Spectral flow of trimer states of two heavy impurities and one light condensed boson

The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interaction and that an impurity and a boson have a zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schr\"odinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presence of the condensate when the energy scale corresponding to the coherence length becomes of order the trimer binding energy in the absence of the condensate. We find that the Efimov scaling property is reflected in the critical values of the condensate coherence length at which the trimers are pushed into the continuum.Comment: 10 pages including appendices, 4 figures, revised versio

Efimov States of Heavy Impurities in a Bose-Einstein Condensate

We consider the problem of two heavy impurity particles embedded in a gas of weakly-interacting light mass bosonic particles in the condensed state. Using the Bogoliubov approach to describe the bosonic gas and the Born-Oppenheimer approximation for the three-body dynamics, we calculate the modification to the heavy-heavy two-body potential due to the presence of the condensate. For the case of resonant interaction between the light bosons and the impurities, we present (semi)-analytical results for the potential in the limit of a large condensate coherence length. In particular, we find a formula for the modification of the Efimov scaling factor due to the presence of a degenerate bosonic gas background.Comment: 6 pages, 3 figures, final versio

Strongly interacting mesoscopic systems of anyons in one dimension

Using the fractional statistical properties of so-called anyonic particles, we present exact solutions for up to six strongly interacting particles in one-dimensional confinement that interpolate the usual bosonic and fermionic limits. Specifically, we consider two-component mixtures of anyons and use these to eludicate the mixing-demixing properties of both balanced and imbalanced systems. Importantly, we demonstrate that the degree of demixing depends sensitively on the external trap in which the particles are confined. We also show how one may in principle probe the statistical parameter of an anyonic system by injection a strongly interacting impurity and doing spectral or tunneling measurements.Comment: 6 pages, 5 figures, final version with corrected equation (A3

Physical approach to quantum networks with massive particles

This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by crossing two quantum wires, and we consider a massive particle in such an X well. The system is analyzed using a variational method based on an expansion into modes with fast convergence and it provides a very clear intuition for the physics of the problem. The particle is found to have a ground state that is exponentially localized to the center of the X well, and the other symmetric solutions are formed so to be orthogonal to the ground state. This is in contrast to the predictions of the conventionally used so-called Kirchoff boundary conditions in quantum graph theory that predict a different sequence of symmetric solutions that cannot be physically realized. Numerical methods have previously been the only source of information on the ground-state wave function and our results provide a different perspective with strong analytical insights. The ground-state wave function has the shape of a solitonic solution to the non-linear Schr{\"o}dinger equation, enabling an analytical prediction of the wave number. When combining multiple X wells into a network or grid, each site supports a solitonic localized state. The solitons only couple to each other and are able to jump from one site to another as if they were trapped in a discrete lattice.Comment: 22 pages, 21 figures, technical appendices included. Webpage abstract slightly abridged. Comments are most welcom

Muon capture on nuclei: random phase approximation evaluation versus data for 6 ≤\le Z ≤\le 94 nuclei

We use the random phase approximation to systematically describe the total muon capture rates on all nuclei where they have been measured. We reproduce the experimental values on these nuclei to better than 15% accuracy using the free nucleon weak form factors and residual interactions with a mild $A$ dependency. The isospin dependence and the effects associated with shell closures are fairly well reproduced as well. However, the calculated rates for the same residual interactions would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant is employed to other than the true Gamow-Teller amplitudes. Our calculation thus suggests that no quenching is needed in the description of semileptonic weak processes involving higher multipole transitions and momentum transfer $\sim m_{\mu}$, with obvious importance to analogous weak processes.Comment: RevTeX4 10 pages, 2 figures. Revised according to referee report. Table 1 expanded. Accepted for publication in PR

Galactic abundances as a relic neutrino detection scheme

We propose to use the threshold-free process of neutrino capture on beta-decaying nuclei (NCB) using all available candidate nuclei in the Milky Way as target material in order to detect the presence of the Cosmic neutrino background. By integrating over the lifetime of the galaxy one might be able to see the effect of NCB processes as a slightly eschewed abundance ratio of selected beta-decaying nuclei. First, the candidates must be chosen so that both the mother and daughter nuclei have a lifetime comparable to that of the Milky Way or the signal could be easily washed out by additional decays. Secondly, relic neutrinos have so low energy that their de Broglie wavelengths are macroscopic and they may therefore scatter coherently on the electronic cloud of the candidate atoms. One must therefore compare the cross sections for the two processes (induced beta-decay by neutrino capture, and coherent scattering of the neutrinos on atomic nuclei) before drawing any conclusions. Finally, the density of target nuclei in the galaxy must be calculated. We assume supernovae as the only production source and approximate the neutrino density as a homogenous background. Here we perform the full calculation for 187-Re and 138-La and find that one needs abundance measurements with 24 digit precision in order to detect the effect of relic neutrinos. Or alternatively an enhancement of of the relic neutrino density by a factor of $10^{15}$ to produce an effect within the current abundance measurement precision.Comment: 16 pages, 4 figure