Three-body Interaction Potential Research Articles

The condensation of a trapped dilute Bose gas with three-body interactions

We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the system is a convex superposition of minimizers of a 3D energy-critical nonlinear Schr\"odinger functional where the nonlinear coupling constant is proportional to the scattering energy of the interaction potential. In particular, the $N$-body ground state exhibits complete Bose--Einstein condensation if the nonlinear Schr\"odinger minimizer is unique up to a complex phase.

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects.

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

On deformation and fracture of PBX simulant employing modified three-body potential peridynamics model with deformation-based failure criteria

The modified three-body potential peridynamics (PD) model is used to study the macroscopic mechanical responses of polymer bonded explosive (PBX) mock materials. Combined with PD functions, under small deformation conditions, bond shear form of the PD model is derived from the micro-potential incorporating modified three-body interaction potential, giving some attention to the applicable condition for its two expression forms, i.e., general form and bond shear form. Subsequently, an improved mode Ⅱ failure criterion considering collective shear deformation of family members is proposed to enhance the deformation-based failure criteria adopted in the present study. A series of PBX simulants associated with elastic deformation and brittle fracture behaviors are carried out by the proposed numerical method. And the numerical results are verified by experimental and other numerical ones published previously, which show that the proposed numerical method is suitable for modeling PBX mock materials.

Equation of state of solid parahydrogen using ab initio two-body and three-body interaction potentials.

We present the equation of state of solid parahydrogen between 0.024 and 0.1Å-3 at T = 4.2 K, calculated using path integral Monte Carlo simulations, with ab initio two-body and three-body interaction potentials. We correct for finite size simulation errors using potential tail corrections. Trotter factorization errors are accounted for either via extrapolation or by using a suitably small imaginary time step. We incorporate the three-body interaction using two methods: (1) the full inclusion method, where pair and three-body interactions are used in both Monte Carlo sampling and in the energy estimators, and (2) the perturbative method, where three-body interactions are omitted from sampling but are still present in energy estimations. Both treatments of the three-body interaction return very similar total energies and pressures. The presence of three-body interactions has only minor effects on the structural properties of the solid. Whereas the pair interaction, on its own, significantly overestimates the pressure of solid parahydrogen, the additional presence of the three-body interaction causes a severe underestimation of the pressure. Our findings suggest that accurate simulations of solid parahydrogen require four-body and possibly higher-order many-body interactions. It may also be the case that static interaction potentials are entirely unsuitable for simulations of solid parahydrogen at high densities.

Development of a fully analytical equation of state using ab initio interaction potentials. Application to pure simple fluids: Noble gases Ne, Ar, Kr, and Xe

In this work, we have extended the first-order mean spherical approximation (FMSA) equation of state (EOS) of Tang and Lu [J. Chem. Phys., 99, 9828 (1993)] in order to predict accurately fluid phase diagrams using ab initio potentials. At this level of development, we restricted to simple spherical compounds.The original equation based on hard-core two-Yukawa (HC2Y) was improved by the following:•Adding a new approximate simple correction to include higher orders in the development of Tang and Lu to get an analytical model closer to the full MSA.•Including a term to a better account for the long-range behavior of two-body potentials.•Adding a three-body interaction term (1st order perturbation) based on Axilrod-Teller potential.A general recommendation for setting the hard-sphere diameter value was also given.The predictive capability of the EOS was tested in a systematic manner. First, we checked that various simple theoretical potential (Mie n-6 and Exp n-6) phase diagrams are well reproduced. Second, the EOS was used for predicting fluid phase diagrams of the pure noble gases fluid series Ne, Ar, Kr, and Xe using realistic (i.e. derived from ab initio) two-body and three-body interaction potentials. The model is in good agreement with the experimental phase diagrams.As a conclusion, the simple statistical-mechanics-based fully analytical EOS developed in this work predicts accurately fluid phase diagrams of simple spherical compounds using ab initio potentials. No adjustable parameter was used. This EOS constitutes a strong basis for future development of a predictive model based on ab initio potentials and applicable to more complex compounds.

