Two-body Interaction Research Articles

The coherence of nonlinear Bloch dynamics of Bose-Einstein condensate in deep optical lattices

Abstract Atomic interaction leads to dephasing and damping of the Bloch oscillations (BOs) in optical lattices, which limits the observation and application of BOs. How to obtain persistent BOs is particularly important. Here, the nonlinear Bloch dynamics of Bose-Einstein condensate with two-body and three-body interactions in deep optical lattices is studied. The damping rate induced by interactions is obtained. The damping induced by two-body interaction plays a dominant role, while the damping induced by three-body interaction is weak. However, when the two-body and three-body interactions satisfy a threshold, long-lived coherent BOs are observed. Furthermore, the Bloch dynamics with periodical modulation of linear force is studied. The frequencies of linear force corresponding to resonance and pseudoresonance are obtained, and rich dynamical phenomena, i.e., stable and strong BOs, drifting and dispersion of wave packet, are predicted. The controllable Bloch dynamics is provided with the periodic modulation of the linear force.

Epidemic extinction in a simplicial susceptible-infected-susceptible model

We study the extinction of epidemics in a simplicial susceptible-infected-susceptible model, where each susceptible individual becomes infected either by two-body interactions ( S+I→2I ) with a rate β or by three-body interactions ( S+2I→3I ) with a rate β(1+δ) , and each infected individual spontaneously recovers (I → S) with a rate µ. We focus on the case δ > 0 that embodies a synergistic reinforcement effect in group interactions. By using the theory of large fluctuations to solve approximately for the master equation, we reveal two different scenarios for an optimal path to extinction, and derive the associated action S for βb<β<βc and for β>βc , where βb=4(1+δ)/(2+δ)2 and βc=1 are two different bifurcation points. The action S shows different scaling laws with the distance of the infectious rate to the transition points β b and β c , characterized by two different exponents: 3/2 and 1, respectively. Interestingly, the second-order derivative of S with respect to β is discontinuous at β=βc , while S and its first-order derivative are both continuous, reminiscent of the second-order phase transitions in equilibrium systems. Finally, a rare-event simulation method is used to compute the mean extinction time, which depends exponentially on S and the size N of the population. The simulation results are in good agreement with the proposed theory.

An analogy between effective potential representing prime numbers and Schwarzschild black hole

The effective two body interaction is derived using the single particle Schrödinger equation for the prime numbers with probability density based on the prime counting function (which is the number of primes below a certain x). Though the speculative connection of primes to Schwarzschild spacetime or black hole has been there for a long time, here for the first time our derived potential serendipitously shows the unique similarity with the effective potential derived from general theory of relativity (GTR) for Schwarzschild spacetime. Also, we report the existence of ISCO and photon sphere in prime potential and compare with GTR. It is found that when the prime numbers are represented by a quantum system, the two-body interactions mimic the effective general relativistic gravitational interaction in black hole with the four-acceleration diverging. We also establish an analogy between Einstein's static universe and the universe of primes. The question is: “Who ordered that?”

Fast particle-mesh code for Milgromian dynamics

Context. Modified Newtonian dynamics (MOND) is a promising alternative to dark matter. To further test the theory, there is a need for fluid- and particle-dynamics simulations. The force in MOND is not a direct particle-particle interaction, but derives from a potential for which a nonlinear partial differential equation (PDE) needs to be solved. Normally, this makes the problem of simulating dynamical evolution computationally expensive. Aims. We intend to develop a fast particle-mesh (PM) code for MOND (the AQUAL formalism). Methods. We transformed the nonlinear equation for MOND into a system of linear PDEs plus one algebraic equation. An iterative scheme with the fast Fourier transform (FFT) produces successively better numerical approximations. Results. The algorithm was tested for dynamical systems in MOND where analytical solutions are known: the two-body problem, a body with a circular ring, and a spherical distribution of particles in thermal equilibrium in the self-consistent potential. Conclusions. The PM code can accurately calculate the forces at subpixel scale and reproduces the analytical solutions. Four iterations are required for the potential, but when the spatial steps are small compared to the kernel width, one iteration is suffices. The use of a smoothing kernel for the accelerations is inevitable in order to eliminate the self-gravity of the point particles. Our PDE solver is 15 to 42 times as slow as a standard Poisson solver. However, the smoothing and particle propagation takes up most of the time above one particle per 103 pixels. The FFTs, the smoothing, and the propagation part in the code can all be parallelized.

