Time-dependent coupled-cluster method for atomic nuclei

We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method.Comment: 10 pages, 9 pdf figure

Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.Fil: Rubio García, A.. Instituto de Estructura de la Materia; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Dukelsky, J.. Consejo Superior de Investigaciones Científicas; España. Instituto de Estructura de la Materia; Españ

Shortcuts through Colocation Facilities

Network overlays, running on top of the existing Internet substrate, are of perennial value to Internet end-users in the context of, e.g., real-time applications. Such overlays can employ traffic relays to yield path latencies lower than the direct paths, a phenomenon known as Triangle Inequality Violation (TIV). Past studies identify the opportunities of reducing latency using TIVs. However, they do not investigate the gains of strategically selecting relays in Colocation Facilities (Colos). In this work, we answer the following questions: (i) how Colo-hosted relays compare with other relays as well as with the direct Internet, in terms of latency (RTT) reductions; (ii) what are the best locations for placing the relays to yield these reductions. To this end, we conduct a large-scale one-month measurement of inter-domain paths between RIPE Atlas (RA) nodes as endpoints, located at eyeball networks. We employ as relays Planetlab nodes, other RA nodes, and machines in Colos. We examine the RTTs of the overlay paths obtained via the selected relays, as well as the direct paths. We find that Colo-based relays perform the best and can achieve latency reductions against direct paths, ranging from a few to 100s of milliseconds, in 76% of the total cases; 75% (58% of total cases) of these reductions require only 10 relays in 6 large Colos.Comment: In Proceedings of the ACM Internet Measurement Conference (IMC '17), London, GB, 201

Method For Making 2-Electron Response Reduced Density Matrices Approximately N-representable

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schr\"odinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not $N$-representable. That is, the response 2-RDM does not correspond to an actual physical $N$-electron wave function. We present a new algorithm for making these non-$N$-representable 2-RDMs approximately $N$-representable, i.e. it has the right symmetry and normalization and it fulfills the $P$-, $Q$- and $G$-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties that is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between the initial 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, $Q$- and $G$-matrices are positive semidefinite, i.e. their eigenvalues are non-negative. Our method is suitable for fixing non-N-respresentable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.Comment: 13 pages, 8 figure

Diagonalization of multicomponent wave equations with a Born-Oppenheimer example

A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed

Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries

We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA) 200

Ab initio coupled-cluster theory for open-shell nuclei

We develop a new method to describe properties of truly open-shell nuclei. This method is based on single-reference coupled-cluster theory and the equation-of-motion method with extensions to nuclei with $A\pm 2$ nucleons outside a closed shell. We perform proof-of-principle calculations for the ground states of the helium isotopes $^{3-6}$He and the first excited $2^+$ state in $^6$He. The comparison with exact results from matrix diagonalization in small model spaces demonstrates the accuracy of the coupled-cluster methods. Three-particle--one-hole excitations of $^4$He play an important role for the accurate description of $^6$He. For the open-shell nucleus $^6$He, the computational cost of the method is comparable with the coupled-cluster singles-and-doubles approximation while its accuracy is similar to coupled-cluster with singles, doubles and triples excitations

An importance sampling algorithm for generating exact eigenstates of the nuclear Hamiltonian

We endow a recently devised algorithm for generating exact eigensolutions of large matrices with an importance sampling, which is in control of the extent and accuracy of the truncation of their dimensions. We made several tests on typical nuclei using a correlated basis obtained from partitioning the shell model space. The sampling so implemented allows not only for a substantial reduction of the shell model space but also for an extrapolation to exact eigenvalues and E2 strengths.Comment: A compressed file composed of a text in latex of 19 pages and 9 figures in p

Variational Hilbert space truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters

We study the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a series of finite-size clusters with features inspired by the fullerenes. Frustration due to the presence of pentagonal rings makes such structures challenging in the context of quantum Monte-Carlo methods. We use an exact diagonalization approach combined with a truncation method in which only the most important basis states of the Hilbert space are retained. We describe an efficient variational method for finding an optimal truncation of a given size which minimizes the error in the ground state energy. Ground state energies and spin-spin correlations are obtained for clusters with up to thirty-two sites without the need to restrict the symmetry of the structures. The results are compared to full-space calculations and to unfrustrated structures based on the honeycomb lattice.Comment: 22 pages and 12 Postscript figure