N-body Interactions Research Articles

A calibrated model for N-body dynamical friction acting on supermassive black holes

Abstract Black holes are believed to be crucial in regulating star formation in massive galaxies, which makes it essential to faithfully represent the physics of these objects in cosmological hydrodynamics simulations. Limited spatial and mass resolution and the associated discreteness noise make following the dynamics of black holes especially challenging. In particular, dynamical friction, which is responsible for driving massive black holes towards the centres of galaxies, cannot be accurately modelled with softened N-body interactions. A number of subgrid models have been proposed to mimic dynamical friction or directly include its full effects in simulations. Each of these methods has its individual benefits and shortcomings, while all suffer from a common issue of being unable to represent black holes with masses below a few times the simulated dark matter particle mass. In this paper, we propose a correction for unresolved dynamical friction, which has been calibrated on simulations run with the code KETJU, in which gravitational interactions of black holes are not softened. We demonstrate that our correction is able to sink black holes with masses greater than the dark matter particle mass at the correct rate. We show that the impact of stochasticity is significant for low-mass black holes (MBH ≤ 5MDM) and propose a correction for stochastic heating. Combined, this approach is applicable to next generation cosmological hydrodynamics simulations that jointly track galaxy and black hole growth with realistic black hole orbits.

Flexible Ansatz for N-Body Perturbation Theory.

We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrödinger equation for arbitrary wave functions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly nonlinear wave functions.

Planetesimal and planet formation in transient dust traps

The ring-like structures in protoplanetary discs that are observed in the cold dust emission by ALMA might be explained by dust aggregates trapped aerodynamically in pressure maxima. We investigate the effect of a transient pressure maximum that develops between two regimes with different turbulent levels. We study how such a pressure maximum collects dust aggregates and transforms them into large planetesimals and Moon-mass cores that can further grow into a few Earth-mass planets by pebble accretion, and eventually into giant planets by accreting a gaseous envelope. We developed a numerical model, incorporating the evolution of a gaseous disc, the growth and transport of pebbles, N-body interactions of growing planetary cores, and their backreaction to a gas disc by opening a partial gap. Planetesimal formation by streaming instability is parametrised in our model. A transient pressure maximum efficiently accumulates dust particles that can grow larger than millimetre-sized. If this happens, dust aggregates can be transformed by the streaming instability process into large planetesimals, which can grow further by pebble accretion according to our assumptions. As the gas evolves towards a steady state, the pressure maximum vanishes, and the concentrated pebbles not transformed into planetesimals and accreted by the growing planet drift inward. During this inward drift, if the conditions of the streaming instability are met, planetesimals are formed in the disc within a wide radial range. A transient pressure maximum is a favourable place for planetesimal and planet formation during its lifetime and the concentration of pebbles induces continuous formation of planetesimals even after its disappearance. In addition, the formation of a planet can trigger the formation of planetesimals over a wide area of the protoplanetary disc.

Annealing for prediction of grand canonical crystal structures: Implementation of n -body atomic interactions

We propose an annealing scheme usable on modern Ising machines for crystal structures prediction (CSP) by taking into account the general n-body atomic interactions and in particular three-body interactions which are necessary to simulate covalent bonds. The crystal structure is represented by discretizing a unit cell and placing binary variables which express the existence or nonexistence of an atom on every grid point. The resulting quadratic unconstrained binary optimization (QUBO) or higher-order unconstrained binary optimization (HUBO) problems implement the CSP problem and is solved using simulated and quantum annealing. Using the example of Lennard-Jones clusters we show that it is not necessary to include the target atom number in the formulation allowing for simultaneous optimization of both the particle density and the configuration and argue that this is advantageous for use on annealing machines as it reduces the total amount of interactions. We further provide a scheme that allows for reduction of higher-order interaction terms that is inspired by the underlying physics. We show for a covalently bonded monolayer MoS2 crystal that we can simultaneously optimize for the particle density as well as the crystal structure using simulated annealing. We also show that we reproduce ground states of the interatomic potential with high probability that are not represented on the initial discretization of the unit cell. Published by the American Physical Society 2024