Ground state energy of the low density Bose gas with three-body interactions

We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of the interaction potential. The corresponding result for two-body interactions was proved in seminal papers of Dyson [Phys. Rev. 106, 20–26 (1957)] and of Lieb and Yngvason [Phys. Rev. Lett. 80, 2504–2507 (1998)].

Accessing the applicability of the MBE approach for constructing potential energy surfaces of nitrogen clusters

The many-body expansion approach (MBE) is employed to build potential energy surfaces (PESs) for nitrogen clusters, which serve as a possible candidate of high energy density materials. The ground-state global PES of N 4 developed by Truhlar’s group is utilized to construct the two-body, three-body, and four-body interaction potentials. The energy of nitrogen clusters is thus obtained by summing the many-body interaction energies up to four-body term. This work found that such a many-body expansion could give reasonable energy predictions for loose chain nitrogen molecules while produce bad predictions for compact structures. The failure is caused by the neglect of high-order ( n ≥ 5) n -body interactions that are significant in the bonding area. The difficulties in applying the MBE method to construct the potential energy surface of nitrogen clusters are analyzed.

Many-body quantum system in the presence of solvable potential

This article introduces a four-particle quantum system presented with a discrete energy spectrum, including harmonic potential and three-body interaction potential. By defining each particle’s Jacobi coordinates separately, one coordinate is eliminated as a transition in the energy spectrum. Then, the system is studied in polar coordinates, and by using the variables separation method, the Schrodinger equation of the system is transformed into three separate differential equations. Therefore, energy eigenvalues and wave eigenfunctions are calculated in each dimension. Additionally, the wave eigenfunctions figures are investigated in one and three dimensions. Then, we consider this quantum model with N particles in one dimension, and energy eigenvalues and wave eigenfunctions are obtained in ground and evoked states.

A Non-Ordinary State-Based Peridynamic Constitutive Model Based on Three-Body Interaction Potential and Its Implementation on Algorithm

In the framework of peridynamics (PD), bond-based constitutive model is more intuitional but less universal than that of state-based one. In order to demonstrate the advantages of these two models, a non-ordinary state-based peridynamic constitutive model is developed based on three-body interaction potential. An explicit general relation between PD material parameters and elastic constants (Young’s modulus and Poisson’s ratio) is rigorously derived, without the need for any particular assumptions about the modes of deformation. Two numerical examples, namely, the uniaxial tension of a bar and the penetration of a plate impacted by a rigid ball, respectively, are presented. Results show that the proposed constitutive model can be used to correctly and effectively characterize the Poisson’s effect of solid deformation and fragmentation caused by impact.

Effects of an attractive three-body interaction on a spin-1 Bose Hubbard model

We study the effects of an attractive three-body interaction potential on a spin-1 ultracold Bose gas using the mean field approach (MFA). For an antiferromagnetic interaction, the third Mott insulator (MI) lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of interaction strength. However, no significant change is observed beyond the fourth MI lobe. The formation of the spin singlet (nematic) MI phase and the different order of phase transitions to the superfluid phase have been carefully scrutinized with the help of spin eigenvalues and the spin nematic order parameter. In the ferromagnetic case, the phase diagram shows similar features to that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of interaction potential via a perturbation expansion in both cases.

Structure and dynamics of B2O3 melts and glasses: From ab initio to classical molecular dynamics simulations

Boron oxide (B2O3) is investigated by a combination of ab initio (DFT-based) molecular dynamics (MD) simulations and classical MD simulations. From the trajectories of the ab initio MD simulation, we derive a three-body interaction potential which is used in classical MD simulations to study various structural and dynamic properties on larger time and length scales than possible in the ab initio simulations. Differences and similarities to the structure and dynamics of other network glass formers such as SiO2 and GeO2 are discussed. Moreover, various properties as obtained from the simulations are compared to those from experiments of B2O3.

