Among the numerous concepts of time in quantum scattering, Smith’s dwell time [F. T. Smith, Phys. Rev. 118, 349–356 (1960)] and Eisenbud & Wigner’s time delay [E. P. Wigner, Phys. Rev. 98, 145 (1955)] are the most well established. The dwell time represents the amount of time spent by the particle inside a given coordinate range (typically a potential barrier interaction region), while the time delay measures the excess time spent in the interaction region because of the potential. In this paper, we use the exact trajectory-ensemble reformulation of quantum mechanics, recently proposed by one of the authors (Poirier), to study how tunneling and reflection unfold over time, in a one-dimensional rectangular potential barrier. Among other dynamical details, the quantum trajectory approach provides an extremely robust, accurate, and straightforward method for directly computing the dwell time and time delay, from a single quantum trajectory. The resultant numerical method is highly efficient, and in the case of the time delay, completely obviates the traditional need to energy-differentiate the scattering phase shift. In particular, the trajectory variables provide a simple expression for the time delay that disentangles the contribution of the self-interference delay. More generally, quantum trajectories provide interesting physical insight into the tunneling process.

In this work we propose an exact derivation of the Hamilton formulation of quantum mechanical stationary scattering in one-dimensional curved space.

Diabatic potential energy curves for the $^4{\Pi} $ states of SH

The multi-scale approaches of theoretical chemistry to understand the molecular complexity of the Interstellar medium

Context. Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular 7Li, and the evolution of their rotation rates. For the Sun, inversions of helioseismic data indicate that the radial profile of angular velocity in its radiative zone is nearly uniform, which implies the existence of angular momentum transport mechanisms that are efficient over evolutionary timescales. While there are many independent transport models for angular momentum and chemical species, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the present-day observations of solar lithium abundances and radial rotation profiles. Aims. We explore how additional transport processes can improve the agreement between evolutionary models of rotating stars and observations for 7Li depletion, the rotation evolution of solar-type stars, and the solar rotation profile. Methods. Models of solar-type stars are computed including atomic diffusion and rotation-induced mixing with the code STAREVOL. We explore different additional transport processes for chemicals and for angular momentum such as penetrative convection, tachocline mixing, and additional turbulence. We constrain the resulting models by simultaneously using the evolution of the sur- face rotation rate and 7Li abundance in the solar-type stars of open clusters with different ages, and the solar surface and internal rotation profile as inverted from helioseismology when our models reach the age of the Sun. Results. We show the relevance of penetrative convection for the depletion of 7Li in pre-main sequence and early main sequence stars. The rotational dependence of the depth of penetrative convection yields an anti-correlation between the initial rotation rate and7Li depletion in our models of solar-type stars that is in agreement with the observed trend. Simultaneously, the addition of an ad hoc vertical viscosity νadd leads to efficient transport of angular momentum between the core and the envelope during the main sequence evolution and to solar-type models that match the observed profile of the Sun. We also self-consistently compute for the first time the thickness of the tachocline and find that it is compatible with helioseismic estimations at the age of the Sun, but we highlight that the associated turbulence does not allow the observed 7Li depletion to be reproduced. The main sequence depletion of 7Li in solar-type stars is only reproduced when adding a parametric turbulent mixing below the convective envelope. Conclusions. The need for additional transport processes in stellar evolution models for both chemicals and angular momentum in addition to atomic diffusion, meridional circulation, and turbulent shear is confirmed. We identify the rotational dependence of the penetrative convection as a key process. Two additional and distinct parametric turbulent mixing processes (one for angular momentum and one for chemicals) are required to simultaneously explain the observed surface 7Li depletion and the solar internal rotation profile. We highlight the need of additional constraints for the internal rotation of young solar-type stars and also for the beryllium abundances of open clusters in order to test our predictions.

The goal of this work is to study magnetic fields of the cool, eclipsing binary star UV Piscium (UV Psc). This system contains two active late-type stars, UV Psc A (G5V) and B (K3V). To obtain a complete picture, the properties of both global and local magnetic field structures are studied for both components. High-resolution intensity and circular polarisation spectra, collected in 2016 with the ESPaDOnS spectropolarimeter at the CFHT, were used to analyse the magnetic field of UV Psc. To increase the signal-to-noise ratio, the multi-line technique of least-squares deconvolution (LSD) was used to obtain average Stokes IV profiles. Then, a Zeeman-Doppler imaging (ZDI) code was employed to obtain the large-scale magnetic field topology and brightness distribution for both components of UV Psc. In addition, the small-scale magnetic fields, not visible to ZDI, were studied using the Zeeman intensification of Fe I lines. Maps of the surface magnetic field for both components of UV Psc were obtained, the large-scale magnetic fields feature strong toroidal and non-axisymetric components. UV Psc A and B have average global field strengths of 137 G and 88 G, respectively. The small-scale fields are notably stronger, with average strengths of 2.5 and 2.2 kG, respectively. Our results are in agreement with previous studies of partly-convective stars. Overall, UV Psc A has a stronger magnetic field compared to UV Psc B. Due to the eclipsing binary geometry, certain magnetic field features are not detectable using circular polarisation only. An investigation into theoretical linear polarisation profiles shows that they could be used to reveal antisymmetric components of the magnetic field. This result also has implications for the study of exoplanetary transit hosts.