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In this paper, we develop an analytical stability criterion for a five-body symmetrical system, called the Caledonian Symmetric Five-Body Problem (CS5BP), which has two pairs of equal masses and a fifth mass located at the centre of mass. The CS5BP is a planar problem that is configured to utilise past–future symmetry and dynamical symmetry. The introduction of symmetries greatly reduces the dimensions of the five-body problem. Sundman's inequality is applied to derive boundary surfaces to the allowed real motion of the system. This enables the derivation of a stability criterion valid for all time for the hierarchical stability of the CS5BP. We show that the hierarchical stability depends solely on the Szebehely constant C 0 which is a dimensionless function involving the total energy and angular momentum. We then explore the effect on the stability of the whole system of varying the relative sizes of the masses. The CS5BP is hierarchically stable for C 0 > 0.065946 . This criterion can be applied in the investigation of the stability of quintuple hierarchical stellar systems and symmetrical planetary systems. [ABSTRACT FROM AUTHOR]

We present a drag force model for evolving chaotic few-body interactions with the inclusion of orbital energy losses, such as tidal dissipation and gravitational wave (GW) emission. The main effect from such losses is the formation of two-body captures that for compact objects result in GW mergers and for stars lead to either compact binaries, mergers, or disruptions. Studying the inclusion of energy loss terms in few-body interactions is therefore likely to be important for modelling and understanding the variety of transients that soon will be observed by current and upcoming surveys. However, including especially tides in few-body codes has been shown to be technically difficult and computationally heavy, which has led to very few systematic tidal studies. In this paper we derive a drag force term that can be used to model the effects from tidal, as well as other energy losses in few-body interactions, if the two-body orbit averaged energy loss is known a priori. This drag force model is very fast to evolve and gives results in agreement with other approaches, including the impulsive and affine tide approximations. [ABSTRACT FROM AUTHOR]

We review recent progress in S=−2 hypernuclei such as double-Λ hypernuclei and Ξ hypernuclei, which are composed of a nucleus and one or two hyperons, such as a Λ or a Ξ particle. Through observations of He, such as the Nagara event, we obtain important information about the ΛΛ interaction. Using this information, we perform a four-body calculation of ααΛΛ for Be, which was observed at KEK as the Demachi–Yanagi event. We interpret this event as the excited state. We calculate energy levels of Be within the framework of an ααnΛΛ five-body cluster model, and then interpret the Hida event, which was observed at KEK as the ground state of Be. Motivated by observation of the Kiso event of C, by using the Skyrme–Hartree–Fock and relativistic mean-field frameworks, we calculate the energy spectra of this hypernucleus. We interpret this event as the 14N(g.s.)+Ξ−(0p) state. Finally, we propose an experiment on H and Li to extract information about the spin- and isospin-averaged parts of the ΞN interaction. [ABSTRACT FROM AUTHOR]

We present a half-life formalism for describing the disruption of gravitationally bound few-body systems, with a focus on binary–binary scattering. For negative total encounter energies, the four-body problem has three possible decay products in the point-particle limit. For each decay product and a given set of initial conditions, we obtain directly from numerical scattering simulations the half-life for the distribution of disruption times. As in radioactive decay, the half-lives should provide a direct prediction for the relative fractions of each decay product. We test this prediction with simulated data and find good agreement with our hypothesis. We briefly discuss applications of this feature of the gravitational four-body problem to populations of black holes in globular clusters. This paper, the second in the series, builds on extending the remarkable similarity between gravitational chaos at the macroscopic scale and radioactive decay at the microscopic scale to larger-N systems. [ABSTRACT FROM AUTHOR]

These notes are a short summary of a set of lectures givenwithin the frame of the "Critical Stability of Quantum Few-Body Systems" International School held in theMax Planck Institute for the Physics of Complex Systems (Dresden). The main goal of the lectures has been to provide the basic ingredients for the description of few-body systems in coordinate space. The hyperspherical harmonic and the adiabatic expansion methods are introduced in detail, and subsequently used to describe bound and continuum states. The expressions for the cross sections and reaction rates for three-body processes are derived. The case of resonant scattering and the complex scaling method as a tool to obtain the resonance energy and width is also introduced. [ABSTRACT FROM AUTHOR]