Structures and stability of K+ cation solvated in Arn clusters

The solvation of K+ cation plays an important role in various phenomena such as biological procedures, geological time, and archaeological properties. Monte Carlo (MC) simulation and DFT method are employed to study the structural and energetic characteristics of the K + Arn (n = 1–14) clusters. The potential model (PM) and the Basin-Hopping (BH) method are the foundation of the MC simulation. The pairwise PM (PW-PM) is improved by introducing the N-body interactions via the polarizable potential model (PPM). On the other side, the DFT functional M05–2X, combined with the 6–311++G(3d2f,2p) basis set, and the Grimme dispersion correction GD3 was used to deeply investigate the geometrical properties and the relative stability of the K + Arn clusters. Starting from n = 12, a structural transition from square antiprism (SA) to icosahedron (ICOS) form is detected. Additionally, the PPM allows us to examine the largest sizes (n = 15–54). Herein, the first ICOS layers are found for n = 12 and 54 cluster sizes, respectively. The binding energy and the second energy difference as a function of cluster size are used to evaluate the relative stability of K + Arn clusters. The obtained data are in concordance with the available results in the literature.

A treecode algorithm based on tricubic interpolation

Treecode algorithms efficiently approximate N-body interactions in O(N) or O(NlogN). In order to treat general 3D kernels, recent developments employ polynomial interpolation to approximate the kernels. The polynomials are a tensor product of 1-dimensional polynomials. Here, we develop an O(NlogN) tricubic interpolation based treecode method for 3D kernels. The tricubic interpolation is inherently three-dimensional and as such does not employ a tensor product. The form allows for easy evaluation of the derivatives of the kernel, required in dynamical simulations, which is not the case for the tensor product approach. We develop both a particle-cluster and cluster-particle variants and present results for the Coulomb, screened Coulomb and the real space Ewald kernels. We also present results of an MD simulation of a Lennard-Jones liquid using the tricubic treecode.

Iterative mean-field approach to the spherical collapse of dark matter haloes

ABSTRACT Gravitational collapse of dark matter overdensities leads to the formation of dark matter haloes which embed galaxies and galaxy clusters. An intriguing feature of dark matter haloes is that their density profiles closely follow a universal form irrespective of the initial condition or the corresponding growth history. This represents a class of dynamical systems with emergent universalities. We propose an ‘iterative mean-field approach’ to compute the solutions of the gravitational collapse dynamics. This approach iteratively searches for the evolution of the interaction field ϕ(t) – in this case the enclosed mass profile M(r, t) – that is consistent with the dynamics, thus that ϕ(t) is the fix-point of the iterative mapping, $\mathcal {H}(\phi) = \phi$. The formalism replaces the N-body interactions with one-body interactions with the coarse-grained interaction field, and thus shares the spirit of the mean-field theory in statistical physics. This ‘iterative mean-field approach’ combines the versatility of numerical simulations and the comprehensiveness of analytical solutions, and is particularly powerful in searching for and understanding intermediate asymptotic states in a wide range of dynamical systems where the solutions can not be obtained through the traditional self-similar analysis.

A gravitational and dynamical framework of star formation: the Orion nebula

ABSTRACT The Orion Nebula Cluster (ONC) is the most massive region of active star formation within a kpc of the Sun. Using Gaia DR3 parallaxes and proper motions, we examine the bulk motions of stars radially and tangentially relative to the cluster centre. We find an age gradient with distance to the stars in the ONC, from 385 pc for the oldest stars, to 395 pc for the younger stars, indicating that the star-forming front is propagating into the cloud. We find an organized signature of rotation of the central cluster, but it is present only in stars younger than 2 Myr. We also observe a net infall of young stars into the centre of the ONC’s deep gravitational potential well. The infalling sources lie preferentially along the filament; on the other hand, outflowing sources are distributed spherically around the cluster, and they have larger velocity dispersion. We further propose a solution to a long-standing question of why the ONC shows a weak signature of expansion even though the cluster is likely bound: much of this expansion may be driven by unstable N-body interactions among stars, resulting in low-velocity ejections. Though analysing signatures imprinted on stellar dynamics across different spatial scales, these observation shed new light on the signatures of formation and evolution of young clusters.

