The Cumulant Expansion for the Anderson Lattice with Finite U: The Completeness Problem

``Completeness'' (i.e. probability conservation) is not usually satisfied in the cumulant expansion of the Anderson lattice when a reduced state space is employed for $U\to \infty$. To understand this result, the well known ``Chain'' approximation is first calculated for finite $U$, followed by taking $U\to \infty$. Completeness is recovered by this procedure, but this result hides a serious inconsistency that causes completeness failure in the reduced space calculation. Completeness is satisfied and the inconsistency is removed by choosing an adequate family of diagrams. The main result of this work is that using a reduced space of relevant states is as good as using the whole space.Comment: Latex 22 pages, 6 figures with postscript files attached, accepted for publication in the Int. J. of Mod. Phys. B (1998). Subject field : Strongly Correlated System

Can stellar activity make a planet seem misaligned?

Several studies have shown that the occultation of stellar active regions by the transiting planet can generate anomalies in the high-precision transit light curves, and these anomalies may lead to an inaccurate estimate of the planetary parameters (e.g., the planet radius). Since the physics and geometry behind the transit light curve and the Rossiter- McLaughlin effect (spectroscopic transit) are the same, the Rossiter-McLaughlin observations are expected to be affected by the occultation of stellar active regions in a similar way. In this paper we perform a fundamental test on the spin-orbit angles as derived by Rossiter-McLaughlin measurements, and we examine the impact of the occultation of stellar active regions by the transiting planet on the spin-orbit angle estimations. Our results show that the inaccurate estimation on the spin-orbit angle due to stellar activity can be quite significant (up to 30 degrees), particularly for the edge-on, aligned, and small transiting planets. Therefore, our results suggest that the aligned transiting planets are the ones that can be easily misinterpreted as misaligned owing to the stellar activity. In other words, the biases introduced by ignoring stellar activity are unlikely to be the culprit for the highly misaligned systems.Comment: 8 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules

The relation between high-harmonic spectra and the geometry of the molecular orbitals in position and momentum space is investigated. In particular we choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such that the highest occupied molecular orbital of the former exhibit at least one nodal plane. The imprint of such planes is a strong suppression in the harmonic spectra, for particular alignment angles. We are able to identify two distinct types of nodal planes. If the nodal planes are determined by the atomic wavefunctions only, the angle for which the yield is suppressed will remain the same for both types of molecules. In contrast, if they are determined by the linear combination of atomic orbitals at different centers in the molecule, there will be a shift in the angle at which the suppression occurs for the heteronuclear molecules, with regard to their homonuclear counterpart. This shows that, in principle, molecular imaging, which uses the homonuclear molecule as a reference and enables one to observe the wavefunction distortions in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order to comply with the arXiv size requirement

Tuning of heat and charge transport by Majorana fermions

We investigate theoretically thermal and electrical conductances for the system consisting of a quantum dot (QD) connected both to a pair of Majorana fermions residing the edges of a Kitaev wire and two metallic leads. We demonstrate that both quantities reveal pronounced resonances, whose positions can be controlled by tuning of an asymmetry of the couplings of the QD and a pair of MFs. Similar behavior is revealed for the thermopower, Wiedemann-Franz law and dimensionless thermoelectric figure of merit. The considered geometry can thus be used as a tuner of heat and charge transport assisted by MFs