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Different approaches for considering barrier crossing times are analyzed, with special emphasis on recent experiments which attempt to measure what is commonly referred to as the Larmor tunneling time. We show that that these experiments cannot reveal the Larmor time, due to the finite energy width of the incident particles. The Larmor time, which measures changes in spin polarization, is classified together with other measurements such as the Buttiker–Landauer oscillating barrier time as indirect measurements of interaction times of scattered particles. In contrast, we present a direct quantum mechanical measure of a barrier crossing time taken to be the difference between the mean flight time for a particle transmitted through a potential barrier incident on a screen and the time it would take to reach the same screen without the barrier. These metrics are asymptotic, in the sense that they infer a time from a measurement after the scattering event is over, whereas other measures like the dwell time are local. Some time measures are well-defined only for incident states which are monochromatic in energy, others are well-defined also for incident wavepackets whose incident energy width is finite. In this paper we compare the different approaches to conclude that only the flight time can be used to answer the provocative (but ultimately ill-posed) question: how much time does it take to tunnel through a barrier? [ABSTRACT FROM AUTHOR]

Wavepacket tunneling, in the relativistic limit, is studied via solutions to the Dirac equation for a square barrier potential. Specifically, the arrival time distribution (the time-dependent flux) is computed for wavepackets initiated far away from the barrier, and whose momentum is well below the threshold for above-barrier transmission. The resulting distributions exhibit peaks at shorter times than those of photons with the same initial wavepacket transmitting through a vacuum. However, this apparent superluminality in time is accompanied by very low transmission probabilities. We discuss these observations, and related observations by other authors, in the context of published objections to the notion that tunneling can be superluminal in time. We find that many of these objections are not consistent with our observations, and conclude that post-selected (for transmission) distributions of arrival times can be superluminal. However, the low probability of tunneling means a photon will most likely be seen first and therefore the superluminality does not imply superluminal signaling. [ABSTRACT FROM AUTHOR]

Results for elastic atom-atom scattering are obtained as a first practical application of RmatReact, a new code for generating high-accuracy scattering observables from potential energy curves. RmatReact has been created in response to new experimental methods which have paved the way for the routine production of ultracold (μK) atoms and molecules, and hence the experimental study of chemical reactions involving only a small number of partial waves. Elastic scattering between argon atoms is studied here. There is an unresolved discrepancy between different potential energy curves which give different numbers of vibrational bound states and different scattering lengths for the dimer. Depending on the number of bound states, the scattering length is either large and positive or large and negative. Scattering observables, specifically the scattering length, effective range, and partial and total cross-sections, are computed at low collision energies and compared to previous results. In general, good agreement is obtained, although our full scattering treatment yields resonances which are slightly lower in energy and narrower than previous determinations using the same potential energy curve. [ABSTRACT FROM AUTHOR]

Accurate and complete rotational, rotational-vibrational and rotational-vibrational-electronic line lists are calculated for sodium hydride: both the NaH and NaD isotopologues are considered. These line lists cover all ro-vibrational states of the ground (X ¹Σ+) and first excited (A ¹Σ+) electronic states. The calculations use available spectroscopically-determined potential energy curves and new high-quality, ab initio dipole moment curves. Partition functions for both isotopologues are calculated and the effect of quasi-bound states is considered. The resulting line lists are suitable for temperatures up to about 7000 K and are designed for studies of exoplanet atmospheres, brown dwarfs and cool stars. In particular, the NaH A - X band is found to show a broad absorption feature at about 385 nm which should provide a signature for the molecule. All partition functions, lines and transitions are available as supplementary information to this article and at www.exomol.com. [ABSTRACT FROM AUTHOR]

Accurate and complete rotational, rotational-vibrational and rotational-vibrational-electronic line lists are calculated for sodium hydride: both the NaH and NaD isotopologues are considered. These line lists cover all ro-vibrational states of the ground (A¹ Σ+) and first excited (X¹ Σ+) electronic states. The calculations use available spectroscopically-determined potential energy curves and new high-quality, ab initio dipole moment curves. Partition functions for both isotopologues are calculated and the effect of quasi-bound states is considered. The resulting line lists are suitable for temperatures up to about 7000 K and are designed for studies of exoplanet atmospheres, brown dwarfs and cool stars. In particular, the NaH A -- X band is found to show a broad absorption feature at about 385 nm which should provide a signature for the molecule. All partition functions, lines and transitions are available as supplementary information to this article and at www.exomol.com. [ABSTRACT FROM AUTHOR]

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ -barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a 'screen' is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ -barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles. [ABSTRACT FROM AUTHOR]