The origin of early-type runaway stars from open clusters

Runaway stars are ejected from their place of birth in the Galactic disk, with some young B-type runaways found several tens of kiloparsecs from the plane traveling at speeds beyond the escape velocity, which calls for violent ejection processes. Young open clusters are a likely place of origin, and ejection may be either through N-body interactions or in binary supernova explosions. The most energetic events may require dynamical interaction with massive black holes. The excellent quality of Gaia astrometry opens up the path to study the kinematics of young runaway stars to such a high precision that the place of origin in open stellar clusters can be identified uniquely even when the star is a few kiloparsecs away. We developed an efficient minimization method to calculate whether two or more objects may come from the same place, which we tested against samples of Orion runaways. Our fitting procedure was then used to calculate trajectories for known runaway stars, which have previously been studied from HIPPARCOS astrometry as well as known open clusters. For runaways in our sample we used Gaia data and updated radial velocities, and found that only half of the sample could be classified as runaways. The other half of the sample moves so slowly (< 30 km s−1) that they have to be considered as walkaway stars. Most of the latter stars turned out to be binaries. We identified parent clusters for runaways based on their trajectories. We then used cluster age and flight time of the stars to investigate whether the ejection was likely due to a binary supernova or due to a dynamical ejection. In particular we show that the classical runaways AE Aurigae and μ Columbae might not have originated together, with μ Columbae having an earlier ejection from Collinder 69, a cluster near the ONC. The second sample investigated comprises a set of distant runaway B stars in the halo which have been studied carefully by quantitative spectral analyses. We are able to identify candidate parent clusters for at least four stars including the hyper-runaway candidate HIP 60350. The ejection events had to be very violent, ejecting stars at velocities as large as 150–400 km s−1.

N-body Interactions will be Detectable in the HR-8799 System within 5 yr with VLTI-GRAVITY

Abstract While Keplerian orbits account for the majority of the astrometric motion of directly-imaged planets, perturbations due to N-body interactions allow us to directly constrain exoplanet masses in multiplanet systems. This has the potential to improve our understanding of massive directly-imaged planets, which nearly all currently have only model-dependent masses. The VLTI-GRAVITY instrument has demonstrated that interferometry can achieve 100x better astrometric precision than existing methods, a level of precision that makes detection of planet–planet interactions possible. In this study, we show that in the HR-8799 system, planet–planet deviations from currently used Keplerian approximations are expected to be up to one-quarter of a milliarcsecond within five years, which will make them detectable with VLTI-GRAVITY. Modeling of this system to directly constrain exoplanet masses will be crucial in order to make precise predictions.

An Efficient Dual-Hierarchy t-SNE Minimization.

t-distributed Stochastic Neighbour Embedding (t-SNE) has become a standard for exploratory data analysis, as it is capable of revealing clusters even in complex data while requiring minimal user input. While its run-time complexity limited it to small datasets in the past, recent efforts improved upon the expensive similarity computations and the previously quadratic minimization. Nevertheless, t-SNE still has high runtime and memory costs when operating on millions of points. We present a novel method for executing the t-SNE minimization. While our method overall retains a linear runtime complexity, we obtain a significant performance increase in the most expensive part of the minimization. We achieve a significant improvement without a noticeable decrease in accuracy even when targeting a 3D embedding. Our method constructs a pair of spatial hierarchies over the embedding, which are simultaneously traversed to approximate many N-body interactions at once. We demonstrate an efficient GPGPU implementation and evaluate its performance against state-of-the-art methods on a variety of datasets.

