effect increases with the strength of the vector coupling in the baryon-rich quark matter. Converting quarks and antiquarks to hadrons via the quark coalescence model, we further study the dependence of the transverse momentum integrated relative elliptic flow differences between protons and antiprotons, lambdas and anti-lambdas, and positively and negatively charged kaons on the strength of the quark vector coupling. These results are then compared with the experimental data measured by the STAR Collaboration in the Beam Energy Scan program at the Relativistic Heavy Ion Collider.

A solar dynamo model driven by mean-field alpha and Babcock-Leighton sources: fluctuations, grand-minima-maxima, and hemispheric asymmetry in sunspot cycles

Extreme solar activity fluctuations and the occurrence of solar grand minima and maxima episodes, are well established, observed features of the solar cycle. Nevertheless, such extreme activity fluctuations and the dynamics of the solar cycle during Maunder minima-like episodes remain ill-understood. We explore the origin of such extreme solar activity fluctuations and the role of dual poloidal field sources, namely the Babcock-Leighton mechanism and the mean-field alpha effect in the dynamics of the solar cycle. We mainly concentrate on entry and recovery from grand minima episodes such as the Maunder minimum and the dynamics of the solar cycle. We use a kinematic solar dynamo model with a novel set-up in which stochastic perturbations force two distinct poloidal field alpha effects. We explore different regimes of operation of these poloidal sources with distinct operating thresholds, to identify the importance of each. The perturbations are implemented independently in both hemispheres which allows one to study the level of hemispheric coupling and hemispheric asymmetry in the emergence of sunspots. From the simulations performed we identify a few different ways in which the dynamo can enter a grand minima episode. While fluctuations in any of the $\alpha$ effects can trigger intermittency we find that the mean-field alpha effect is crucial for the recovery of the solar cycle from a grand minima episode which a Babcock-Leighton source alone, fails to achieve. Our simulations also demonstrate other cycle dynamics. We conclude that stochastic fluctuations in two interacting poloidal field sources working with distinct operating thresholds is a viable candidate for triggering episodes of extreme solar activity and that the mean-field alpha effect capable of working on weak, sub-equipartition fields is critical to the recovery of the solar cycle following an extended solar minimum.

Collective Target Tracking Mean Field Control for Markovian Jump-Driven Models of Electric Water Heating Loads

Load control has traditionally been viewed as a useful tool for peak load reduction in power systems. With the increasing renewable energy penetration in the grid, load control is also considered as a tool to exploit the storage in dispersed devices naturally present in power systems such as electric water heaters to mitigate generation variability. Tapping into the storage dispersed across the power system is challenging because of the large number of devices that need to be coordinated to produce desirable system level behavior. In this paper a mean field game theoretic based control architecture is proposed as a load control mechanism to limit the required flows of information, and produce local constraints conscious decentralized individual controls which aggregate to a desired mean behavior. A Markovian jump-driven model of individual electric water heating loads is employed where the mean field effect is mediated through the quadratic cost function parameters under the form of an integral error. The corresponding system of mean field Nash equilibrium inducing equations is developed and numerical simulation results are presented.

Zero sound in a two-dimensional dipolar Fermi gas

We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.