102 research outputs found
Superatom molecular orbitals: a new type of long-lived electronic states
We present ab initio calculations of the quasiparticle decay times in a
Buckminsterfullerene based on the many-body perturbation theory. A particularly
lucid representation arises when the broadening of the quasiparticle states is
plotted in the angular momentum and energy coordinates. In this representation
the main spectroscopic features of the fullerene consist of two occupied nearly
parabolic bands, and delocalized plane-wave-like unoccupied states with a few
long-lived electronic states (the superatom molecular orbitals, SAMOs) embedded
in the continuum of Fermi-liquid states. SAMOs have been recently uncovered
experimentally by M. Feng, J. Zhao, and H. Petek [Science 320, 359 (2008)]
using scanning tunneling spectroscopy. The present calculations offer an
explanation of their unusual stability and unveil their long-lived nature
making them good candidates for applications in the molecular electronics. From
the fundamental point of view these states illustrate a concept of the
Fock-space localization [B. L. Altshuler, Y. Gefen, A. Kamenev, and L. S.
Levitov, Phys. Rev. Lett. 78, 2803 (1997)] with properties drastically
different from the Fermi-liquid excitations
1, 2, and 6 qubits, and the Ramanujan-Nagell theorem
A conjecture of Ramanujan that was later proved by Nagell is used to show on
the basis of matching dimensions that only three -qubit systems, for , can share an isomorphism of their symmetry groups with the rotation
group of corresponding dimensions . Topological analysis, however,
rules out the last possibility
Taming singularities of the diagrammatic many-body perturbation theory
In a typical scenario the diagrammatic many-body perturbation theory
generates asymptotic series. Despite non-convergence, the asymptotic expansions
are useful when truncated to a finite number of terms. This is the reason for
popularity of leading-order methods such as approximation in condensed
matter, molecular and atomic physics. Emerging higher-order implementations
suffer from the appearance of nonsimple poles in the frequency-dependent
Green's functions and negative spectral densities making self-consistent
determination of the electronic structure impossible. Here a method based on
the Pad\'e approximation for overcomming these difficulties is proposed and
applied to the Hamiltonian describing a core electron coupled to a single
plasmonic excitation. By solving the model purely diagrammatically, expressing
the self-energy in terms of combinatorics of chord diagrams, and regularizing
the diverging perturbative expansions using the Pad\'e approximation the
spectral function is determined self-consistently using 3111 diagrams up to the
sixth order
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