Mean-field Effects Research Articles

Excitonic theory of doping-dependent optical response in atomically thin semiconductors

The interaction of optically excited excitons in atomically thin semiconductors with residual doping densities leads to many-body effects which are continuously tunable by external gate voltages. Here, we develop a fully microscopic theory to describe the doping-dependent manipulation of the excitonic properties in atomically thin transition metal dichalcogenides. In particular, we establish a diagonalization approach for the Schr\"odinger equation which characterizes the interaction of a virtual exciton with the Fermi sea of dopants. Solving this many-body Schr\"odinger equation provides access to trions as well as a continuum of scattering states. The dynamics of coupled excitons, trions, and scattering continua is subsequently described by Heisenberg equations of motion including mean-field contributions and correlation effects due to the interaction of excitons with trions and scattering continuum states. Our calculations for optical excitation close to the band edge reveal the influence of doping on the exciton resonances in combination with the simultaneous identification of not only ground-, but also excited-, state trion resonances.

Pairing strength in the relativistic mean-field theory determined from the fission barrier heights of actinide nuclei and verified by pairing rotation and binding energies

Abstract We have studied the strength of the Bardeen–Cooper–Schrieffer (BCS) pairing force, used as a residual interaction to the relativistic mean-field approach, to reproduce the height of the inner fission barriers for actinide nuclei. It was found that increasing the pairing strength by about $13\%$ makes the reproduction of the inner fission barriers better over a wide range of actinide nuclei. This result was verified by using the moment of inertia of the pairing rotational energy, which was introduced to avoid mean-field and odd-mass effects in the pairing interaction, to deduce purely the pairing strength. The pairing interaction thus determined could also improve the description of the binding energy of heavy nuclei. As a result, a consistent picture among inner fission barrier, binding energy, and pairing moment of inertia could be obtained in terms of the relativistic mean-field + BCS theory for a broad region of the actinide nuclei.

Pattern formation in quantum ferrofluids: From supersolids to superglasses

Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems. In equilibrium, quantum ferrofluids formed from ultracold atoms were recently shown to spontaneously develop coherent density patterns, manifesting a supersolid. We theoretically investigate the phase diagram of such quantum ferrofluids in oblate trap geometries and find an even wider range of exotic states of matter. Two-dimensional supersolid crystals formed from individual ferrofluid quantum droplets dominate the phase diagram at low densities. For higher densities we find honeycomb and labyrinthine states, as well as a pumpkin phase. We discuss scaling relations which allow us to find these phases for a wide variety of trap geometries, interaction strengths, and atom numbers. Our study illuminates the origin of the various possible patterns of quantum ferrofluids and shows that their occurrence is generic of strongly dipolar interacting systems stabilized by beyond mean-field effects.

Finite-range effects in the two-dimensional repulsive Fermi polaron

We study the repulsive Fermi polaron in a two-component, two-dimensional system of fermionic atoms inspired by the results of a recent experiment with $^{173}$Yb atoms [N. Darkwah Oppong \textit{et al.}, Phys. Rev. Lett. \textbf{122}, 193604 (2019)]. We use the diffusion Monte Carlo method to report properties such as the polaron energy and the quasi-particle residue that have been measured in that experiment. To provide insight on the quasi-particle character of the problem, we also report results for the effective mass. We show that the effective range, together with the scattering length, is needed in order to reproduce the experimental results. Using different model potentials for the interaction between the Fermi sea and the impurity, we show that it is possible to establish a regime of universality, in terms of these two parameters, that includes the whole experimental regime. This illustrates the relevance of quantum fluctuations and beyond mean-field effects to correctly describe the Fermi polaron problem.

Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.

Finite-temperature spin dynamics of a two-dimensional Bose-Bose atomic mixture

We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures of dilute ultracold atomic gases. We use a mean-field Hartree-Fock theory to derive analytical predictions for the miscible-immiscible transition. A nontrivial result of this theory is that a fully miscible phase at $T=0$ may become unstable at $T\neq0$, as a consequence of a divergent behaviour in the spin susceptibility. We test this prediction by performing numerical simulations with the Stochastic (Projected) Gross-Pitaevskii equation, which includes beyond mean-field effects. We calculate the equilibrium configurations at different temperatures and interaction strengths and we simulate spin oscillations produced by a weak external perturbation. Despite some qualitative agreement, the comparison between the two theories shows that the mean-field approximation is not able to properly describe the behavior of the two-dimensional mixture near the miscible-immiscible transition, as thermal fluctuations smoothen all sharp features both in the phase diagram and in spin dynamics, except for temperature well below the critical temperature for superfluidity.

