The ground state energy at unitarity

Three-body scattering and quantization conditions from $S$ matrix unitarity

Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity'' method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the relativistic effective field theory results directly from $S$ matrix unitarity. In this work, we provide a simple proof of the relativistic effective field theory form of the scattering equations directly from unitarity. Motivated by the fini…

Shear viscosity of a superfluid Fermi gas in the unitarity limit

We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature T limit the shear viscosity scales as xi^5/T^5, where the universal parameter 'xi' relates the chemical potential and the Fermi energy, mu=xi E_F. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature T_c. A naive extrapola…

Unitarity potentials and neutron matter at the unitary limit

We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $ξ=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $ξ\sim 0.44(1)$. In the present work we calculate this ratio $ξ$ using a family of hard-core squar…

Nuclear Physics Around the Unitarity Limit

We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence…

Ground-state properties of unitary bosons: from clusters to matter

The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this paper we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two- …

围绕幺正极限展开的三体和四体玻色子系统：应用于$^4$He

Three- and four-boson systems expanded around the unitarity limit: Application to $^4$He molecules

利用短程有效场论，在领先阶取幺正极限并微扰处理有限散射长度、有效程和四体力修正，通过Faddeev-Yakubovsky形式和图解方法研究三体和四体玻色子系统的束缚能与半径，成功再现$^4$He原子团簇的精确结果。

Universal tetramer limit-cycle at the unitarity limit

We demonstrate that a four-boson limit-cycle independent of the Efimov one appears in Hamiltonian systems at the unitary limit. The model interaction contains two-, three- and four-body short-range potentials, which disentangle the interwoven three- and four-boson cycles, for the universal trimer and tetramer energy levels, respectively. The limit-cycle associated with the correlation between the energies of two successive universal tetramer levels for fixed weakly bound trimer is found to be largely model independent. This is a universal manifestation of an independent four-boson scale associ…