Short-range Two-body Interactions Research Articles

Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions

Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions

Dynamics of large boson systems with attractive interaction and a derivation of the cubic focusing NLS equation in R3

We consider a system of N bosons where the particles experience a short-range two-body interaction given by N−1vN(x) = N3β−1v(Nβx), where v∈Cc∞(R3), without a definite sign on v. We extend the results of Grillakis and Machedon [Commun. Math. Phys. 324(2), 601–636 (2013)] and Kuz [Differ. Integral Equations 30(7/8), 587–630 (2017)] regarding the second-order correction to the mean-field evolution of systems with repulsive interaction to systems with attractive interaction for 0<β<12. Our extension allows for a more general set of initial data, which includes coherent states. We also provide both a derivation of the focusing nonlinear Schrödinger equation in 3D from the many-body system and its rate of convergence toward mean-field for 0<β<13.

Triple- X and beyond: Hadronic systems of three and more X(3872)

The $X(3872)$ resonance has been conjectured to be a $J^{PC} = 1^{++}$ charm meson-antimeson two-body molecule. Meanwhile, there is no experimental evidence for larger, few-body compounds of multiple charm meson-antimeson pairs which would resemble larger molecules or nuclei. Here, we investigate such multi-meson states to the extent of what can be deduced theoretically from essentials of the interaction between uncharged $D^{0}$ and $D^{*0}$ mesons. From a molecular $X(3872)$, we predict a $4X$ ($4^{++}$) octamer with a binding energy \mbox{$B_{4X} > 2.08\,{\rm MeV}$,} assuming a $D^{*0} \bar{D}^0$ system close to the unitary limit (as suggested by the mass of the $X(3872)$). If we consider heavy-quark spin symmetry explicitly, the $D^{*0} \bar{D}^{*0}$ ($2^{++}$) system is close to unitarity, too. In this case, we predict a bound $3X$ ($3^{++}$) hexamer with $B_{3X} > 2.29\,{\rm MeV}$ and a more deeply bound $4X$ octamer with $B_{4X} > 11.21\,{\rm MeV}$. These results exemplify with hadronic molecules a more general phenomenon of equal-mass two-species Bose systems comprised of equal number of either type: the emergence of unbound four- and six-boson clusters in the limit of a short-range two-body interaction which acts only between bosons of different species. Finally, we also study the conditions under which a $2X$ ($2^{++}$) tetramer might form.

Cold-atom–dimer reaction rates with He4, Li6,7 , and Na23

Atom-dimer exchange and dissociation reaction rates are predicted for different combinations of two $^4$He atoms and one of the alkaline species among $^{6}$Li, $^{7}$Li and $^{23}$Na, by using three-body scattering formalism with short-range two-body interactions. Our study was concerned with low-energy reaction rates in which the $s-$, $p-$ and $d-$ wave contributions are the relevant ones. The $^4$He is chosen as one of the atoms in the binary mixture, in view of previous available investigations and laboratory accessibilities. Focusing on possible experimental cold-atom realizations with two-atomic mixtures, in which information on atom-dimer reaction rates can be extracted, we predict the occurrence of a dip in the elastic reaction rate for colliding energies smaller than 20 mK, when the dimer is the $^4$He$^{23}$Na molecule. We are also anticipating a zero in the elastic $p-$wave contribution for the $^4$He + $^4$He$^7$Li and $^4$He + $^4$He$^{23}$Na reaction processes. With weakly-bound molecules reacting with atoms at very low colliding energies, we interpret our results on the light of Efimov physics which supports model independence and robustness of our predictions. Specific sensitivities on the effective range were evidenced, highlighted by the particular inversion role of the $p-$ and $d-$waves in the atom exchange and dissociation processes.

Dynamics of one-dimensional correlated nuclear systems within non-equilibrium Green’s function theory

Theory of non-equilibrium Green’s function (NGF) provides a practical framework for studying quantum many-body systems out of equilibrium. Extending the previous mean field approach developed for nuclear systems in one dimension with NGF, we introduce isospin degrees of freedom to the Green’s functions and incorporate short-range two-body interactions in the second-order self-consistent approximation to correlations, which represents the scattering of momentum orbitals in the Born approximation. We discuss the preparation of a finite nuclear system and examine the impact of correlations on the ground state. We also excite a finite symmetric nuclear system to oscillate in an isovector dipole mode and explore the dissipation effects in the oscillation. Finally, we demonstrate how to boost a slab to a constant and stable motion in a box, based on Galilean covariance of the theory. The studies in this paper lay the ground for the future exploration of collisions of correlated nuclear systems in one dimension.

Ground-state properties of dilute spinless fermions in fractional dimensions

We analyze zero-temperature universal properties of the simplest Galilean-invariant model of spinless low-dimensional fermions with short-range two-body interactions. In particular, it is shown that after proper renormalization of the coupling constant, even the dilute system possesses rich phase diagram that includes the superfluid state and the metastable `upper branch' behavior.