We calculate the spatial distributions and the dynamics of a few-body two-component strongly interacting Bose gas confined to an effectively one-dimensional trapping potential. We describe the densities for each component in the trap for different interaction and population imbalances. We calculate the time evolution of the system and show that, for a certain ratio of interactions, the minority population travels through the system as an effective wave packet. [ABSTRACT FROM AUTHOR]

This article is based on the notes (arxiv:1710.11228) written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop "Critical Stability of Quantum Few-Body Systems". The last part of the article includes the specific topic presented in the workshop related to the dimensional effects in three-body systems. These notes are primarily dedicated to the students and are only a tentative to show a technique, among many others, to solve problems in a very rich area of the contemporary physics--the Few-Body Physics. [ABSTRACT FROM AUTHOR]

For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell nonlocality. [ABSTRACT FROM AUTHOR]

The reconstruction of the state of a multipartite quantum mechanical system represents a fundamental task in quantum information science. At its most basic, it concerns a state of a bipartite quantum system whose subsystems are subjected to local operations. We compare two different methods for obtaining the original state from the state resulting from the action of these operations. The first method involves quantum operations called Petz recovery maps, acting locally on the two subsystems. The second method is called matrix (or state) reconstruction and involves local, linear maps that are not necessarily completely positive. Moreover, we compare the quantities on which the maps employed in the two methods depend. We show that any state that admits Petz recovery also admits state reconstruction. However, the latter is successful for a strictly larger set of states. We also compare these methods in the context of a finite spin chain. Here, the state of a finite spin chain is reconstructed from the reduced states of a few neighbouring spins. In this setting, state reconstruction is the same as the matrix product operator reconstruction proposed by Baumgratz et al. [Phys. Rev. Lett. 111, 020401 (2013)]. Finally, we generalize both these methods so that they employ long-range measurements instead of relying solely on short-range correlations embodied in such local reduced states. Long-range measurements enable the reconstruction of states which cannot be reconstructed from measurements of local few-body observables alone and hereby we improve existing methods for quantum state tomography of quantum many-body systems. [ABSTRACT FROM AUTHOR]

Para- and ortho-Ps atoms are formed in the photodetachment of positronium negative ion. Since the lifetime against the pair annihilation is much shorter for para-Ps( ns) than for ortho-Ps( ns), the production ratio of para- and ortho-Ps atoms is important for the photodetachment experiments. We have derived the ratio explicitly. [ABSTRACT FROM AUTHOR]

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The Efimov scenario is a universal three-body effect addressing many areas of modern quantum physics. It plays an important role in the transition between few- and many-body physics and has enabled important breakthroughs in the understanding of the universal few-body theory. We review the basic concepts of the Efimov scenario with specific emphasis on the similarities and differences between homonuclear and heteronuclear systems. In the latter scenario, the existence of a second, independently tunable interaction parameter enables novel few-body phenomena that are universal and have no counterexamples in the homonuclear case. We discuss recent experimental approaches using ultracold atomic gases with magnetically tunable interactions and elucidate the role of short-range interactions in the emergence of universal and non-universal behavior. [ABSTRACT FROM AUTHOR]

The light double hypernuclei, and , are studied as three-body and cluster systems in halo/cluster effective field theory at leading order. We find that the system in spin-0 channel does not exhibit a limit cycle whereas the system in spin-1 channel and the system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the system in the spin-0 channel we estimate the scattering length for -wave hyperon-hypertriton scattering as fm. We also discuss that studying the cutoff dependences in the and systems, the bound state of is not an Efimov state but formed due to a high energy mechanism whereas that of may be regarded as an Efimov state. [ABSTRACT FROM AUTHOR]

We present a quantum reaction approach that unambiguously quantifies the complete and incomplete fusion of weakly-bound few-body nuclei. Calculations carried out within a simple model for $${\text{}^{6}}$$ Li + $${\text{}^{209}}$$ Bi at energies near the Coulomb barrier show that converged probabilities for the total, complete and incomplete fusion as well as for the scattering process can be obtained with the time-dependent wave-packet dynamics. [ABSTRACT FROM AUTHOR]

