Universal van der Waals Force between Heavy Polarons in Superfluids.

We investigate the long-range behavior of the induced Casimir interaction between two spinless heavy impurities, or polarons, in superfluid cold atomic gases. With the help of effective field theory (EFT) of a Galilean invariant superfluid, we show that the induced impurity-impurity potential at long distance universally shows a relativistic van der Waals-like attraction (∼1/r^{7}) resulting from the exchange of two superfluid phonons. We also clarify finite temperature effects from the same two-phonon exchange process. The temperature T introduces the additional length scale c_{s}/T with the speed of sound c_{s}. Leading corrections at finite temperature scale as T^{6}/r for distances r≪c_{s}/T smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior (∼T/r^{6}) instead of the relativistic one. Our EFT formulation applies not only to weakly coupled Bose or Fermi superfluids but also to those composed of strongly correlated unitary fermions with a weakly coupled impurity. The sound velocity controls the magnitude of the van der Waals potential, which we evaluate for the fermionic superfluid in the BCS-BEC crossover.

Universal Properties of Weakly Bound Two-Neutron Halo Nuclei.

We construct an effective field theory of a two-neutron halo nucleus in the limit where the two-neutron separation energy B and the neutron-neutron two-body virtual energy ε_{n} are smaller than any other energy scale in the problem, but the scattering between the core and a single neutron is not fine-tuned, and the Efimov effect does not operate. The theory has one dimensionless coupling which formally runs to a Landau pole in the ultraviolet. We show that many properties of the system are universal in the double fine-tuning limit. The ratio of the mean-square matter radius and charge radius is found to be ⟨r_{m}^{2}⟩/⟨r_{c}^{2}⟩=Af(ε_{n}/B), where A is the mass number of the core and f is a function of the ratio ε_{n}/B which we find explicitly. In particular, when B≫ε_{n}, ⟨r_{m}^{2}⟩/⟨r_{c}^{2}⟩=2/3A. The shape of the E1 dipole strength function also depends only on the ratio ε_{n}/B and is derived in explicit analytic form. We estimate that for the ^{22}C nucleus higher-order corrections to our theory are of the order of 20% or less if the two-neutron separation energy is less than 100 keV and the s-wave scattering length between a neutron and a ^{20}C nucleus is less than 2.8 fm.

Microscopic Theory of Fluctuating Hydrodynamics in Nonlinear Lattices.

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK)-like formula for the bare transport coefficients are presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK-like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.