Hartree-Fock and Many-Body Perturbation Theory with Correlated Realistic NN-Interactions

We employ correlated realistic nucleon-nucleon interactions for the description of nuclear ground states throughout the nuclear chart within the Hartree-Fock approximation. The crucial short-range central and tensor correlations, which are induced by the realistic interaction and cannot be described by the Hartree-Fock many-body state itself, are included explicitly by a state-independent unitary transformation in the framework of the unitary correlation operator method (UCOM). Using the correlated realistic interaction V_UCOM resulting from the Argonne V18 potential, bound nuclei are obtained already on the Hartree-Fock level. However, the binding energies are smaller than the experimental values because long-range correlations have not been accounted for. Their inclusion by means of many-body perturbation theory leads to a remarkable agreement with experimental binding energies over the whole mass range from He-4 to Pb-208, even far off the valley of stability. The observed perturbative character of the residual long-range correlations and the apparently small net effect of three-body forces provides promising perspectives for a unified nuclear structure description.Comment: 14 pages, 8 figures, 3 tables, using REVTEX

Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

Neutrino Masses and the Gluino Axion Model

We extend the recently proposed gluino axion model to include neutrino masses. We discuss how the canonical seesaw model and the Higgs triplet model may be realized in this framework. In the former case, the heavy singlet neutrinos are contained in superfields which do not have any vacuum expectation value, whereas the gluino axion is contained in one which does. We also construct a specific renormalizable model which realizes the mass scale relationship $M_{SUSY} \sim f_a^2/M_U$, where $f_a$ is the axion decay constant and $M_U$ is a large effective mass parameter.Comment: 8 pages, no figur

Chiral Symmetry Breaking and Pion Wave Function

We consider here chiral symmetry breaking through nontrivial vacuum structure with quark antiquark condensates. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode in vacuum. We illustrate the above with Nambu Jona-Lasinio model to calculate different pionic properties in terms of the vacuum structure for breaking of exact or approximate chiral symmetry, as well as the condensate fluctuations giving rise to $\sigma$ mesons.Comment: latex, revtex, 16 page

Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate

We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from $\hat{G}$, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an "improper" structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.Comment: 9 pages, 6 gigure

Once again on electromagnetic properties of a domain wall interacting with charged fermions

The response to a magnetic flux is considered of the vacuum state of charged Dirac fermions interacting with a domain wall made of a neutral spinless field in (3+1) dimensions with the fermion mass having a phase variation across the wall. It is pointed out that due to simple C parity arguments the spontaneous magnetization for this system is necessarily zero, thus invalidating some claims to the contrary in the literature. The cancellation of the spontaneous magnetization is explicitly demonstrated in a particular class of models. The same calculation produces a general formula for the electric charge density induced by the magnetic flux -- an effect previously discussed in the literature for axionic domain walls. The distribution of the induced charge is calculated in specific models.Comment: 15 page

Coupling curvature to a uniform magnetic field; an analytic and numerical study

The Schrodinger equation for an electron near an azimuthally symmetric curved surface $\Sigma$ in the presence of an arbitrary uniform magnetic field $\mathbf B$ is developed. A thin layer quantization procedure is implemented to bring the electron onto $\Sigma$, leading to the well known geometric potential $V_C \propto h^2-k$ and a second potential that couples $A_N$, the component of $\mathbf A$ normal to $\Sigma$ to mean surface curvature, as well as a term dependent on the normal derivative of $A_N$ evaluated on $\Sigma$. Numerical results in the form of ground state energies as a function of the applied field in several orientations are presented for a toroidal model.Comment: 12 pages, 3 figure

High-precision calculations of In I and Sn II atomic properties

We use all-order relativistic many-body perturbation theory to study 5s^2 nl configurations of In I and Sn II. Energies, E1-amplitudes, and hyperfine constants are calculated using all-order method, which accounts for single and double excitations of the Dirac-Fock wave functions.Comment: 10 pages, accepted to PRA; v2: Introduction changed, references adde

On The Existence of Roton Excitations in Bose Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

Within the last decade, artificially engineered Bose Einstein Condensation has been achieved in atomic systems. Bose Einstein Condensates are superfluids just like bosonic Helium is and all interacting bosonic fluids are expected to be at low enough temperatures. One difference between the two systems is that superfluid Helium exhibits roton excitations while Bose Einstein Condensates have never been observed to have such excitations. The reason for the roton minimum in Helium is its proximity to a solid phase. The roton minimum is a consequence of enhanced density fluctuations at the reciprocal lattice vector of the stillborn solid. Bose Einstein Condensates in atomic traps are not near a solid phase and therefore do not exhibit roton minimum. We conclude that if Bose Einstein Condensates in an optical lattice are tuned near a transition to a Mott insulating phase, a roton minimum will develop at a reciprocal lattice vector of the lattice. Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition.Comment: 4 pages, 5 figure

Chiral non-linear sigma-models as models for topological superconductivity

We study the mechanism of topological superconductivity in a hierarchical chain of chiral non-linear sigma-models (models of current algebra) in one, two, and three spatial dimensions. The models have roots in the 1D Peierls-Frohlich model and illustrate how the 1D Frohlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a point-like topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.Comment: 5 pages, revtex, no figure