4,646 research outputs found
Transport through a vibrating quantum dot: Polaronic effects
We present a Green's function based treatment of the effects of
electron-phonon coupling on transport through a molecular quantum dot in the
quantum limit. Thereby we combine an incomplete variational Lang-Firsov
approach with a perturbative calculation of the electron-phonon self energy in
the framework of generalised Matsubara Green functions and a Landauer-type
transport description. Calculating the ground-state energy, the dot
single-particle spectral function and the linear conductance at finite carrier
density, we study the low-temperature transport properties of the vibrating
quantum dot sandwiched between metallic leads in the whole electron-phonon
coupling strength regime. We discuss corrections to the concept of an
anti-adiabatic dot polaron and show how a deformable quantum dot can act as a
molecular switch.Comment: 10 pages, 8 figures, Proceedings of "Progress in Nonequilibrium
Green's Function IV" Conference, Glasgow 200
Hooke's law correlation in two-electron systems
We study the properties of the Hooke's law correlation energy (\Ec),
defined as the correlation energy when two electrons interact {\em via} a
harmonic potential in a -dimensional space. More precisely, we investigate
the ground state properties of two model systems: the Moshinsky atom (in
which the electrons move in a quadratic potential) and the spherium model (in
which they move on the surface of a sphere). A comparison with their Coulombic
counterparts is made, which highlights the main differences of the \Ec in
both the weakly and strongly correlated limits. Moreover, we show that the
Schr\"odinger equation of the spherium model is exactly solvable for two values
of the dimension (), and that the exact wave function is
based on Mathieu functions.Comment: 7 pages, 5 figure
Two electrons on a hypersphere: a quasi-exactly solvable model
We show that the exact wave function for two electrons, interacting through a
Coulomb potential but constrained to remain on the surface of a
-sphere (), is a polynomial in the
interelectronic distance for a countably infinite set of values of the
radius . A selection of these radii, and the associated energies, are
reported for ground and excited states on the singlet and triplet manifolds. We
conclude that the model bears the greatest similarity to normal
physical systems.Comment: 4 pages, 0 figur
Ground state of two electrons on concentric spheres
We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79},
062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on
concentric spheres with different radii. The strengths and weaknesses of
several electronic structure models are analyzed, ranging from the mean-field
approximation (restricted and unrestricted Hartree-Fock solutions) to
configuration interaction expansion, leading to near-exact wave functions and
energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the
asymptotic expansion for the large-spheres regime are also considered. We also
study the position intracules derived from approximate and exact wave
functions. We find evidence for the existence of a long-range Coulomb hole in
the large-spheres regime, and infer that unrestricted Hartree-Fock theory
over-localizes the electrons.Comment: 10 pages, 10 figure
High-density correlation energy expansion of the one-dimensional uniform electron gas
We show that the expression of the high-density (i.e small-) correlation
energy per electron for the one-dimensional uniform electron gas can be
obtained by conventional perturbation theory and is of the form \Ec(r_s) =
-\pi^2/360 + 0.00845 r_s + ..., where is the average radius of an
electron. Combining these new results with the low-density correlation energy
expansion, we propose a local-density approximation correlation functional,
which deviates by a maximum of 0.1 millihartree compared to the benchmark DMC
calculations.Comment: 7 pages, 2 figures, 3 tables, accepted for publication in J. Chem.
Phy
Is there a Jordan geometry underlying quantum physics?
There have been several propositions for a geometric and essentially
non-linear formulation of quantum mechanics. From a purely mathematical point
of view, the point of view of Jordan algebra theory might give new strength to
such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of
the algebra of observables, in the same way as Lie groups belong to the Lie
part. Both the Lie geometry and the Jordan geometry are well-adapted to
describe certain features of quantum theory. We concentrate here on the
mathematical description of the Jordan geometry and raise some questions
concerning possible relations with foundational issues of quantum theory.Comment: 30 page
Invariance of the correlation energy at high density and large dimension in two-electron systems
We prove that, in the large-dimension limit, the high-density correlation
energy \Ec of two opposite-spin electrons confined in a -dimensional space
and interacting {\em via} a Coulomb potential is given by \Ec \sim -1/(8D^2)
for any radial confining potential . This result explains the observed
similarity of \Ec in a variety of two-electron systems in three-dimensional
space.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let
Infiltration/cure modeling of resin transfer molded composite materials using advanced fiber architectures
A model was developed which can be used to simulate infiltration and cure of textile composites by resin transfer molding. Fabric preforms were resin infiltrated and cured using model generated optimized one-step infiltration/cure protocols. Frequency dependent electromagnetic sensing (FDEMS) was used to monitor in situ resin infiltration and cure during processing. FDEMS measurements of infiltration time, resin viscosity, and resin degree of cure agreed well with values predicted by the simulation model. Textile composites fabricated using a one-step infiltration/cure procedure were uniformly resin impregnated and void free. Fiber volume fraction measurements by the resin digestion method compared well with values predicted using the model
Note on Moufang-Noether currents
The derivative Noether currents generated by continuous Moufang
tranformations are constructed and their equal-time commutators are found. The
corresponding charge algebra turns out to be a birepresentation of the tangent
Mal'ltsev algebra of an analytic Moufang loop.Comment: LaTeX2e, 6 pages, no figures, presented on "The XVth International
Colloquium on Integrable Systems and Quantum Symmetries, Prague, 15-17 June,
2006
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