We have investigated in this paper the few-body bound systems in a simple semi-relativistic scheme. For this aim, we introduced a spin independent relativistic description for a few-identical body system by presenting the analytical solution of few-particle Klein-Gordon equation. Performing calculations in D-dimensional configuration on the basis of the hypercentral approach, we reduced the few-body Klein-Gordon equation to a Schrödinger-like form. This equation is solved by using the Nikiforov-Uvarov method, through which the energy equations and eigenfunctions for a few-body bound system are obtained. We used the spin- and isospin-independent generalized Yukawa potential in our calculations, and the dependence of the few-body binding energies on the potential parameters has been investigated. [ABSTRACT FROM AUTHOR]

Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We find that a discrete variable representation with the slow variable discretization method along the hyperradial degree of freedom results in energies consistent with the literature. However, using a Laguerre basis results in missing energy, even when extrapolated to an infinite number of basis functions and channels. We do not include the isospin T = 3/2 contribution in our analysis. [ABSTRACT FROM AUTHOR]

We extend the continuum discretized coupled channel method (CDCC) to a microscopic version, where the projectile is described by a microscopic cluster model. This generalization (MCDCC) only relies on nucleon-target interactions, and therefore presents an important predictive power. We briefly present an outline of the model, and provide recent examples with Li and B elastic scattering on different light and heavy targets. We show that the model can be applied to high energies, as well as to low energies. [ABSTRACT FROM AUTHOR]

Results obtained by the authors in recent works on the exploration of universality in systems living inside the Efimov window are critically analyzed. We discuss how to take into account finite-range corrections by introducing a finite-range parameter necessary to make comparisons to the universal predictions of the Efimov zero-range theory. Firstly we apply our analysis to two different calculations published by other authors. The first one has been used with success to describe ultracold Cs atoms close to a Feshbach resonance and the second one describes a four He atom system with a realistic interaction. Finally we use the finite-range parameter to analyze recombination data in experiments with ultracold Li atoms. The three selected cases support the introduction of the finite-range parameter as a valuable tool to extend the use of the zero-range theory to describe systems having finite-range interactions. [ABSTRACT FROM AUTHOR]

We investigate three-body recombination rates into deep dimers in cold atomic gases with large scattering length within hyper-spherical adiabatic zero-range approach. We derive closed analytic expressions for the rates for one- and two-species gases. Although the deep dimers are beyond the zero-range theory the latter can still describe the recombination into deep dimers by use of one additional short-range absorption parameter. The recombination rate, as function of the scattering length, retains the known universal behavior-the fourth power trend with characteristic log-periodic peaks-however increasing the short-range absorption broadens the peaks until they are eventually completely smeared out. Increasing the heavy-to-light mass ratio in a two-species system with two identical bosons and a third particle decreases the distance between the peaks and increases the overall scale of the recombination rate. [ABSTRACT FROM AUTHOR]

In this paper, we review our main results involving the single particle momentum distribution of bosonic trimer states in two and three dimensions. A summary table makes easier the comparison between the matrix elements and the different terms of the momentum distributions. We also show a practical method to continuously interpolate between different dimensions. [ABSTRACT FROM AUTHOR]

We study the quenched dynamics of the momentum distribution of a unitary Bose gas under isotropic harmonic confinement within a time-dependent density functional approach based on our recently calculated Monte Carlo bulk equation of state. In our calculations the inter-atomic s-wave scattering length of the trapped bosons is suddenly increased to a very large value and the real-time evolution of the system is studied. Prompted by the very recent experimental data of Rb atoms at unitarity (Makotyn et al. in Nat Phys 10:116, ) we focus on the momentum distribution as a function of time. Our results suggest that at low momenta, a quasi-stationary momentum distribution is reached after a long transient, contrary to what found experimentally for large momenta which equilibrate on a time scale shorter than the one for three body losses. [ABSTRACT FROM AUTHOR]