Guidance and Control Systems for Multi-Satellite Assembly using Decentralized Nonlinear Model Predictive Control

Assembly of multiple satellites enables to replace the functionality of one large satellite by multiple smaller satellites for many applications and missions such as formation flying, multi robot planetary exploration, and satellites warms. In this paper, a novel decentralized guidance and control (G&amp;C) algorithms is developed for multi-satellite assembly in proximity operations based on Non linear Model Predictive Control (NMPC).The two-body relative motion model is utilized in designing the G&amp;C systems. Decentralization avoids the single point of failure (i.e., the leader satellite), which enhances the robustness of the system. The NMPC is utilized because of itsability to handle the output and the input constraints. Collision avoidance is ensured by defining a quadratic constraint equation. Moreover, the optimal thrust vector is computed while considering the control input saturation. The mission is to assemblemultiple satellites into a cubic configuration, where each satellite approaches a cube vertex. Totes the algorithms’ effectiveness and to increase the level of confidence prior flight, the proposed closed-loop G&amp;C system is demonstrated by using MATLAB andtested for a relative motion model with J2 perturbation. The simulation results showsmooth conversion of all satellites to the target while satisfying the input and outputconstraints.

Proton-neutron pairing, quartet condensation and α− transfer in N=Z nuclei

In the past years various studies have shown that the proton-neutron pairing correlations in N=Z nuclei can be accurately described by a condensate of α-like quartets. It was also shown that the α-like quartets, defined as 4- body collective structures built with two neutrons and two protons, are also able to describe the correlations induced by general two-body interactions of shell-model type. In this paper we summarise the studies mentioned above and then we discuss how the fingerprints of the quartet condensation could be investigated by α-transfer reactions.

Behavior of the continuum coupling correlation energy in the vicinity of the particle emission threshold - Gamow shell model study

The Gamow shell model provides the open quantum system formulation of nuclear shell model. In the coupled-channel representation, Gamow shell model provides the unified theory of nuclear structure and reactions which is well suited for the study of resonances and clustering. In this work, we apply this approach to study the continuum-coupling correlation energy for selected near-threshold states of 7Li, 7Be, using a translationally invariant Hamiltonian with an effective finite-range two-body interaction.

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

ESPRESSO Observations of Gaia BH1: High-precision Orbital Constraints and no Evidence for an Inner Binary

We present high-precision radial velocity observations of Gaia BH1, the nearest known black hole (BH). The system contains a solar-type G star orbiting a massive dark companion, which could be either a single BH or an inner BH + BH binary. A BH + BH binary is expected in some models where Gaia BH1 formed as a hierarchical triple, which is attractive because they avoid many of the difficulties associated with forming the system through isolated binary evolution. Our observations test the inner binary scenario. We have measured 115 precise RVs of the G star, including 40 from ESPRESSO with a precision of 3–5 m s−1, and 75 from other instruments with a typical precision of 30–100 m s−1. Our observations span 2.33 orbits of the G star and are concentrated near a periastron passage, when perturbations due to an inner binary would be largest. The RVs are well-fit by a Keplerian two-body orbit and show no convincing evidence of an inner binary. Using REBOUND simulations of hierarchical triples with a range of inner periods, mass ratios, eccentricities, and orientations, we show that plausible inner binaries with periods P inner ≳ 1.5 days would have produced larger deviations from a Keplerian orbit than observed. Binaries with P inner ≲ 1.5 days are consistent with the data, but these would merge within a Hubble time and would thus imply fine-tuning. We present updated parameters of Gaia BH1's orbit. The RVs yield a spectroscopic mass function fMBH=3.9358±0.0002M⊙ —about 7000σ above the ∼2.5 M ⊙ maximum neutron star mass. Including the inclination constraint from Gaia astrometry, this implies a BH mass of M BH = 9.27 ± 0.10 M ⊙.