50 million atoms scale molecular dynamics modelling on a single consumer graphics card

This paper presents a dynamic cell-list method for realizing large scale molecular dynamics (MD) simulations with more than 50 million atoms on a single consumer graphics card. It adapts the cell-list algorithm by introducing an efficient two-step atom location scheme and a dynamic memory allocation scheme such that only those cells containing atoms consume device memory. In addition, a large amount of memory is saved since it does not use the neighbour list. The computational efficiency is improved by reducing the memory loading times and maximizing coalesced memory access as compared to methods utilizing neighbour lists, since memory bandwidth is becoming the bottle-neck of the latest GPUs. As a result, MD simulations with more than 50 million atoms utilizing advanced three-body interaction potential are made possible on a consumer graphics card with just 11 GB of graphics memory. The proposed framework is designed to run totally on the graphics card, with all the data stored in the graphics memory to avoid the time-consuming data transfer between host and device. It achieves 2.5 times the speed and 20 times the atom number of the latest Lammps GPU package on the NVIDIA GTX 1080Ti GPU. The proposed framework is expected to help adapt existing MD packages for supporting large scale MD simulations on personal desktops and thereby extend MD to a wider range of researchers and engineers.

Quantum phases of a spin-1 ultracold Bose gas with three-body interactions

We study the effects of a three-body interaction potential on a spin-1 ultracold Bose gas using mean-field approach (MFA). For an antiferromagnetic (AF) interaction, we have found the existence of the odd-even asymmetry in the Mott insulating (MI) lobes in the presence of both the repulsive two- and three-body interactions. In case of a purely three-body repulsive interaction, the higher-order MI lobes stabilize against the superfluid phase. Also the spin nematic (singlet) formation occurs for all the odd (even) MI lobes for the former, while there is neither any asymmetry, nor spin nematic (singlet) formation being observed for the latter case. The results are confirmed after carefully scrutinizing the spin eigenvalue and spin nematic order parameter for both the cases. We have compared our MFA results with the analytic phase diagrams obtained using a perturbation mean-field (PMFA) expansion.

The hyperbolic plane, three-body problems, and Mnëv’s universality theorem

We show how to construct the hyperbolic plane with its geodesic flow as the reduction of a three-problem whose potential is proportional to I/Δ2 where I is the moment of inertia of this triangle whose vertices are the locations of the three bodies and Δ is its area. The reduction method follows [11]. Reduction by scaling is only possible because the potential is homogeneous of degree −2. In trying to extend the assertion of hyperbolicity to the analogous family of planar N-body problems with three-body interaction potentials we run into Mn¨ev’s astounding universality theorem which implies that the extended assertion is doomed to fail.

Nonadditive three-body potential and third to eighth virial coefficients of carbon dioxide.

A new nonadditive three-body interaction potential for carbon dioxide was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] level of theory for 9401 configurations. A physically motivated analytical function with terms for describing nonadditive dispersion, induction, and exchange contributions was fitted to the calculated nonadditive three-body interaction energies. For the 7996 configurations with a total interaction energy of less than 3000 K, the mean absolute error of the analytical function is 0.32 K. The new nonadditive three-body potential was applied together with a previously published pair potential [R. Hellmann, Chem. Phys. Lett. 613, 133 (2014)] to calculate the third to seventh virial coefficients of CO2 at subcritical and supercritical temperatures up to 2000 K. The eighth virial coefficient was also calculated, but using only the pair potential and only at temperatures from 600 K to 2000 K because of the enormous computational costs. A simple analytical function was fitted individually to the calculated values of each virial coefficient, including previously determined values of the second virial coefficient, to obtain an analytical virial equation of state (VEOS). For densities at which the VEOS is converged, the agreement in pressure with the reference EOS of Span and Wagner [J. Phys. Chem. Ref. Data 25, 1509 (1996)] is mostly within ±0.5%. However, for temperatures above about 700 K, much larger deviations occur at higher densities, which we ascribe mainly to deficiencies of the reference EOS due to the lack of accurate data for these experimentally difficult conditions.

Towards a dissociative SPC-like water model - probing the impact of intramolecular Coulombic contributions.

