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Register a new userUniversality of excited three-body bound states in one dimension
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We study a heavy-heavy-light three-body system confined to one space dimension provided the binding energy of an excited state in the heavy-light subsystems approaches zero. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy-light state and (ii) the presence of deeply-bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy-light subsystems.
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We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio via the direct calculation of the Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is not equal to another two identical particles. We can obtain not only the binding energies but also the corresponding wave functions. When the mass of impurity atom is vary large, there are at most three three-body bound states. We then study the effect of three-body zero-range interaction and unveil that it can induces one more three-body bound state at a certain region of coupling strength ratio under a fixed mass ratio.
We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finite-range attractive heavy-light interaction potentials. In case of the zero-range potential, we apply the method of Skorniakov and Ter-Martirosian to explore the accuracy of the Born-Oppenheimer approach. For the finite-range potentials, we solve the Schrodinger equation numerically using a pseudospectral method. We demonstrate that when the two-body ground state energy approaches zero, the three-body bound states display a universal behavior, independent of the shape of the interaction potential.
Under certain circumstances, three or more interacting particles may form bound states. While the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of eleven precisely determined three- and four-body features are found in the inelastic loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, while a systematic deviation from universality is found when comparing features across the resonance.
Traditional anyons in two dimensions have generalized exchange statistics governed by the braid group. By analyzing the topology of configuration space, we discover that an alternate generalization of the symmetric group governs particle exchanges when there are hard-core three-body interactions in one-dimension. We call this new exchange symmetry the traid group and demonstrate that it has abelian and non-abelian representations that are neither bosonic nor fermionic, and which also transform differently under particle exchanges than braid group anyons. We show that generalized exchange statistics occur because, like hard-core two-body interactions in two dimensions, hard-core three-body interactions in one dimension create defects with co-dimension two that make configuration space no longer simply-connected. Ultracold atoms in effectively one-dimensional optical traps provide a possible implementation for this alternate manifestation of anyonic physics.
The small-scale structure problems of the universe can be solved by self-interacting dark matter that becomes strongly interacting at low energies. A particularly predictive model is resonant short-range self-interactions, with a dark-matter mass of about 19 GeV and a large S-wave scattering length of about 17 fm. Such a model makes definite predictions for the few-body physics of weakly bound clusters of the dark-matter particles. We calculate the production of two-body bound clusters by three-body recombination in the early universe under the assumption that the dark matter particles are identical bosons, which is the most favorable case for forming larger clusters. The fraction of dark matter in the form of two-body bound clusters can increase by as much as 4 orders of magnitude when the dark-matter temperature falls below the binding energy, but its present value remains less than 10^(-6).
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