One-body Field Research Articles

Neural force functional for non-equilibrium many-body colloidal systems

Abstract We combine power functional theory and machine learning to study non-equilibrium overdamped many-body systems of colloidal particles at the level of one-body fields. We first sample in steady state the one-body fields relevant for the dynamics from computer simulations of Brownian particles under the influence of randomly generated external fields. A neural network is then trained with this data to represent locally in space the formally exact functional mapping from the one-body density and velocity profiles to the one-body internal force field. The trained network is used to analyse the non-equilibrium superadiabatic force field and the transport coefficients such as shear and bulk viscosities. Due to the local learning approach, the network can be applied to systems much larger than the original simulation box in which the one-body fields are sampled. Complemented with the exact non-equilibrium one-body force balance equation and a continuity equation, the network yields viable predictions of the dynamics in time-dependent situations. Even though training is based on steady states only, the predicted dynamics is in good agreement with simulation results. A neural dynamical density functional theory can be straightforwardly implemented as a limiting case in which the internal force field is that of an equilibrium system. The framework is general and directly applicable to other many-body systems of interacting particles following Brownian dynamics.

Diffusion in inhomogeneous fluids: Hard spheres to polymer coatings.

We investigate diffusion in fluids near surfaces that may be coated with polymer films. We first consider diffusion in hard sphere fluids near a planar hard wall. We specifically consider color diffusion, where hard spheres are labeled A or B but are otherwise identical in all respects. In this inhomogeneous fluid, we consider a surface reaction-diffusion problem. At the left wall, a particle of species A is converted to one of species B upon a wall collision. At the opposing wall, the reverse reaction takes place: B → A. Using molecular dynamics simulation, we study the steady state of this system. We demonstrate that in the homogeneous region, a diffusing particle is subject to an equilibrium oscillatory force, the solvation force, that arises from the interfacial structuring of the fluid at the wall. For the hard sphere/hard wall system, the solvation force can be determined in various ways. We use the solvation force [the potential of mean force (PMF)] to solve the continuum diffusion equation. This provides an adequate and accurate description of the reaction-diffusion problem. The analysis is then extended to consider both color diffusion in the presence of a slowly varying one-body field such as gravity and a more applied problem of diffusion of free species through a surface film consisting of tethered chains. In both cases, the PMF experienced by the free particles is affected, but the diffusion problem can be treated in the same way as for the simpler hard sphere color diffusion case.

Three-body continuum states and Efimov physics in noninteger geometry

Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent $d$ method employing noninteger dimension, $d$, in a spherical calculation with a dimension-dependent angular momentum barrier. We focus on dimensions close to the critical dimension, $d={d}_{E}$, between 2 and 3, defined by zero two-body energies, where the Efimov effect can occur. We design for this dimension region a schematic, long-distance realistic, square-well based, three-body spherical model, which is used to derive analytic expressions for the wave functions, scattering lengths, phase shifts, and elastic-scattering cross sections. The procedure and the results are universal, valid for all short-range potentials, and for large scattering lengths. We discuss the properties and validity of the derived expressions by means of the simplest system of three identical bosons. The derived expressions are particularly useful for very small energies, where full numerical calculations are often not feasible. For energies where the numerical calculations can be performed, a good agreement with the analytic results is found. These model results may be tested by scattering experiments for three particles in an equivalent external deformed oscillator potential. The cross sections all vanish in the zero-energy limit for $d<3$ with definite $d$-dependent power of energy.

Efimov effect in non-integer dimensions induced by an external field

The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent to the strength of an external oscillator field. The effect most clearly appears when the crucial two-body systems are unbound in three, but bound in two, dimensions. We discuss energy variation, conditions for occurrence, and number of Efimov states, as functions of the dimension. We use practical examples from cold atom physics of 133Cs-133Cs-133Cs, 87Rb-87Rb-87Rb, 133Cs-133Cs-6Li, and 87Rb-87Rb-39K. Laboratory tests of the effect can be performed with two independent parameters, i.e. the external one-body field and the Feshbach two-body tuning. The scaling and (dis)appearance of these Efimov states occur precisely as already found in three dimensions.

Structural Nonequilibrium Forces in Driven Colloidal Systems.

We identify a structural one-body force field that sustains spatial inhomogeneities in nonequilibrium overdamped Brownian many-body systems. The structural force is perpendicular to the local flow direction, it is free of viscous dissipation, it is microscopically resolved in both space and time, and it can stabilize density gradients. From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations, and a novel power functional approximation, we obtain a quantitative understanding of viscous and structural forces, including memory and shear migration.

Embedded random matrix ensembles from nuclear structure and their recent applications

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with [Formula: see text]-body random interactions and its relation to the Sachdev–Ye–Kitaev (SYK) model for majorana fermions.