Dynamical dimerization phase in Jaynes–Cummings lattices

We report on an emergent dynamical phase of a strongly-correlated light–matter system, which is governed by dimerization processes due to short-range and long-range two-body interactions. The dynamical phase is characterized by the spontaneous symmetry breaking of the translational invariance and appears in an intermediate regime of light–matter interaction between the resonant and dispersive cases. We describe the quench dynamics from an initial state with integer filling factor of a finite-sized array of coupled resonators, each doped with a two-level system, in a closed and open scenario. The closed system dynamics has an effective Hilbert space description that allows us to demonstrate and characterize the emergent dynamical phase via time-averaged quantities, such as fluctuations in the number of polaritons per site and linear entropy. We prove that the dynamical phase is governed by intrinsic two-body interactions and the lattice topological structure. In the open system dynamics, we show evidence about the robustness of dynamical dimerization processes under loss mechanisms. Our findings can be used to determine the light–matter detuning range, where the dimerized phase emerges.

Many-Body Interactions in Ice.

Many-body effects in ice are investigated through a systematic analysis of the lattice energies of several proton ordered and disordered phases, which are calculated with different flexible water models, ranging from pairwise additive (q-TIP4P/F) to polarizable (TTM3-F and AMOEBA) and explicit many-body (MB-pol) potential energy functions. Comparisons with available experimental and diffusion Monte Carlo data emphasize the importance of an accurate description of the individual terms of the many-body expansion of the interaction energy between water molecules for the correct prediction of the energy ordering of the ice phases. Further analysis of the MB-pol results, in terms of fundamental energy contributions, demonstrates that the differences in lattice energies between different ice phases are sensitively dependent on the subtle balance between short-range two-body and three-body interactions, many-body induction, and dispersion energy. By correctly reproducing many-body effects at both short range and long range, it is found that MB-pol accurately predicts the energetics of different ice phases, which provides further support for the accuracy of MB-pol in representing the properties of water from the gas to the condensed phase.

Jack 3/5 State from Two-Body Interaction

We investigate the Read–Rezayi parafermion state of correlated electrons at the fractional Landau level filling ν = 3/5. It is a Jack polynomial generated by contact four-body repulsion. We show by exact diagonalization that it is also emerges from a suitable short-range two-body interaction. We find that it closely matches Coulomb ground state in the second Landau level of non-relativistic fermions, and thus possibly describes the ν = 13/5 (and, by conjugation, ν = 12/5) fractional quantum Hall effect in GaAs.

Dynamical stability of dipolar Bose-Einstein condensates with temporal modulation of the s-wave scattering length.

We study the stabilization properties of dipolar Bose-Einstein condensate by temporal modulation of short-range two-body interaction. Through both analytical and numerical methods, we analyze the mean-field Gross-Pitaevskii equation with short-range two-body and long-range, nonlocal, dipolar interaction terms. We derive the equation of motion and effective potential of the dipolar condensate by variational method. We show that there is an enhancement of the condensate stability due to the inclusion of dipolar interaction in addition to the two-body contact interaction. We also show that the stability of the dipolar condensate increases in the presence of time varying two-body contact interaction; the temporal modification of the contact interaction prevents the collapse of dipolar Bose-Einstein condensate. Finally we confirm the semi-analytical prediction through the direct numerical simulations of the governing equation.

Ultracold three-body recombination in two dimensions

We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semi-analytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and found a slow approach to universal predictions as a function of the scattering length.

Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap

We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic traps with external spin-orbit potentials and short range two-body interactions. Using a truncated basis of total angular momentum eigenstates, non-perturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.

Surface Majorana fermions and bulk collective modes in superfluidHe3−B

The theoretical study of topological superfluids and superconductors has so far been carried out largely as a translation of the theory of noninteracting topological insulators into the superfluid language, whereby one replaces electrons by Bogoliubov quasiparticles and single-particle band Hamiltonians by Bogoliubov--de Gennes Hamiltonians. Band insulators and superfluids are, however, fundamentally different: While the former exist in the absence of interparticle interactions, the latter are broken symmetry states that owe their very existence to such interactions. In particular, unlike the static energy gap of a band insulator, the gap in a superfluid is due to a dynamical order parameter that is subject to both thermal and quantum fluctuations. In this work, we explore the consequences of bulk quantum fluctuations of the order parameter in the $B$ phase of superfluid $^{3}\mathrm{He}$ on the topologically protected Majorana surface states. Neglecting the high-energy amplitude modes, we find that one of the three spin-orbit Goldstone modes in $^{3}\mathrm{He}\ensuremath{-}B$ couples to the surface Majorana fermions. This coupling in turn induces an effective short-range two-body interaction between the Majorana fermions, with coupling constant inversely proportional to the strength of the nuclear dipole-dipole interaction in bulk $^{3}\mathrm{He}$. A mean-field theory suggests that the surface Majorana fermions in $^{3}\mathrm{He}\ensuremath{-}B$ may be in the vicinity of a metastable gapped time-reversal-symmetry-breaking phase.