Flexible ansatz for N-body configuration interaction

We present a Flexible Ansatz for N-body Configuration Interaction (FANCI) that includes any multideterminant wavefunction. This ansatz is a generalization of the Configuration Interaction (CI) wavefunction, where the coefficients are replaced by a specified function of certain parameters. By making an appropriate choice for this function, we can reproduce popular wavefunction structures like CI, Coupled-Cluster, Tensor Network States, and geminal-product wavefunctions. The universality of this framework suggests a programming structure that allows for the easy construction and optimization of arbitrary wavefunctions. Here, we will discuss the structures of the FANCI framework and its implications for wavefunction properties, particularly accuracy, cost, and size-consistency. We demonstrate the flexibility of this framework by reconstructing popular wavefunction ansätze and modifying them to construct novel wavefunction forms. FANCI provides a powerful framework for exploring, developing, and testing new wavefunction forms.

Phase Separation and Multibody Effects in Three-Dimensional Active Brownian Particles.

Simulation studies of the phase diagram of repulsive active Brownian particles in three dimensions reveal that the region of motility-induced phase separation between a high and low density phase is enclosed by a region of gas-crystal phase separation. Near-critical loci and structural crossovers can additionally be identified in analogy with simple fluids. Motivated by the striking similarity to the behavior of equilibrium fluids with short-ranged pairwise attractions, we show that a direct mapping to pair potentials in the dilute limit implies interactions that are insufficiently attractive to engender phase separation. Instead, this is driven by the emergence of multibody effects associated with particle caging that occurs at sufficiently high number density. We quantify these effects via information-theoretical measures of n-body effective interactions extracted from the configurational structure.

Full-Potential KKR Calculations for Interaction Energies in Al-Rich AlX (X = H～Sn) Alloys: I. Fundamental Features and Thermal Electronic Contribution due to Fermi-Dirac Distribution

We presented systematical ab-initio calculations for the n-body (n = 1-4) interaction energies (IEs) in Al-rich AlX (X = H～Sn) alloys, by using the full-potential Korringa-Kohn- Rostoker Green's function (FPKKR) method, and clarified the fundamental features and the thermal electronic contribution due to the Fermi Dirac (FD) distribution for these IEs. We show the calculated results for the IEs: (1) the 2-body IEs of the X = 3d and 4d impurities are strongly repulsive at the 1st-nearest neighbor (nn) and show the oscillating behavior with the interatomic distance; (2) the 1st-nn 2-body IEs of the X = Ne, Ar, and Kr (inert gas elements) impurities are strongly attractive; (3) the 1st-nn 2-body IEs around X = N (2sp element) are repulsive and relatively high; (4) the thermal electronic contribution due to the FD distribution is considerably high for the X = d impurities, while very low for the X = sp impurities; (5) the n-body (n = 1-4) IEs of the X = 3d and 4d impurities in Al and the thermal electronic contribution for these n-body IEs may be in general lower and lower with the increase in n. It is also discussed that the fundamental features (attraction or repulsion) of the calculated 2-body IEs may be understood by considering the strength differences among the X−X, Al−X, and Al−Al interactions.

The Orion Protostellar Explosion and Runaway Stars Revisited: Stellar Masses, Disk Retention, and an Outflow from the Becklin–Neugebauer Object

Abstract The proper motions of the three stars ejected from Orion’s OMC1 cloud core are combined with the requirement that their center of mass is gravitationally bound to OMC1 to show that radio source I (Src I) is likely to have a mass around 15 M ⊙ consistent with recent measurements. Src I, the star with the smallest proper motion, is suspected to be either an astronomical-unit-scale binary or a protostellar merger remnant produced by a dynamic interaction ∼550 yr ago. Near-infrared 2.2 μm images spanning ∼21 yr confirm the ∼55 km s−1 motion of “source x” (Src x) away from the site of stellar ejection and point of origin of the explosive OMC1 protostellar outflow. The radial velocities and masses of the Becklin–Neugebauer (BN) object and Src I constrain the radial velocity of Src x to be km s−1. Several high proper-motion radio sources near BN, including Zapata 11 ([ZRK2004] 11) and a diffuse source near IRc 23, may trace a slow bipolar outflow from BN. The massive disk around Src I is likely the surviving portion of a disk that existed prior to the stellar ejection. Though highly perturbed, shocked, and reoriented by the N-body interaction, enough time has elapsed to allow the disk to relax with its spin axis roughly orthogonal to the proper motion.