Quantified Gamow shell model interaction for psd -shell nuclei

The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interactions approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow Shell Model (GSM) provides such a framework as it is capable of describing resonant and non-resonant many-body states on equal footing. To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the $psdf$ shell model space. The resulting interaction is expected to describe nuclei with $5 \leqslant A \leqslant 12$ at the $p-sd$-shell interface. The optimized one-body potential reproduces nucleon-$^4$He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the Helium, Lithium, and Beryllium isotopes up to $A=9$. A very good agreement with experiment was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the $psd$ region of the nuclear chart.

Nonequilibrium Ornstein-Zernike relation for Brownian many-body dynamics

We derive a dynamic Ornstein-Zernike equation for classical fluids undergoing overdamped Brownian motion and driven out of equilibrium. Inhomogeneous two-time correlation functions are obtained from functional differentiation of the one-body density and current with respect to an appropriately chosen external field. Functional calculus leads naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a space- and time-nonlocal power dissipation functional. We propose an excess (over ideal gas) dissipation functional that both generates mode-coupling theory for the two-body correlations and extends dynamical density functional theory for the one-body fields, thus unifying the two approaches.

Dynamical probes of pairing correlations: two-particle transfer and two-particle break-up reactions

We investigate the role played by pairing correlations in two typical classes of nuclear reactions specifically involving pairs of particles: two-particle transfer reactions, where a pair of nucleons is exchanged between the reaction partners, and two-particle break-up reactions, where a pair of nucleons is emitted. In both cases we find that, although the process is mainly induced by the repeated action on each particle by the one-body field created by the reaction partner, a coherent enhancing effect is generated by the pair correlation present in the initial wave function, acting during the process and again present (in the case of two-particle transfer) in the final wave function. In the case of reactions involving weakly-bound nuclei the low-density features characterizing the vicinity of the drip line and the suggested consequent enhancement of the pairing correlations should show up as clear signature in both processes. From the point of view of their theoretical description, the vicinity of the drip lines will involve heavily the continuum part of the spectrum and we will test in simple models the validity of different discretization procedures used in the description of both structure and reaction.

Two-neutron halo nuclei in one dimension: dineutron correlation and breakup reaction

We propose a simple schematic model for two-neutron halo nuclei. In this model, the two valence neutrons move in a one-dimensional mean field, interacting with each other via a density-dependent contact interaction. We first investigate the ground-state properties and demonstrate that the dineutron correlation can be realized with this simple model due to the admixture of even- and odd-parity single-particle states. We then solve the time-dependent two-particle Schrödinger equation under the influence of a time-dependent one-body external field, in order to discuss the effect of dineutron correlation on nuclear breakup processes. The time evolution of two-particle density shows that the dineutron correlation enhances the total breakup probability, especially for the two-neutron breakup process, in which both the valence neutrons are promoted to continuum scattering states. We find that the interaction between the two particles definitely favors a spatial correlation of the two outgoing particles, which are mainly emitted in the same direction.

HBT Pion Interferometry with Phenomenological Mean Field Interaction

To extract information on hadron production dynamics in the ultrarelativistic heavy ion collision, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interaction, taking place during penetrating through a cloud formed by evaporating particles, in terms of a one-body mean field potential localized in the vicinity of the source region. By adopting the semiclassical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and mean field interaction obtained using a phenomenological $\pi\pi$ forward scattering amplitude in the elastic channels. The p-wave scattering with $\rho$ meson resonance leads to an attractive mean field interaction, and the presence of the absorptive part is mainly attributed to the formation of this resonance. We also incorporate a simple time dependence of the potential reflecting the dynamics of the evaporating source. Using the obtained potential, we examine how and to what extent the so-called HBT Gaussian radius is varied by the modification of the propagation.

Asymmetric bias in free-energy perturbation measurements using two Hamiltonian-based models

We present two model systems that are suitable for the study of bias in free-energy perturbation (FEP) calculations which are performed in molecular simulations. The models exhibit the asymmetry that is sometimes seen in these calculations, in which the magnitude of the bias is greater when the calculation is performed in one direction ( A-->B , sampling system A and perturbing into system B ) versus the other (B-->A) . Both models are formulated as a system of N independent particles, each sampling a space in the presence of a one-body field that is different for the A and B systems. In one model the field is a harmonic potential. The other model is discrete, such that each particle can be at one of two points (or states) of different energy. The neglected-tail bias model is applied to each system to estimate the average bias as a function of the amount of FEP sampling, and numerical calculations are performed to show that the bias model is effective. We show that the bias is significantly smaller when sampling is performed on the system having a broader work distribution (we designate this direction "insertion") compared to the bias for FEP calculations that sample the system with a narrower distribution ("deletion").

Regularity and chaos in interacting two-body systems

We study classical and quantum chaos for two interacting particles on the plane. This is the simplest nontrivial case which sheds light on chaos in interacting many-body systems. The system consists of a confining one-body potential, assumed to be a deformed harmonic oscillator, and a two-body interaction of Coulomb type. In general, the dynamics is mixed with regular and chaotic trajectories. The relative roles of the one-body field and the two-body interaction are investigated. Chaos sets in as the strength of the two-body interaction increases. However, the degree of chaoticity strongly depends on the shape of the one-body potential and, for some shapes of the harmonic oscillator, the dynamics remains regular for all values of the two-body interaction. Scaling properties are found for the classical as well as for the quantum mechanical problem.

