175 research outputs found
N-body decomposition of bipartite networks
In this paper, we present a method to project co-authorship networks, that
accounts in detail for the geometrical structure of scientists collaborations.
By restricting the scope to 3-body interactions, we focus on the number of
triangles in the system, and show the importance of multi-scientists (more than
2) collaborations in the social network. This motivates the introduction of
generalized networks, where basic connections are not binary, but involve
arbitrary number of components. We focus on the 3-body case, and study
numerically the percolation transition.Comment: 5 pages, submitted to PR
Concurrence in Disordered Systems
Quantum systems exist at finite temperatures and are likely to be disordered
to some level. Since applications of quantum information often rely on
entanglement, we require methods which allow entanglement measures to be
calculated in the presence of disorder at non-zero temperatures. We demonstrate
how the disorder averaged concurrence can be calculated using thermal many-body
perturbation theory. Our technique can also be applied to other entanglement
measures. To illustrate, we find the disorder averaged concurrence of an XX
spin chain. We find that concurrence can be increased by disorder in some
parameter regimes.Comment: 14 pages, 5 figure
Magnetotransport in the Kondo model with ferromagnetic exchange interaction
We consider the transport properties in an applied magnetic field of the spin
S=1/2 Kondo model with ferromagnetic exchange coupling to electronic
reservoirs, a description relevant for the strong coupling limit of
underscreened spin S=1 Kondo impurities. Because the ferromagnetic Kondo
interaction is marginally irrelevant, perturbative methods should prove
accurate down to low energies. For the purpose of this study, we use a
combination of Majorana diagrammatic theory with Density Matrix Numerical
Renormalization Group simulations. In the standard case of antiferromagnetic
Kondo exchange, we first show that our technique recovers previously obtained
results for the T-matrix and spin relaxation at weak coupling (above the Kondo
temperature). Considering then the ferromagnetic case, we demonstrate how the
low-energy Kondo anomaly splits for arbitrary small values of the Zeeman
energy, in contrast to fully screened Kondo impurities near the strong coupling
Fermi liquid fixed point, and in agreement with recent experimental findings
for spin S=1 molecular quantum dots.Comment: 14 pages, 13 figures, minor changes in V
Finite temperature Dicke phase transition of a Bose-Einstein condensate in an optical cavity
Dicke model predicts a quantum phase transition from normal to superradiant
phases for a two-level atomic ensemble coupled with an optical cavity at zero
temperature. In a recent pioneer experiment [Nature 464, 1301 (2010)], such a
phase transition has been observed using a Bose-Einstein condensate (BEC) in an
optical cavity. Compared with the original Dicke model, the experimental system
features finite temperature and strong atom-photon nonlinear interaction in
BEC. In this Letter, we develop a finite temperature theory for the Dicke phase
transition of a BEC in an optical cavity, taking into account the atom-photon
nonlinear interaction. In addition to explaining the experimentally observed
transition from normal to superradiant phases at finite-temperature, we point
it out that a new phase, the coexistence of normal and superradient phases, was
also observed in the experiment. We show rich finite temperature phase diagrams
existing in the experimental system by tuning various experimental parameters.
We find that the specific heat of the BEC can serve as a powerful tool for
probing various phases.Comment: 5 pages, 5 figure
Remarks on hard Lefschetz conjectures on Chow groups
We propose two conjectures of Hard Lefschetz type on Chow groups and prove
them for some special cases. For abelian varieties, we shall show they are
equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic
Stochastic evaluation of second-order Dyson self-energies
A stochastic method is proposed that evaluates the second-order perturbation corrections to the Dyson self-energies of a molecule (i.e., quasiparticle energies or correlated ionization potentials and electron affinities) directly and not as small differences between two large, noisy quantities. With the aid of a Laplace transform, the usual sum-of-integral expressions of the second-order self-energy in many-body Greens function theory are rewritten into a sum of just four 13-dimensional integrals, 12-dimensional parts of which are evaluated by Monte Carlo integration. Efficient importance sampling is achieved with the Metropolis algorithm and a 12-dimensional weight function that is analytically integrable, is positive everywhere, and cancels all the singularities in the integrands exactly and analytically. The quasiparticle energies of small molecules have been reproduced within a few mEh of the correct values with 108 Monte Carlo steps. Linear-to-quadratic scaling of the size dependence of computational cost is demonstrated even for these small molecules.open9
Investigation of lunar surface chemical contamination by LEM descent engine and associated equipment Final report
Lunar surface contamination from LEM rocket exhaust - methods of minimizing sample contaminatio
Temperature dependence of the electronic structure of semiconductors and insulators
The renormalization of electronic eigenenergies due to electron-phonon
coupling is sizable in many materials with light atoms. This effect, often
neglected in ab-initio calculations, can be computed using the
perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic
harmonic approximation. After a short description of the numerous recent
progresses in this field, and a brief overview of the theory, we focus on the
issue of phonon wavevector sampling convergence, until now poorly understood.
Indeed, the renormalization is obtained numerically through a q-point sampling
inside the BZ. For q-points close to G, we show that a divergence due to
non-zero Born effective charge appears in the electron-phonon matrix elements,
leading to a divergence of the integral over the BZ for band extrema. Although
it should vanish for non-polar materials, unphysical residual Born effective
charges are usually present in ab-initio calculations. Here, we propose a
solution that improves the coupled q-point convergence dramatically. For polar
materials, the problem is more severe: the divergence of the integral does not
disappear in the adiabatic harmonic approximation, but only in the
non-adiabatic harmonic approximation. In all cases, we study in detail the
convergence behavior of the renormalization as the q-point sampling goes to
infinity and the imaginary broadening parameter goes to zero. This allows
extrapolation, thus enabling a systematic way to converge the renormalization
for both polar and non-polar materials. Finally, the adiabatic and
non-adiabatic theory, with corrections for the divergence problem, are applied
to the study of five semiconductors and insulators: a-AlN, b-AlN, BN, diamond
and silicon. For these five materials, we present the zero-point
renormalization, temperature dependence, phonon-induced lifetime broadening and
the renormalized electronic bandstructure.Comment: 27 pages and 26 figure
Vertex Corrections and the Korringa Ratio in Strongly Correlated Electron Materials
We show that the Korringa ratio, associated with nuclear magnetic resonance
in metals, is unity if vertex corrections for the dynamic spin susceptibility
are negligible and the hyperfine coupling is momentum independent. In the
absence of vertex corrections we also find a Korringa behaviour for , the
nuclear spin relaxation rate, i.e., , and a temperature
independent Knight shift. These results are independent of the form and
magnitude of the self-energy (so far as is consistent with neglecting vertex
corrections) and of the dimensionality of the system.Comment: 5 pages. accepted for publication in J. Phys.: Condens. Matte
Liquid-gas phase transition in nuclear matter from realistic many-body approaches
The existence of a liquid-gas phase transition for hot nuclear systems at
subsaturation densities is a well established prediction of finite temperature
nuclear many-body theory. In this paper, we discuss for the first time the
properties of such phase transition for homogeneous nuclear matter within the
Self-Consistent Green's Functions approach. We find a substantial decrease of
the critical temperature with respect to the Brueckner-Hartree-Fock
approximation. Even within the same approximation, the use of two different
realistic nucleon-nucleon interactions gives rise to large differences in the
properties of the critical point.Comment: REVTEX4 - 23 pages, 5 figures, 1 table; corrections added, final
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