The dissociative water potential introduced by Garofalini et al. proved to be a simple and effective description to account for proton transfer in aqueous media, enabling for instance the execution of simulation studies at different pH values. In this model the charge of each particle is represented by a point-charge surrounded by a Gaussian charge-cloud of opposite sign, thus four Coulombic terms (point-charge-point-charge, point-charge-charge-cloud, charge-cloud-point-charge and charge-cloud-charge-cloud) are required per atom pair. In this work it is demonstrated that the Gaussian charge distributions can be removed from the model after a minor modification of the overall atomic point-charges. Despite this substantial modification of the model, structural properties obtained via pair- and angle distributions remain largely unaffected and the change in dynamical properties (vibrational frequencies, proton transfer properties) was found to be minor. As an additional improvement an adjustment of the bending mode vibration was carried out by carefully evaluating the parametrization of the three-body interaction potential, thereby retaining the good agreement of the transfer properties of the aqueous excess proton reported in an earlier study. The proposed simple point-charge (SPC) type parametrization of the Coulombic interactions not only leads to a notable decrease in computational demand but generalizes the dissociative model by improving its transferability to established third-party simulation software and enabling the application of different theoretical approaches such as Ewald summation techniques not considered in the original parametrization. The outlined optimization strategy demonstrates that despite the complex and challenging formulation of the force field, various dynamical properties can be selectively adjusted without influencing other critical parameters of the simulated systems.

Ternary fission of 260No in equatorial configuration

Spontaneous ternary fission is one of the observed decay modes of heavy nuclei. We systematically investigate the equatorial ternary fission of the 260No isotope. In the framework of the three-cluster model, the three-body interaction potential is calculated in terms of the folded M3Y-Reid nucleon-nucleon force and the Coulomb one. The relative orientations of the deformed heavy nuclei participating in the fragmentation process are taken into account. All possible emitted light particles with even mass numbers $A = 4$ -52 are considered. The favored fragmentation channels are estimated as the ones characterized with peaks in the Q-value and local minima in the fragmentation potential. In the absence of nuclear deformations, the closed shell effects are found to play the key role in determining the channels of minimum fragmentation potential and the involved two heavier fragments tend to be of comparable sizes. Inclusion of nuclear deformations manifest the participation of highly deformed prolate nuclei, with large mass asymmetry, as heavy fragment partners in the estimated favored fragmentation channels. The results indicate that the equatorial ternary fission of 260No is most favored with the light emitted nuclei 4,6,8 2He and 10 4Be through the fragmentation channels 155 60Nd + 4 2He + 101 0Zr, 153 60Nd + 6 2He + 101 40Zr, 152 60Nd + 8 2He + 100 40Zr, and 152 0Nd + 10 4Be + 98 38Sr, respectively.

THE DENSE MATTER EQUATION OF STATE FROM NEUTRON STAR RADIUS AND MASS MEASUREMENTS

ABSTRACT We present a comprehensive study of spectroscopic radius measurements of twelve neutron stars obtained during thermonuclear bursts or in quiescence. We incorporate, for the first time, a large number of systematic uncertainties in the measurement of the apparent angular sizes, Eddington fluxes, and distances, in the composition of the interstellar medium, and in the flux calibration of X-ray detectors. We also take into account the results of recent theoretical calculations of rotational effects on neutron star radii, of atmospheric effects on surface spectra, and of relativistic corrections to the Eddington critical flux. We employ Bayesian statistical frameworks to obtain neutron star radii from the spectroscopic measurements as well as to infer the equation of state from the radius measurements. Combining these with the results of experiments in the vicinity of nuclear saturation density and the observations of ∼ 2 M ⊙ ?> neutron stars, we place strong and quantitative constraints on the properties of the equation of state between ≈ 2 – 8 ?> times the nuclear saturation density. We find that around M = 1.5 M ⊙ , ?> the preferred equation of state predicts radii between 10.1 and 11.1 km. When interpreting the pressure constraints in the context of high density equations of state based on interacting nucleons, our results suggest a relatively weak contribution of the three-body interaction potential.

Many-body critical Casimir interactions in colloidal suspensions.

We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the Z(2) symmetry of the system is broken by the particles. We present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions.

Dynamics and Matter-Wave Solitons in Bose-Einstein Condensates with Two- and Three-Body Interactions

By means of similarity transformation, this paper proposes the matter-wave soliton solutions and dynamics of the variable coefficient cubic-quintic nonlinear Schrödinger equation arising from Bose-Einstein condensates with time-dependent two- and three-body interactions. It is found that, under the effect of time-dependent two- and three-body interaction and harmonic potential with time-dependent frequency, the density of atom condensates will gradually diminish and finally collapse.