Energy levels of terbium(III) in the elpasolite Cs2NaTbBr6. II. A correlation crystal field analysis

A set of more than 100 electronic energy levels in Cs2NaTbBr6, extending from the ground state to 5H4, is used to test different models of the correlation crystal field (CCF). These are based on Judd's orthogonal giQ (k) two-electron operators, and more specifically on contributions due to spin-correlation, or ligand polarization. Similar data from Cs2NaTbCl6 and Cs2NaTbF6 has also been analysed. Only fourth-rank operators make clear improvements to the quality of the fit in deviant multiplets. Empirically the g7 (4) and g9 (4) operators are found to be the most effective. Although fourth-rank operators achieve modest success in correcting the calculated spread of the multiplets, no single operator has a significant impact on the shortcomings of the one-body crystal field. This result is discussed in terms of the limitations of an effective-operator Hamiltonian.

Solvation forces between rough surfaces

We investigate the role of surface roughness on solvation forces and solvation free energies. Roughness is introduced by dividing a surface into an array of square tiles that are then randomly displaced in the direction perpendicular to the wall. The integrated wall strength of these tiled surfaces is independent of the surface roughness and hence this class of rough walls is ideally suited for isolating roughness effects. We use grand canonical Monte Carlo simulations of a Lennard-Jones fluid confined in a slit pore with rough walls to generate the solvation interactions as a function of roughness, tile size, and surface area. The simulation data are compared to a simple superposition approximation of smooth wall solvation interactions (obtained from simulation or density functional theory), based on a distribution of wall separations. We find that this approximation provides a surprisingly accurate route to the solvation interaction of rough surfaces. In general, increased roughness leads to a reduction of oscillations in the solvation forces and surface free energies. However, nonmonotonic behavior of the oscillation amplitude with roughness can be observed for finite surfaces. The washing out of the oscillations found for large surface roughness produces a solvation force that exhibits a broad repulsive peak with separation. The broad repulsion is a consequence of the resistance to squeezing out fluid from the smallest gaps between two opposing rough surfaces. It is as much a reflection of packing effects as are the solvation oscillations for perfectly smooth pores. In addition, we present results for patterned and undulating surfaces produced by an analogous modification of the one-body external field for smooth walls. Finally, we discuss the implications of our results for a number of experimental systems including self-assembled monolayers, microporous materials, protein solutions, and DNA crystals.

RESULTS FROM SHELL-MODEL MONTE CARLO STUDIES

▪ Abstract We review results obtained using Shell-Model Monte Carlo (SMMC) techniques. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; the resultant path integral is evaluated stochastically. After a brief review of the methods, we discuss a variety of nuclear-physics applications. These include studies of the ground-state properties of pf-shell nuclei, Gamow-Teller strength distributions, thermal and rotational pairing properties of nuclei near N = Z, γ-soft nuclei, and ββ-decay in76Ge. Several other illustrative calculations are also reviewed. Finally, we discuss prospects for further progress in SMMC and related calculations.

Multifragmentation with Brownian one-body dynamics

A first application is made of Brownian One-Body Dynamics to nuclear multifragmentation. A gold nucleus is compressed to double density and then let free to evolve under the combined influence of the effective one-body field and the residual two-body collision processes, with the effects of the fluctuations included whenever local spinodal instability occurs. The system quickly expands into a hollow and unstable configuration which transforms into several intermediate-mass fragments. The analysis of the resulting fragment pattern suggests that the model provides a physically reasonable description of nuclear multifragmentation processes.

Fluctuations in nuclear dynamics: Comparison of different methods

We compare several methods for incorporating the effect of the fluctuating collision integral in Boltzmann-Uehling-Uhlenbeck simulations of nuclear dynamics: the method of correlated pseudo-particle collisions proposed by Bayer, Bertsch and Das Gupta, the method of projection onto collective variables (specifically the local quadrupole moment of the momentum distribution) proposed by Ayik and Gregoire, and the method of direct simulation on a lattice in phase space recently proposed by Burgio, Chomaz and Randrup. Considering a periodic two-dimensional nucleon gas in a constant one-body field, we examine the evolution of the fluctuations of the phase-space occupancy and their correlations.

Dynamical fluctuations and nuclear multifragmentation

Energetic nucleus-nucleus collisions display spontaneous symmetry breaking, such as multifragmentation, and we report on current efforts to extend BUU-type dynamical models to incorporate the fluctuations arising from the stochastic nature of the two-body collision integral, in the presence of the instabilities caused by the effective one-body field.

A derivation of external fields that create step function density profiles at wall-fluid interfaces

The statistical mechanics of a wall-fluid interface with a step function density profile is considered. The one-body external field necessary to create such a step function profile is derived from coarse grained density functional theory. Results for a variety of bulk fluid boundary conditions are described and their significance discussed.