Mapping the two-component atomic Fermi gas to the nuclear shell-model

The physics of a two-component cold fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1-100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic fermi gas in a tight external trap can be mapped to the nuclear shell model so that readily available many-body techniques in nuclear physics, such as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.

Universal Aspects of Neutron Halos in Light Exotic Nuclei

The theoretical few-body aspects associated with universal properties of weakly-bound neutron-rich light nuclei close to the drip line will be reviewed briefly, considering recent theoretical and experimental works. We will address low-energy properties of the one- and two-neutron halo of light exotic nuclei, which are dominated by s-wave short-range two-body interactions. In view of recent experiments with light neutron-rich nuclei, we will discuss properties of exotic nuclei as 11Li, 14Be, 20C and 22C, within a three-bodyneutron–neutron-core model. Particular emphasis will be given to model independent properties associated to halo neutrons, which obey universal scaling laws. We discuss how the scaling laws for the s-wave observables of two-neutron halo will be identified with limit-cycles and Thomas–Efimov effect in a zero-range three-body model.

Single-particle potential from resummed ladder diagrams

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by calculating the complex single-particle potential U(p, k f ) + i W(p, k f ) p > k f . The on-shell single-particle potential is constructed by means of a complex-valued in-medium loop that includes corrections from a test particle of momentum \(\vec p\) added to the filled Fermi sea. The single-particle potential U(k f , k f ) at the Fermi surface as obtained from the resummation of the combined particle and hole ladder diagrams is shown to satisfy the Hugenholtz-Van-Hove theorem. The perturbative contributions at various orders a n in the scattering length are deduced and checked against the known analytical results at order a 1 and a 2. The limit a → ∞ is studied as a special case and a strong momentum dependence of the real (and imaginary) single-particle potential is found. This feature indicates an instability against a phase transition to a state with an empty shell inside the Fermi sphere such that the density gets reduced by about 5%. The imaginary single-particle potential vanishes linearly at the Fermi surface. For comparison, the same analysis is performed for the resummed particle-particle ladder diagrams alone. In this truncation an instability for hole excitations near the Fermi surface is found at strong coupling. For the set of particle-hole ring diagrams the single-particle potential is calculated as well. Furthermore, the resummation of in-medium ladder diagrams to all orders is studied for a two-dimensional Fermi gas with a short-range two-body contact interaction.

Stripe, gossamer, and glassy phases in systems with strong nonpairwise interactions

We study structure formation in systems of classical particles in two dimensions with long-range attractive short-range repulsive two-body interactions and repulsive three-body interactions. Stripe, gossamer, and glass phases are found as a result of nonpairwise interaction.

Spin Josephson vortices in two tunnel-coupled spinor Bose gases.

We study topological excitations in spin-one Bose-Einstein condensates trapped in an elongated double-well optical potential. This system hosts a new topological defect, the spin Josephson vortex (SJV), which forms due to the competition between the interwell atomic tunneling and short-range ferromagnetic two-body interaction. We identify the spin structure and formation dynamics of the SJV and determine the phase diagram of the system. By exploiting the intrinsic stability of the SJV, we propose a dynamical method to create SJVs under realistic experimental conditions.

Bound 0+ Excited States of Three-Body Systems with Short-Range Two-Body Interactions

The Faddeev equations are solved to investigate the bound states of three-body systems with short-range two-body interactions. Different bound 0+ excited states are obtained depending on the mass ratios of particles, when there is no bound state for two-body sub-systems. On the one hand, a number of bound 0+ excited states appear in the system with two heavy particles and a light particle. On the other hand, a weakly bound 0+ excited state is obtained in the system with two light particles and a heavy particle, which has not been reported in previous works as far as we know.

Predicting Organic Crystal Lattice Energies with Chemical Accuracy

A fast, fragment-based hybrid many-body interaction model is used to optimize the structures of five small-molecule organic crystals (with fixed experimental lattice parameters) and predict their lattice energies with accuracies of ∼2−4 kJ/mol compared to experiment. This model treats individual molecules in the central unit cell and their short-range two-body interactions quantum mechanically, while long-range electrostatics and many-body induction are treated with a classical polarizable force field. For the hydrogen bonded ice, formamide, and acetamide crystals, MP2 calculations extrapolated to the complete-basis-set limit provide good accuracy. However, MP2 exhibits difficulties for crystals such as benzene and imidazole, where π-stacking dispersion interactions are important, and post-MP2 corrections determined from small-basis-set CCSD(T) calculations are required to achieve chemical accuracy. Using these techniques, accurate crystal lattice energy predictions for small-molecule organic crystals are...