A bound state of a proton, p, and its counterpart antiproton, $${\bar{\rm p}}$$ , is a protonium atom $${Pn = (\bar{\rm p} {\rm p})}$$ . The following three-charge-particle reaction: $${\bar{\rm p} +({\rm p} \mu^-)_{1s} \rightarrow (\bar{\rm p} \rm{p})_{1s} + \mu^-}$$ is considered in this work, where $${\mu^-}$$ is a muon. At low-energies muonic reaction $${Pn}$$ can be formed in the short range state with α = 1 s or in the first excited state: α = 2 s/2 p, where $${\bar{\rm p}}$$ and p are placed close enough to each other and the effect of the $${\bar{\rm p}}$$ -p nuclear interaction becomes significantly stronger. The cross sections and rates of the Pn formation reaction are computed in the framework of a few-body approach based on the two-coupled Faddeev-Hahn-type (FH-type) equations. Unlike the original three-body Faddeev method the FH-type equation approach is formulated in terms of only two but relevant components: $${{\it \Psi}_1}$$ and $${\it \Psi_2}$$ , of the system's three-body wave function $${\it \Psi}$$ , where $${{\it \Psi}={\it \Psi}_1+{\it \Psi}_2}$$ . In order to solve the FH-type equations $${\it \Psi_1}$$ is expanded in terms of the input channel target eigenfunctions, i.e. in this work in terms of the $${(\rm{p} \mu^-)}$$ eigenfunctions. At the same time $${\it \Psi_2}$$ is expanded in terms of the output channel two-body wave function, that is in terms of the protonium $${(\bar{\rm{p}} \rm{p})}$$ eigenfunctions. A total angular momentum projection procedure is performed, which leads to an infinite set of one-dimensional coupled integral-differential equations for unknown expansion coefficients. [ABSTRACT FROM AUTHOR]

We present a detailed analysis of the charged four-body system in hyperspherical coordinates in the large hyperradial limit. In powers of R for any masses and charges, the adiabatic Hamiltonian is expanded to third order in the dimer-dimer limit and to first order in the particle-trimer limit. [ABSTRACT FROM AUTHOR]

A formalism based on the complex-scaling method is used to solve a four-nucleon scattering problem above the breakup threshold using the realistic nuclear Hamiltonians. This method allows to solve diverse scattering problems based on very trivial boundary conditions and is compatible with the techniques used to solve bound state problems. [ABSTRACT FROM AUTHOR]

Few- and many-fermion systems on the verge of stability, and consisting of strongly interacting particles, appear in many areas of physics. The theoretical modeling of such systems is a very difficult problem. In this work we present a theoretical framework that is based on the rigged Hilbert space formulation. The few-body problem is solved by exact diagonalization using a basis in which bound, resonant, and non-resonant scattering states are included on an equal footing. Current experiments with ultracold atoms offer a fascinating opportunity to study universal properties of few-body systems with a high degree of control over parameters such as the external trap geometry, the number of particles, and even the interaction strength. In particular, particles can be allowed to tunnel out of the trap by applying a magnetic-field gradient that effectively lowers the potential barrier. The result is a tunable open quantum system that allows detailed studies of the tunneling mechanism. In this Paper we introduce our method and present results for the decay rate of two distinguishable fermions in a one-dimensional trap as a function of the interaction strength. In particular, we present for the first time several technical and numerical details of our approach, recently published in Lundmark et al. (Phys Rev A 91:041601, ). We also show results from a careful analysis of the numerical convergence. [ABSTRACT FROM AUTHOR]

In this work we investigate the connection between discretized three-body continuum wave functions, in particular via a box boundary condition, and the wave functions computed with the correct asymptotics. The three-body wave functions are in both cases obtained by means of the adiabatic expansion method. The information concerning all the possible incoming and outgoing channels, which appears naturally when the continuum is not discretized, seems to be lost when the discretization is implemented. In this work we show that both methods are fully equivalent, and the full information contained in the three-body wave function is actually preserved in the discrete spectrum. Therefore, in those cases when the asymptotic behaviour is not known analytically, i.e., when the Coulomb interaction is involved, the discretization technique can be safely used. [ABSTRACT FROM AUTHOR]