Hidden Complexities in the Phase Behavior of Low-Complexity Disordered Proteins

Liquid-liquid phase separation (LLPS) is the underlying driving force for membrane-less compartmentalization in cells. LLPS plays key roles in fundamental cell biological processes and is often mediated by disordered low-complexity domains (LCDs). How the driving forces for LLPS are encoded in LCDs and how the phase behavior can be predicted from their sequence is incompletely understood. We are using the stickers-and-spacers framework to reconstruct the full phase behavior. Stickers form non-covalent inter- and intramolecular crosslinks, whereas spacers either enable or suppress the formation of these crosslinks. We have previously shown that aromatic residues are the stickers in the polar prion-like LCD of hnRNPA1. However, the balance of tyrosine and phenylalanine residues varies across LCDs and charged residues may contribute to LLPS in sequences with higher charge content. Herein we (i) extend the stickers-and-spacers model to account for interactions of charged residues and (ii) disentangle the interaction strength of phenylalanine and tyrosine for themselves and for each other. We demonstrate that tyrosine is a stronger sticker than phenylalanine and negatively charged residues are solubilizing spacers. Arginines act as stickers through pairwise interactions with aromatic residues. Importantly, low or high values of the net charge per residue weaken the driving force for LLPS via mean-field electrostatic effects. We further demonstrate that the phase behavior correlates well with the single-chain dimensions of LCD variants with different fractions of aromatic residues, but that this correlation can be broken by mean-field electrostatic effects. Our results support that the stickers-and-spacers model can be adapted for LCDs with a wide range of sequence characteristics, promising precise prediction of phase behavior from the sequence alone.

New look at Geiger-Nuttall law and α clustering of heavy nuclei * *Supported by the National Natural Science Foundation of China (12075121, 11605089, 11975167, 11535004, 11761161001), the Natural Science Foundation of Jiangsu Province (BK20150762, BK20190067), the National Major State Basic Research and Development Program of China (2016YFE0129300)

The Geiger-Nuttall (GN) law of α decay is commonly explained in terms of the quantum tunneling phenomenon. In this study, we show that such an explanation is actually not enough regarding the α particle clustering. Such a conclusion is drawn after exploring the involved coefficients of the GN law based on the conventional description of α decay, namely the formation of an α cluster and its subsequent penetration. The specific roles of the two former processes, in the GN law, manifest themselves via the systematical analysis of the calculated and experimental α decay half-lives versus the decay energies across the and shell closures. The α-cluster preformation probability is then found to behave in a GN-like pattern. This previously ignored point is explicitly demonstrated as the product of an interplay between the mean-field and pairing effect, which in turn reveals the structural influence on the formation of the α cluster in a simple and clear manner. In addition to providing an effective method to evaluate the amount of surface α clustering in heavy nuclei, the present conjecture supports other theoretical treatments of the α preformation probability.

Edge-state dynamics in coupled topological chains

We study time-dependent electrical properties of the Su-Schrieffer-Heeger (SSH) chain and coupled SSH chains on a substrate. Focusing on the midgap edge state dynamics we consider the abrupt transition from the normal to the SSH chain and determine characteristic timescale needed for topological states to develop. We have found that the midgap state is formed from the inside peaks of the normal chain density of states. For a ladderlike system we show that the edge SSH state vanishes in time or oscillates between neighboring sites. Moreover, for nonadiabatical time-dependent perturbations the midgap state can partially leak to other sites leading to induced topological states inside the trivial chain. We also analyze the mean-field correlation effects between the coupled chains revealing the induced Friedel oscillations in nontrivial chains.

Supersolid striped droplets in a Raman spin-orbit-coupled system

We analyze the role played by quantum fluctuations on a Raman Spin-Orbit Coupled system in the stripe phase. We show that beyond mean-field effects stabilize the collapse predicted by mean-field theory and induce the emergence of two phases: a gas and a liquid, which also show spatial periodicity along a privileged direction. We show that the energetically favored phase is determined by the Raman coupling and the spin-dependent scattering lengths. We obtain the ground-state solution of the finite system by solving the extended Gross-Pitaevskii equation and find self-bound, droplet-like solutions that feature internal structure through a striped pattern. We estimate the critical number for binding associated to these droplets and show that their value is experimentally accessible. We report an approximate energy functional in order to ease the evaluation of the Lee-Huang-Yang correction in practical terms.

