Two-body Interaction Research Articles

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.

All Charm Tetraquark Spectra in Coulombic Plus Quadratic Potential

A non-relativistic model with relativistic corrections is used to generate the mass spectra of all charm tetraquark in the diquark-antidiquark system. Fitting parameters are derived by numerically solving the Schrodinger equation for the charmonium meson using the coulombic potential and the harmonic confinement interaction potential. The mass spectra of all charm tetraquark is calculated in present work by systematically reducing a four-body problem to a two-body problem using the parameters obtained from charmonium spectra.

Quantum state discrimination with assisted entanglement

State discrimination is one of the key steps in quantum information tasks. This paper introduces the assisted quantum entanglement to achieve this step. For this purpose, the paper introduces some preliminary knowledge to help enter the research topic, such as the matrix rank, Kronecker product, quantum states and the calculation method of Schmidt decomposition and rank. The latter involves the Singular value decomposition in matrix factorization theory. The method of distinguishing orthogonal states in single and many-body systems is also introduced, by using the so-called positive operator-valued measurements. Then the paper proves the fact that single or multipartite system non-orthogonal states are indistinguishable regardless of whether there are auxiliary resources, which may be either separable or entangled states. The paper further illustrates the feasibility of maximum entangled states acting on two-body systems and gives corresponding examples. At the same time, the feasibility of auxiliary resources for smaller entanglement is also investigated.

A three-dimensional model with two-body interactions for endothelial cells in angiogenesis

We introduce a three-dimensional mathematical model for the dynamics of vascular endothelial cells during sprouting angiogenesis. Angiogenesis is the biological process by which new blood vessels form from existing ones. It has been the subject of numerous theoretical models. These models have successfully replicated various aspects of angiogenesis. Recent studies using particle-based models have highlighted the significant influence of cell shape on network formation, with elongated cells contributing to the formation of branching structures. While most mathematical models are two-dimensional, we aim to investigate whether ellipsoids also form branch-like structures and how their shape affects the pattern. In our model, the shape of a vascular endothelial cell is represented as a spheroid, and a discrete dynamical system is constructed based on the simple assumption of two-body interactions. Numerical simulations demonstrate that our model reproduces the patterns of elongation and branching observed in the early stages of angiogenesis. We show that the pattern formation of the cell population is strongly dependent on the cell shape. Finally, we demonstrate that our current mathematical model reproduces the cell behaviours, specifically cell-mixing, observed in sprouts.

Pointer States and Quantum Darwinism with Two-Body Interactions.

Quantum Darwinism explains the emergence of classical objectivity within a quantum universe. However, to date, most research on quantum Darwinism has focused on specific models and their stationary properties. To further our understanding of the quantum-to-classical transition, it appears desirable to identify the general criteria a Hamiltonian has to fulfill to support classical reality. To this end, we categorize all N-qubit models with two-body interactions, and show that only those with separable interaction of the system and environment can support a pointer basis. We further demonstrate that "perfect" quantum Darwinism can only emerge if there are no intra-environmental interactions. Our analysis is complemented by solving the ensuing dynamics. We find that in systems exhibiting information scrambling, the dynamical emergence of classical objectivity directly competes with the non-local spread of quantum correlations. Our rigorous findings are illustrated through the numerical analysis of four representative models.

Classical dynamics of vortex solitons from perturbative scattering amplitudes

We introduce a novel point-particle effective description of ANO vortex solitons in the critical Abelian Higgs Model (AHM) in d = 2 + 1 based on the small winding expansion. Identifying the effective vortices with the elementary quanta of a complex scalar field, relativistic vortex-vortex scattering amplitudes are calculated as a diagrammatic, perturbative expansion in the winding number N. Making use of powerful techniques recently developed for analyzing the post-Minkowskian two-body problem in general relativity, we efficiently extract the contribution to the loop integrals from the classical potential region, with the resulting velocity expansion subsequently resummed to all orders. The main result of this paper is an analytic expression for the classical, vortex-vortex potential at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(N2), or one-loop, with exact velocity dependence. By truncating the resulting effective Hamiltonian at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(p2) we derive an analytic, perturbative expression for the metric on the 2-vortex moduli space. Finally, the emergence of the critical AHM from the classical limit of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supersymmetric AHM, and the resulting constraints on the point-particle EFT is described in detail using an on-shell superspace construction for BPS states in d = 2 + 1.

