An Infrared Renormalization Group Limit Cycle in QCD

Small increases in the up and down quark masses of QCD would tune the theory to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At critical values of the quark masses, the deuteron binding energy goes to zero and the triton has infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states approaches a universal constant that is close to 515. The proximity of physical QCD to the critical trajectory for this limit cycle explains the success of an effective field theory of nucleons with contact interactions only in describing the low-energy 3-nucleon system.Comment: 4 pages, revtex4, 2 ps figure

The few-body problem for trapped bosons with large scattering length

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm osc}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\theta$. For large positive $a/a_{\mathrm osc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\theta$. For other states the $\theta$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm osc}|\gg1$.Comment: 4 pages, 3 figure

Enhanced Dimer Relaxation in an Atomic/Molecular BEC

We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.Comment: 5 pages, revtex4, 2 PS figures, title changed, final versio

Resonant Dimer Relaxation in Cold Atoms with a Large Scattering Length

Efimov physics refers to universal phenomena associated with a discrete scaling symmetry in the 3-body problem with a large scattering length. The first experimental evidence for Efimov physics was the recent observation of a resonant peak in the 3-body recombination rate for 133Cs atoms with large negative scattering length. There can also be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We calculate the atom-dimer relaxation rate as a function of temperature and show how measurements of the relaxation rate can be used to determine accurately the parameters that govern Efimov physics.Comment: 4 pages, 2 eps figures, normalization error in figures corrected, equations unchange

Temperature-dependent errors in nuclear lattice simulations

We study the temperature dependence of discretization errors in nuclear lattice simulations. We find that for systems with strong attractive interactions the predominant error arises from the breaking of Galilean invariance. We propose a local "well-tempered" lattice action which eliminates much of this error. The well-tempered action can be readily implemented in lattice simulations for nuclear systems as well as cold atomic Fermi systems.Comment: 33 pages, 17 figure

N-body Efimov states from two-particle noise

The ground state energies of universal N-body clusters tied to Efimov trimers, for N even, are shown to be encapsulated in the statistical distribution of two particles interacting with a background auxiliary field at large Euclidean time when the interaction is tuned to the unitary point. Numerical evidence that this distribution is log-normal is presented, allowing one to predict the ground-state energies of the N-body system.Comment: Extended discussion of results; published versio

Limiting Case of Modified Electroweak Model for Contracted Gauge Group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the {\it free} (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere $S_3$. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.Comment: 12 pages, talk given at the XIII Int. Conf. on SYMMETRY METHODS IN PHYSICS, Dubna, Russia, July 6-9, 2009; added references for introduction, clarified motivatio

Virial theorems for trapped cold atoms

We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length $a$ is varied adiabatically in the BEC-BCS crossover, we find that the trapping potential energy as a function of $1/a$ has an inflexion point at unitarity.Comment: A few small correction

Dimer-atom scattering between two identical fermions and a third particle

We use the diagrammatic $T$-matrix approach to analyze the three-body scattering problem between two identical fermions and a third particle (which could be a different species of fermion or a boson). We calculate the s-wave dimer-atom scattering length for all mass ratios, and our results exactly match the results of Petrov. In particular, we list the exact dimer-atom scattering lengths for all available two-species Fermi-Fermi and Bose-Fermi mixtures. In addition, unlike that of the equal-mass particles case where the three-body scattering $T$-matrix decays monotonically as a function of the outgoing momentum, we show that, after an initial rapid drop, this function changes sign and becomes negative at large momenta and then decays slowly to zero when the mass ratio of the fermions to the third particle is higher than a critical value (around 6.5). As the mass ratio gets higher, modulations of the $T$-matrix become more apparent with multiple sign changes, related to the "fall of a particle to the center" phenomenon and to the emergence of three-body Efimov bound states.Comment: 6 pages, 3 figures, and 2 table

Single-Particle Momentum Distribution of an Efimov trimer

Experimental progress in the study of strongly interacting ultracold atoms has recently allowed the observation of Efimov trimers. We study theoretically a non-conventional observable for these trimer states, that may be accessed experimentally, the momentum distribution n(k) of the constitutive bosonic particles. The large momentum part of the distribution is particularly intriguing: In addition to the expected 1/k^4 tail associated to contact interactions, it exhibits a subleading tail 1/k^5 which is a hall-mark of Efimov physics and leads to a breakdown of a previously proposed expression of the energy as a functional of the momentum distribution.Comment: This is a subpart of the (too long to be published) work arXiv:1001.0774. This subpart has 11 pages and 2 figures. Revised version correcting minor error