Mean-Field Dynamo Model in Anisotropic Uniform Turbulent Flow with Short-Time Correlations

The mean-field model is one of the basic models of the dynamo theory, which describes the magnetic field generation in a turbulent astrophysical plasma. The first mean-field equations were obtained by Steenbeck, Krause and Rädler for two-scale turbulence under isotropy and uniformity assumptions. In this article we develop the path integral approach to obtain mean-field equations for a short-correlated random velocity field in anisotropic streams. By this model we analyse effects of anisotropy and show the relation between dynamo growth and anisotropic tensors of helicity/turbulent diffusivity. Considering particular examples and comparing results with isotropic cases we demonstrate several mean-field effects: super-exponential growth at initial times, complex dependence of harmonics growth on the helicity tensor structure, when generation is possible for near-zero component or near-zero helicity trace, increase of the averaged magnetic field inclined to the initial current density that leads to effective Lorentz back-reaction and violation of force-free conditions.

Bose-Einstein condensate immersed in a Fermi sea: Theory of static and dynamic behavior across phase separation

We theoretically study the static and dynamic behavior of a BEC immersed in a large Fermi sea of ultracold atoms under conditions of tunable interspecies interaction. The degenerate Bose-Fermi mixture is kept in an elongated trap, typical for a single-beam optical dipole trap. We focus on the case of repulsive Bose-Fermi interaction and develop mean-field models to simulate the system over a wide range of repulsion strength. We further get analytical solutions in the regimes of phase separation and weak interaction. We obtain static density profiles and the frequency of the radial breathing mode, which is an elementary dynamic phenomenon of the mixture. Our results unveil the structure of the Bose-Fermi interface and describe the origin of the frequency shift of the breathing mode when the components become phase-separated at strong repulsion. We show that the mediated interaction between bosons induced by the Fermi sea can be understood as an adiabatic second-order mean-field effect, which is valid also beyond the weak-interaction regime for relevant experimental conditions. These results are consistent with our recent observations in a mixture of $^{41}$K and $^6$Li.

Transient lensing from a photoemitted electron gas imaged by ultrafast electron microscopy

Understanding and controlling ultrafast charge carrier dynamics is of fundamental importance in diverse fields of (quantum) science and technology. Here, we create a three-dimensional hot electron gas through two-photon photoemission from a copper surface in vacuum. We employ an ultrafast electron microscope to record movies of the subsequent electron dynamics on the picosecond-nanosecond time scale. After a prompt Coulomb explosion, the subsequent dynamics is characterized by a rapid oblate-to-prolate shape transformation of the electron gas, and periodic and long-lived electron cyclotron oscillations inside the magnetic field of the objective lens. In this regime, the collective behavior of the oscillating electrons causes a transient, mean-field lensing effect and pronounced distortions in the images. We derive an analytical expression for the time-dependent focal length of the electron-gas lens, and perform numerical electron dynamics and probe image simulations to determine the role of Coulomb self-fields and image charges. This work inspires the visualization of cyclotron dynamics inside two-dimensional electron-gas materials and enables the elucidation of electron/plasma dynamics and properties that could benefit the development of high-brightness electron and X-ray sources.

The rotation of rigid spheroids in a viscous fluid under mean-field effects

An analytical model capturing the effects of mean-field considerations on the orientation evolution of a plurality of rigid spheroids suspended in a Newtonian matrix is developed. Three approaches are taken with increasing sophistication: a mesoscale view involving the analysis of several distinct layers of material subjected to simple shear flow, a traditional micromechanics inspired approach involving the Reuss assumption that each heterogeneity sees an equivalent stress, and the application of the Mori-Tanaka assumption in the viscous inclusion framework of Wetzel and Tucker (JFM 426, 2001). The resulting model behaviors are explored in simple shear flow and extensional flow. The behavior of the Mori-Tanaka model is qualitatively equivalent to that seen in a recent investigation by Gilormini and Chinesta (JNNFM 270, 2019) which considered the effects of the suspending medium being anisotropic in nature. With increase in concentration, the rate of orientation evolution towards collimation is increased as compared to the dilute case, but the relevant fourth-order orientation tensor component in simple shearing flow is shown to see an increased peak value.