IRAS 09002-4732: A Laboratory for the Formation of Rich Stellar Clusters

Abstract IRAS 09002-4732 is a poorly studied embedded cluster of stars in the Vela Molecular Ridge at a distance of 1.7 kpc. Deep observations with the Chandra X-ray Observatory, combined with existing optical and infrared surveys, produce a catalog of 441 probable pre-main-sequence members of the region. The stellar spatial distribution has two components: most stars reside in a rich, compact, elliptical cluster, but a minority reside within a molecular filament several parsecs long that straddles the cluster. The filament has active distributed star formation with dozens of unclustered protostars. The cluster pre-main-sequence population is ≤0.8 Myr old and deeply embedded; its most massive member is extremely young, producing an ultracompact H ii region. The cluster total population deduced from the X-ray luminosity function is surprisingly rich, twice that of the Orion Nebula Cluster. The cluster core is remarkably dense where strong N-body interactions should be occurring; its initial mass function may be deficient in massive stars. We infer that IRAS 09002-4732 is a rare case where a rich cluster is forming today in a molecular filament, consistent with astrophysical models of cluster formation in clouds that involve the hierarchical formation and merging of groups in molecular filaments.

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

Sampling general N-body interactions with auxiliary fields

We present a general auxiliary field transformation which generates effective interactions containing all possible N-body contact terms. The strength of the induced terms can analytically be described in terms of general coefficients associated with the transformation and thus are controllable. This transformation provides a novel way for sampling 3- and 4-body (and higher) contact interactions non-perturbatively in lattice quantum Monte Carlo simulations. As a proof of principle, we show that our method reproduces the exact solution for a two-site quantum mechanical problem.

The tenfold way redux: Fermionic systems with N-body interactions

We provide a systematic treatment of the tenfold way of classifying fermionic systems that naturally allows for the study of those with arbitrary N-body interactions. We identify four types of symmetries such systems can possess, which consist of one ordinary type (usual unitary symmetries), and three non-ordinary symmetries (such as time reversal, charge conjugation and sublattice). Focusing on systems that possess no non-trivial ordinary symmetries, we demonstrate that the non-ordinary symmetries are strongly constrained. This approach not only leads very naturally to the tenfold classes, but also obtains the canonical representations of these symmetries in each of the ten classes. We also provide a group cohomological perspective of our results in terms of projective representations. We then use the canonical representations of the symmetries to obtain the structure of Hamiltonians with arbitrary N-body interactions in each of the ten classes. We show that the space of N-body Hamiltonians has an affine subspace (of a vector space) structure in classes which have either or both charge conjugation and sublattice symmetries. Our results can help address many open questions including the topological classification of interacting fermionic systems.

Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture

Quantum annealing provides a way of solving optimization problems by encoding them as Ising spin models which are implemented using physical qubits. The solution of the optimization problem then corresponds to the ground state of the system. Quantum tunneling is harnessed to enable the system to move to the ground state in a potentially high non-convex energy landscape. A major difficulty in encoding optimization problems in physical quantum annealing devices is the fact that many real world optimization problems require interactions of higher connectivity, as well as multi-body terms beyond the limitations of the physical hardware. In this work we address the question of how to implement multi-body interactions using hardware which natively only provides two-body interactions. The main result is an efficient circuit design of such multi-body terms using superconducting flux qubits in which effective N-body interactions are implemented using N ancilla qubits and only two inductive couplers. It is then shown how this circuit can be used as the unit cell of a scalable architecture by applying it to a recently proposed embedding technique for constructing an architecture of logical qubits with arbitrary connectivity using physical qubits which have nearest-neighbor four-body interactions. It is further shown that this design is robust to non-linear effects in the coupling loops, as well as mismatches in some of the circuit parameters.