3,115 research outputs found
Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons
We investigate the shape of the spectrum and the spectral fluctuations of the
-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the
number of Bosons while both , the rank of the interaction,
and , the number of single-particle states, are kept fixed. We show that the
relative fluctuations of the low spectral moments do not vanish in this limit,
proving that the ensemble is non-ergodic. Numerical simulations yield spectra
which display a strong tendency towards picket-fence type. The wave functions
also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included
Supplier Corporate Social Responsibility Policies from a Strategic Perspective
Corporate Social Responsibility (CSR) is a corporate initiative to assess and take responsibility for the company\u27s effects on the environment and impact on social welfare (www.Investopedia.com). The goal of CSR is to embrace responsibility for the company\u27s actions and encourage a positive impact through its activities on the environment, consumers, employees, communities, stakeholders and all others who may also be considered stakeholders. The term generally applies to company efforts that go beyond what may be required by regulators or environmental protection groups. CSR policies function as a built-in, self-regulating mechanism whereby a business monitors and ensures its active compliance with the spirit of the law, ethical standards, and international norms. Corporate social responsibility may also be referred to as corporate citizenship and can involve incurring short-term costs that do not provide an immediate financial benefit to the company, but instead promote positive social and environmental change
Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices
We consider spinless Fermions in degenerate single-particle
levels interacting via a -body random interaction with Gaussian probability
distribution and in the limit to infinity (the embedded -body
random ensembles). We address the cases of orthogonal and unitary symmetry. We
derive a novel eigenvalue expansion for the second moment of the Hilbert-space
matrix elements of these ensembles. Using properties of the expansion and the
supersymmetry technique, we show that for , the average spectrum has
the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson
type. Using a generalization of the binary correlation approximation, we show
that for , the spectral fluctuations are Poissonian. This is
consistent with the case which can be solved explicitly. We construct
limiting ensembles which are either fully integrable or fully chaotic and show
that the -body random ensembles lie between these two extremes. Combining
all these results we find that the spectral correlations for the embedded
ensembles gradually change from Wigner-Dyson for to Poissonian for .Comment: 44 pages, 3 postscript figures, revised version including a new proof
of one of our main claim
Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
We introduce machine learning models of quantum mechanical observables of
atoms in molecules. Instant out-of-sample predictions for proton and carbon
nuclear chemical shifts, atomic core level excitations, and forces on atoms
reach accuracies on par with density functional theory reference. Locality is
exploited within non-linear regression via local atom-centered coordinate
systems. The approach is validated on a diverse set of 9k small organic
molecules. Linear scaling of computational cost in system size is demonstrated
for saturated polymers with up to sub-mesoscale lengths
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