On tidal energy in Newtonian two-body motion with infinite initial separation

On tidal energy in Newtonian two-body motion with infinite initial separation

Investigation of the Periodic Planar Oscillations of a Two-Body System in an Elliptic Orbit Using the Polynomial Algebra Methods

Investigation of the Periodic Planar Oscillations of a Two-Body System in an Elliptic Orbit Using the Polynomial Algebra Methods

The discreet charm of the discrete series in dS2

We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS2) with an eye on the group-theoretic organization of single and multi-particle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realize these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén–Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories with SL(N,R) gauge group in dS2 and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to the SL(N,R) BF theory in the large-N limit.

Tidal Disruption Events from the Combined Effects of Two-body Relaxation and the Eccentric Kozai–Lidov Mechanism

Tidal disruption events (TDEs) take place when a star ventures too close to a supermassive black hole (SMBH) and becomes ruptured. One of the leading proposed physical mechanisms often invoked in the literature involves weak two-body interactions experienced by the population of stars within the host SMBH’s sphere of influence, commonly referred to as two-body relaxation. This process can alter the angular momentum of stars at large distances and place them into nearly radial orbits, thus driving them to disruption. On the other hand, gravitational perturbations from an SMBH companion via the eccentric Kozai–Lidov (EKL) mechanism have also been proposed as a promising stellar disruption channel. Here we demonstrate that the combination of EKL and two-body relaxation in SMBH binaries is imperative for building a comprehensive picture of the rates of TDEs. Here we explore how the density profile of the surrounding stellar distribution and the binary orbital parameters of an SMBH companion influence the rate of TDEs. We show that this combined channel naturally produces disruptions at a rate that is consistent with observations and also naturally forms repeated TDEs, where a bound star is partially disrupted over multiple orbits. Recent observations show stars being disrupted in short-period orbits, which is challenging to explain when these mechanisms are considered independently. However, the diffusive effect of two-body relaxation, combined with the secular nature of the eccentricity excitations from EKL, is found to drive stars on short eccentric orbits at a much higher rate. Finally, we predict that rTDEs are more likely to take place in the presence of a steep stellar density distribution.

A Proof of Finite Crystallization via Stratification

We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle interactions and three-body angular potentials favoring bond-angles of the square lattice. To each configuration, we associate its bond graph which is then suitably modified by identifying chains of successive atoms. This method, called stratification, reduces the crystallization problem to a simple minimization that corresponds to a proof via slicing of the isoperimetric inequality in ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^1$$\\end{document}. As a byproduct, we also prove a fluctuation estimate for minimizers of the configurational energy, known as the n3/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n^{3/4}$$\\end{document}-law.

Relativistic Faddeev 3D equations for three-body bound states without two-body t-matrices

Abstract This paper explores a novel revision of the Faddeev equation for three-body (3B) bound states, as initially proposed in Ref. [J. Golak, K. Topolnicki, R. Skibiński, W. Glöckle, H. Kamada, A. Nogga, Few Body Syst. 54, 2427 (2013)]. This innovative approach, referred to as t-matrix-free in this paper, directly incorporates two-body (2B) interactions and completely avoids the 2B transition matrices. We extend this formalism to relativistic 3B bound states using a three-dimensional (3D) approach without using partial wave decomposition. To validate the proposed formulation, we perform a numerical study using spin-independent Malfliet–Tjon and Yamaguchi interactions. Our results demonstrate that the relativistic t-matrix-free Faddeev equation, which directly implements boosted interactions, accurately reproduces the 3B mass eigenvalues obtained from the conventional form of the Faddeev equation, referred to as t-matrix-dependent in this paper, with boosted 2B t-matrices. Moreover, the proposed formulation provides a simpler alternative to the standard approach, avoiding the computational complexity of calculating boosted 2B t-matrices and leading to significant computational time savings.

High-Performance One-Body Electrochemical Torsional Artificial Muscles Built Using Carbon Nanotubes and Ion-Exchange Polymers.