This is a brief review of few relevant topics on tunneling of composite particles and how the coupling to intrinsic and external degrees of freedom affects tunneling probabilities. I discuss the phenomena of resonant tunneling, different barriers seen by subsystems, damping of resonant tunneling by level bunching and continuum effects due to particle dissociation. [ABSTRACT FROM AUTHOR]

Extremely weakly-bound three-boson systems are predicted to exhibit intriguing universal properties such as discrete scale invariance. Motivated by recent experimental studies of the ground and excited helium trimers, this work analyzes the three-body parameter and the structural properties of three helium atoms as the s-wave scattering length is tuned artificially. Connections with theoretical and experimental studies of the Efimov scenario as it pertains to cold atom systems are made. [ABSTRACT FROM AUTHOR]

The structure of three neutron-rich $${\Lambda}$$ hypernuclei, nn $${\Lambda}$$ and $${^6_{\Lambda}}$$ H are studied. For nn $${\Lambda}$$ system, which has been observed by the HyHI collaboration, we investigate the possibility to have a bound state taking $${\Lambda} N-{\Sigma N}$$ coupling explicitly into account. We do not find any nn $${\Lambda}$$ bound state, which is inconsistent with the data by HyHI collaboration. The four-body calculation of $${t+n+n+\Lambda}$$ for $${^6_{\Lambda}}$$ H is done and obtained as a resonant state with respect to H + n + n threshold. This calculation is also consistent with the FINUDA data which reported to have a bound state for $${^6_{\Lambda}}$$ H. [ABSTRACT FROM AUTHOR]

The existence of Efimov states in atomic nuclei has been predicted by several authors considering 3-body systems of the form Core-neutron-neutron. While these states appear elusive and very challenging experimentally, we discuss possible reactions that can be used to produce and study them in exotic (weakly-bound) nuclei. Following simple arguments, we show that cross-sections relative to the ground states should scale with the parameter $${\lambda_0}$$ , which is the same scale factor for binding energies and radii. We derive back of the envelope estimates for: one- and two-neutron transfer reactions, and inelastic scattering. The ( d, p) reaction appears as the most promising approach and we discuss in more detail some experimental considerations using the example of $${^{19}C(d, p)^{20}C}$$ . These initial estimates could serve as a starting point for more refined and realistic calculations, which will be required for careful experimental planning and further analysis. [ABSTRACT FROM AUTHOR]

We study the arising of correlations among some isovector bulk parameters in nonrelativistic and relativistic hadronic mean-field models. For the former, we investigate correlations in the nonrelativistic (NR) limit of relativistic point-coupling models. We provide analytical correlations, for the NR limit model, between the symmetry energy and its derivatives, namely, the symmetry energy slope, curvature, skewness and fourth order derivative, discussing the conditions in which they are linear ones. We also show that some correlations presented in the NR limit model are reproduced for relativistic models presenting cubic and quartic self-interactions in its scalar field. As a direct application of such linear correlations, we remark its association with possible crossing points in the density dependence of the linearly correlated bulk parameter. [ABSTRACT FROM AUTHOR]

We investigate renormalization group limit cycles within the similarity renormalization group (SRG) and discuss their signatures in the evolved interaction. A quantitative method to detect limit cycles in the interaction and to extract their period is proposed. Several SRG generators are compared regarding their suitability for this purpose. As a test case, we consider the limit cycle of the inverse square potential. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schrödinger equation for these systems confined in an harmonic trap, and interacting pairwise, in clusters of two and three particles, by two-body inverse square Calogero potential. Both translationaly and non-translationaly invariant multi-body potentials are added. In each case, the full solutions are provided, namely the normalized regular eigensolutions and the eigenenergies spectrum. The irregular solutions are also studied. We discuss the domains of coupling constants for which these irregular solutions are square integrable. The case of a 'Coulomb-type' confinement is investigated only for the bound states of the four-body systems. [ABSTRACT FROM AUTHOR]