Complex coupled-cluster approach to an ab-initio description of open quantum systems

We develop ab-initio coupled-cluster theory to describe resonant and weakly bound states along the neutron drip line. We compute the ground states of the helium chain 3-10He within coupled-cluster theory in singles and doubles (CCSD) approximation. We employ a spherical Gamow-Hartree-Fock basis generated from the low-momentum N3LO nucleon-nucleon interaction. This basis treats bound, resonant, and continuum states on equal footing, and is therefore optimal for the description of properties of drip line nuclei where continuum features play an essential role. Within this formalism, we present an ab-initio calculation of energies and decay widths of unstable nuclei starting from realistic interactions.Comment: 4 pages, revtex

Medium-mass nuclei from chiral nucleon-nucleon interactions

We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the "bare" chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.Comment: 5 pages, 5 figure

Comment on "Statistical Mechanics of Non-Abelian Chern-Simons Particles"

The second virial coefficient for non-Abelian Chern-Simons particles is recalculated. It is shown that the result is periodic in the flux parameter just as in the Abelian theory.Comment: 3 pages, latex fil

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding $10^{10}$ on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to $N_\mathrm{max} = 22$ and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.Comment: Minor revisions.Accepted for publication in Physical Review

Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

Computation of spectroscopic factors with the coupled-cluster method

We present a calculation of spectroscopic factors within coupled-cluster theory. Our derivation of algebraic equations for the one-body overlap functions are based on coupled-cluster equation-of-motion solutions for the ground and excited states of the doubly magic nucleus with mass number $A$ and the odd-mass neighbor with mass $A-1$. As a proof-of-principle calculation, we consider $^{16}$O and the odd neighbors $^{15}$O and $^{15}$N, and compute the spectroscopic factor for nucleon removal from $^{16}$O. We employ a renormalized low-momentum interaction of the $V_{\mathrm{low-}k}$ type derived from a chiral interaction at next-to-next-to-next-to-leading order. We study the sensitivity of our results by variation of the momentum cutoff, and then discuss the treatment of the center of mass.Comment: 8 pages, 6 figures, 3 table