Existence criteria for stabilization from the scaling behaviour of ionization probabilities

We provide a systematic derivation of the scaling behaviour of various quantities and establish in particular the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as consistency check in explicit analytical expressions, in perturbation theory, in the Kramers-Henneberger and Floquet approximation, in upper and lower bound estimates and fully numerical solutions of the time dependent Schroedinger equation. The scaling invariance leads to a differential equation which has to be satisfied by the ionization probability and which yields an alternative criterium for the existence of atomic bound state stabilization.Comment: 12 pages of Latex, one figur

The quantum brachistochrone problem for non-Hermitian Hamiltonians

Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the time-evolution operator is taken to be non-Hermitian but PT-symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which PT-symmetry is completely broken, i.e. dissipative systems. We observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time-evolution operator associated with a non-Hermitian Hamiltonian. It is not essential that this Hamiltonian is PT-symmetric

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

Spin-dependent beating patterns in thermoelectric properties: Filtering the carriers of the heat flux in a Kondo adatom system

We theoretically investigate the thermoelectric properties of a spin-polarized two-dimensional electron gas hosting a Kondo adatom hybridized with an STM tip. Such a setup is treated within the single-impurity Anderson model in combination with the atomic approach for the Green's functions. Due to the spin dependence of the Fermi wavenumbers the electrical and thermal conductances, together with thermopower and Lorenz number reveal beating patterns as function of the STM tip position in the Kondo regime. In particular, by tuning the lateral displacement of the tip with respect to the adatom vicinity, the temperature and the position of the adatom level, one can change the sign of the Seebeck coefficient through charge and spin. This opens a possibility of the microscopic control of the heat flux analogously to that established for the electrical current

Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation

We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of a non-Hermitian Hamiltonian and pay particular attention to the role played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate the general formalism with three explicit examples: i) the generalized Swanson Hamiltonians, which constitute non-Hermitian extensions of anharmonic oscillators, ii) the spiked harmonic oscillator, which exhibits explicit supersymmetry and iii) the -x^4-potential, which serves as a toy model for the quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos correcte

The contribution of secondary eclipses as astrophysical false positives to exoplanet transit surveys

We investigate in this paper the astrophysical false-positive configuration in exoplanet-transit surveys that involves eclipsing binaries and giant planets which present only a secondary eclipse, as seen from the Earth. To test how an eclipsing binary configuration can mimic a planetary transit, we generate synthetic light curve of three examples of secondary-only eclipsing binary systems that we fit with a circular planetary model. Then, to evaluate its occurrence we model a population of binaries in double and triple system based on binary statistics and occurrence. We find that 0.061% +/- 0.017% of main-sequence binary stars are secondary-only eclipsing binaries mimicking a planetary transit candidate down to the size of the Earth. We then evaluate the occurrence that an occulting-only giant planet can mimic an Earth-like planet or even smaller planet. We find that 0.009% +/- 0.002% of stars harbor a giant planet that present only the secondary transit. Occulting-only giant planets mimic planets smaller than the Earth that are in the scope of space missions like Kepler and PLATO. We estimate that up to 43.1 +/- 5.6 Kepler Objects of Interest can be mimicked by this new configuration of false positives, re-evaluating the global false-positive rate of the Kepler mission from 9.4% +/- 0.9% to 11.3% +/- 1.1%. We note however that this new false-positive scenario occurs at relatively long orbital period compared with the median period of Kepler candidates.Comment: 9 pages, 4 figures, accepted for publication in A&