REAlgo: Rapid and efficient algorithm for estimating MP2/CCSD energy gradients for large molecular clusters.

This work reports the development of an algorithm for rapid and efficient evaluation of energy gradients for large molecular clusters employing correlated methods viz. second-order Møller-Plesset perturbation theory (MP2) theory and couple cluster singles and doubles (CCSD). The procedure segregates the estimation of Hartree-Fock (HF) and correlation components. The HF energy and gradients are obtained by performing a full calculation. The correlation energy is approximated as the corresponding two-body interaction energy. Correlation gradients for each monomer are approximated from the respective monomer-centric fragments comprising its immediate neighbours. The programmed algorithm is explored for the geometry optimization of large molecular clusters using the BERNY optimizer as implemented in the Gaussian suite of software. The accuracy and efficacy of the method are critically probed for a variety of large molecular clusters containing up to 3000 basis functions, in particular large water clusters. The CCSD level geometry optimization of molecular clusters containing ∼800 basis functions employing a modest hardware is also reported.

Kepler Problem under Repulsive Inverse-square Central Forces

In this article, I present important results of the Kepler problem under repulsive inverse-square central forces. While motions of this type have been discussed thoroughly in the classical scattering theory, I do not find available literature that treats the problem as an analog of the Kepler problem under an attractive central force. My results are applicable to motions of dust particles subject to solar radiation pressure accelerations exceeding the solar gravitational acceleration in the two-body problem.

Rigorous derivation of the Efimov effect in a simple model

We consider a system of three identical bosons in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3$$\\end{document} with two-body zero-range interactions and a three-body hard-core repulsion of a given radius a>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ a > 0$$\\end{document}. Using a quadratic form approach, we prove that the corresponding Hamiltonian is self-adjoint and bounded from below for any value of a. In particular, this means that the hard-core repulsion is sufficient to prevent the fall to the center phenomenon found by Minlos and Faddeev in their seminal work on the three-body problem in 1961. Furthermore, in the case of infinite two-body scattering length, also known as unitary limit, we prove the Efimov effect, i.e., we show that the Hamiltonian has an infinite sequence of negative eigenvalues En\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_n$$\\end{document} accumulating at zero and fulfilling the asymptotic geometrical law En+1/En→e-2πs0forn→+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\;E_{n+1} / E_n \\; \\rightarrow \\; e^{-\\frac{2\\pi }{s_0}}\\,\\; \\,\ ext {for} \\,\\; n\\rightarrow +\\infty $$\\end{document} holds, where s0≈1.00624\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_0\\approx 1.00624$$\\end{document}.

Landau levels for a Weyl pair in a monolayer medium and thermal quantities

In this paper, we consider a Weyl pair under the effect of an external uniform magnetic field in a monolayer medium without considering any charge-charge interaction between the particles. Choosing the interaction of the particles with the magnetic field in the symmetric gauge we seek for an analytical solution of the corresponding form of a one-time fully-covariant two-body Dirac equation derived from quantum electrodynamics via the action principle. As it is usual with two-body problems, we separate the relative motion and center of mass motion coordinates. Assuming the center of mass is at rest, we derive a matrix equation in terms of the relative motion coordinates without considering any group theoretical method. This equation gives a wave equation in exactly soluble form and accordingly we obtain the spinor components and complete energy eigen-states (in closed form) for such a spinless composite structure. Our results not only give exact Landau levels for such a Weyl pair in a monolayer medium but also show the considered system behaves as a two-dimensional harmonic oscillator. Furthermore, our findings give exactly the excited states of a Weyl particle under the effect of uniform external magnetic field in a monolayer graphene sheet and there is no imprint to distinguish these modes from each other. This means that the performed experiments based on Landau levels for a monolayer graphene sheet may actually involve many-body effects. Our results provide a suitable basis to analyze the associated thermal quantities and accordingly we discuss the thermal properties by determining free energy, total energy, entropy and specific heat for the composite system in question.