Electrochemical torsional artificial muscles have the potential to replace electric motors in the field of miniaturization. In particular, carbon nanotubes (CNTs) are some of the best materials for electrochemical torsional artificial muscles due to their remarkable mechanical strength and high electrical conductivity. However, previous studies on CNT torsional muscle utilize only half of the whole potential range for torsional actuation because the actuations in the positive and negative voltage ranges offset each other. Here, we used an ion-exchange polymer, poly(sodium 4-styrenesulfonate) (PSS), which leads to the participation of only positive ions in the actuation of CNT muscles so that the whole potential range can be used for torsional actuation. As a result, PSS-coated CNT muscle can provide 1.9 times higher torsional actuation compared to neat CNT torsional muscle. This PSS-coated CNT muscle not only provides high performance but also facilitates a one-body system for electrochemical torsional actuation. From these advantages, we implement a one-body torsional muscle for the realization of the forward motion of a model boat. This high performance and one-body structure for electrochemical torsional muscles can be used for further applications, such as soft robotics and implantable devices.

Four-body bound states in momentum space: the Yakubovsky approach without two-body t − matrices

This study presents a solution to the Yakubovsky equations for four-body bound states in momentum space, bypassing the common use of two-body t − matrices. Typically, such solutions are dependent on the fully-off-shell two-body t − matrices, which are obtained from the Lippmann-Schwinger integral equation for two-body subsystem energies controlled by the second and third Jacobi momenta. Instead, we use a version of the Yakubovsky equations that does not require t − matrices, facilitating the direct use of two-body interactions. This approach streamlines the programming and reduces computational time. Numerically, we found that this direct approach to the Yakubovsky equations, using 2B interactions, produces four-body binding energy results consistent with those obtained from the conventional t − matrix dependent Yakubovsky equations, for both separable (Yamaguchi and Gaussian) and non-separable (Malfliet-Tjon) interactions.

Universal Poisson statistics of a passive tracer diffusing in dilute active suspensions.

The statistics of a passive tracer immersed in a suspension of active particles (swimmers) is derived from first principles by considering a perturbative expansion of the tracer interaction with the microscopic swimmer field. To first order in the swimmer density, the tracer statistics is shown to be exactly represented by a spatial Poisson process combined with independent tracer-swimmer scattering events, rigorously reducing the multiparticle dynamics to two-body interactions. The Poisson representation is valid in any dimension, for arbitrary interaction forces and for a large class of swimmer dynamics. The framework not only allows for the systematic calculation of the tracer statistics in various dynamical regimes but highlights in particular surprising universal features that are independent of the swimmer dynamics such as a time-independent velocity distribution.

Two-body Coulomb problem and hidden g (2) algebra: superintegrability and cubic polynomial algebra

It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a g (2) hidden algebra and a cubic polynomial algebra of integrals. The two integrals are of orders two and four, they are made from two components of the angular momentum and from the modified Laplace-Runge-Lenz vector, respectively. It is demonstrated that the cubic polynomial algebra is an infinite-dimensional subalgebra of the universal enveloping algebra Ug (2).

Two-body dynamic simulations of a combined semi-submersible floating offshore wind turbine and torus wave energy converter

Dynamic responses of a combined wind and wave energy system which consist of a 5MW semi-submersible floating offshore wind turbine (FOWT) and a torus-shaped wave energy converter (WEC) are investigated. In the investigated configuration, the torus WEC is constrained to move only in the heave direction with respect to the FOWT. This results in a two-body dynamic system that allows for the extraction of wave energy through the relative heave motion. A Modelica-based multi-body system (MBS) code is used to perform fully coupled dynamic analyses of the combined system. The wind turbine loads are calculated using the state-of-the-art Blade Element Momentum (BEM) method, while the wave power take-off (PTO) system is modelled as a linear spring and a viscous damper. A case study is presented where the mass of the torus is varied to investigate the impact on the two-body dynamics of the combined system. The system performance is assessed in terms of the maximum wave power absorption and the quality of wind power production.