Mean-field effects on the aging transitions in the damaged networks

We investigate the dynamical robustness property of the damaged network of active and inactive oscillators under the influence of the mean-field diffusion. The tolerance of dynamical activity of the entire coupled network has realized through the aging transition in the coupled dynamical network. We analytically derived the critical threshold of mean-field density and coupling values for the appearance of the aging transition in the damaged network. By using the critical values as a quantifiable measure of dynamical robustness of the damaged network, we showed that higher mean-field value is favorable to increase the dynamical robustness of the entire network. We also perform the numerical experiment on the network of Stuart-Landau oscillators and the obtained numerical results have an excellent agreement with the analytical findings. Finally, we extend our investigation into the coupled time-delayed network and discussed the affirmative influence of the mean-field parameter on the dynamical robustness of the network.

Beam energy dependence of cumulants of the net-baryon, net-charge, and deuteron multiplicity distributions in Au + Au collisions at sNN=3.0–5.0 GeV

Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Lorentz-covariant treatment of nuclear mean-field potential is considered, the fluctuations of net-baryon, net-charge and deuterons multiplicity distributions in Au+Au head-on collisions at $\sqrt{s_{NN}}=3.0-5.0$ GeV are calculated. The results show that the nuclear mean-field potential can significantly enhance the magnitude of baryon number fluctuations in narrow rapidity windows, and this enhancement rapidly weakens with increasing beam energy. However, for proton and net-charge number fluctuations, the mean-field effects are less noticeable than that for baryon number. In addition, for net-charge number fluctuations, the negative binomial distribution agrees well with the calculated results at mid-pseudorapidity window. Finally, the event-by-event fluctuations of deuteron number in the coalescence production picture are calculated as well, it is found that its cumulant ratios decrease linearly with increasing the average multiplicity of deuterons per event, i.e., increase with increasing beam energy.

On the spatial and temporal non-locality of dynamo mean-field effects in supersonic interstellar turbulence

ABSTRACT The interstellar medium (ISM) of the Milky Way and nearby disc galaxies harbour large-scale coherent magnetic fields of microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalize our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent multiphase ISM. By introducing spatially (temporally) modulated mean fields, we extend the previously used test-field method to the spectral realm – providing the Fourier representation of the convolution kernels. The resulting spectra of the dynamo mean-field coefficients that we obtain broadly match expectations and allow to rigorously constrain the degree of scale separation in the Galactic dynamo. A surprising result is found for the diamagnetic pumping term, which increases in amplitude when going to smaller scales. Our results amount to the most comprehensive description of dynamo mean-field effects in the Galactic context to date. Surveying the relevant parameter space and quenching behaviour, this will ultimately enable the development of assumption-free subgrid prescriptions for otherwise unresolved global galaxy simulations.

Dynamics of Planetary Systems within Star Clusters: Aspects of the Solar System’s Early Evolution

Abstract Most planetary systems—including our own—are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster’s mean-field effects, as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well as hyperbolic perturbations upon dissipative disks. We subsequently apply our results to the early evolution of our solar system, where the cluster’s collective potential perturbs the solar system’s plane, and stellar encounters act to increase the velocity dispersion of the Kuiper Belt. Our results are twofold. First, we find that cluster effects can alter the mean plane of the solar system by ≲1° and are thus insufficient to explain the ψ ≈ 6° obliquity of the Sun. Second, we delineate the extent to which stellar flybys excite the orbital dispersion of the cold classical Kuiper Belt and show that while stellar flybys may grow the cold belt’s inclination by the observed amount, the resulting distribution is incompatible with the data. Correspondingly, our calculations place an upper limit on the product of the stellar number density and residence time of the Sun in its birth cluster, η τ ≲ 2 × 104 Myr pc−3.

Observation of quantum depletion in a non-equilibrium exciton\u2013polariton condensate

Superfluidity, first discovered in liquid 4He, is closely related to Bose–Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations—the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton–polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton–polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton–polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton–polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.

Models of protein production along the cell cycle: An investigation of possible sources of noise.

In this article, we quantitatively study, through stochastic models, the effects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fluctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the significant fluctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-field effect.