The Interplay between Tunneling and Parity Violation in Chiral Molecules.

In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund's paradox, with emphasis on mean-field theory and decoherence.

The Electron-Phonon Interaction at Vicinal Metal Surfaces Measured with Helium Atom Scattering.

Recently, it was demonstrated that inelastic helium atom scattering from conducting surfaces provides a direct measurement of the surface electron-phonon coupling constant (mass enhancement factor λ) via the temperature or the incident wave vector dependence of the Debye-Waller exponent. Here, previous published as well as unpublished helium atom scattering diffraction data from the vicinal surfaces of copper (Cu(11α), with α = 3, 5, 7) and aluminum (Al(221) and Al(332)) were analyzed to determine λ. The results suggested an enhancement with respect to the corresponding data for the low-index surfaces (111) and (001) above the roughening transition temperature. The specific role of steps compared to that of terraces is briefly discussed.

Recent Developments in Kramers' Theory of Reaction Rates.

In this short review, we provide an update of recent developments in Kramers' theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers' theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.

The role of high-energy phonons in electron-phonon interaction at conducting surfaces with helium-atom scattering.

In previous works it has been shown that the Debye-Waller (DW) exponent for Helium atom specular reflection from a conducting surface, when measured as a function of temperature in the linear high-temperature regime, allows for the determination of the surface electron-phonon coupling. However, there exist a number of experimental measurements that exhibit non-linearities in the DW exponent as a function of the surface temperature. Such non-linearities have been suggested as due to vibrational anharmonicity or a temperature dependence of the surface carrier concentration. In this work, it is suggested, on the basis of a few recent experimental data, that the deviations from linearity of the DW exponent temperature-dependence, as observed for conducting surfaces or supported metal overlayers with the present high-resolution He-atom scattering, permit to single out the specific role of high-energy phonons in the surface electron-phonon mass-enhancement factor.

Perturbation theory of scattering for grazing-incidence fast-atom diffraction.

Recent grazing-incidence, fast atom diffraction (GIFAD) experiments have highlighted the well known observation that the distance between classical rainbow angles depends on the incident energy. The GIFAD experiments imply an incident vertical scattering angle, facilitating an analytic analysis using classical perturbation theory, which leads to the conclusion that the so called "dynamic corrugation" amplitude, as defined by Bocan et al., Phys. Rev. Lett., 2020 125, 096101 is, within first-order perturbation theory, proportional to the tangent of the rainbow angle. Therefore it provides no further information about the interaction than is gleaned from the rainbow angle and its energy dependence. Perhaps more importantly, the resulting analytic theory reveals how the energy dependence of rainbow angles may be inverted into information on the force field governing the interaction of the incident projectile with the surface.

The Influence of the Symmetry of Identical Particles on Flight Times.

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.

Inter-adsorbate forces and coherent scattering in helium spin-echo experiments.

In studies of dynamical systems, helium atoms scatter coherently from an ensemble of adsorbates as they diffuse on the surface. The results give information on the co-operative behaviour of interacting adsorbates and thus include the effects of both adsorbate-substrate and adsorbate-adsorbate interactions. Here, we discuss a method to disentangle the effects of interactions between adsorbates from those with the substrate. The result gives an approximation to observations that would be obtained if the scattering was incoherent. Information from the experiment can therefore be used to distinguish more clearly between long-range inter-adsorbate forces and the short range effects arising from the local lattice potential and associated thermal excitations. The method is discussed in the context of a system with strong inter-adsorbate interactions, sodium atoms diffusing on a copper (111) surface.

The electron-phonon coupling constant for single-layer graphene on metal substrates determined from He atom scattering.

Recent theory has demonstrated that the value of the electron-phonon coupling strength λ can be extracted directly from the thermal attenuation (Debye-Waller factor) of helium atom scattering reflectivity. This theory is here extended to multivalley semimetal systems and applied to the case of graphene on different metal substrates and graphite. It is shown that λ rapidly increases for decreasing graphene-substrate binding strength. Two different calculational models are considered which produce qualitatively similar results for the dependence of λ on binding strength. These models predict, respectively, values of λHAS = 0.89 and 0.32 for a hypothetical flat free-standing single-layer graphene with cyclic boundary conditions. The method is suitable for analysis and characterization of not only the graphene overlayers considered here, but also other layered systems such as twisted graphene bilayers.

The Electron-Phonon Interaction of Low-Dimensional and Multi-Dimensional Materials from He Atom Scattering.

Atom scattering is becoming recognized as a sensitive probe of the electron-phonon interaction parameter λ at metal and metal-overlayer surfaces. Here, the theory is developed, linking λ to the thermal attenuation of atom scattering spectra (in particular, the Debye-Waller factor), to conducting materials of different dimensions, from quasi-1D systems such as W(110):H(1 × 1) and Bi(114), to quasi-2D layered chalcogenides, and high-dimensional surfaces such as quasicrystalline 2ML-Ba(0001)/Cu(001) and d-AlNiCo(00001). Values of λ obtained using He atoms compare favorably with known values for the bulk materials. The corresponding analysis indicates in addition, the number of layers contributing to the electron-phonon interaction, which is measured in an atom surface collision.

Origin of the Electron-Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering.

He atom scattering has been demonstrated to be a sensitive probe of the electron-phonon interaction parameter λ at metal and metal-overlayer surfaces. Here it is shown that the theory linking λ to the thermal attenuation of atom scattering spectra (the Debye-Waller factor) can be applied to topological semimetal surfaces, such as the quasi-one-dimensional charge-density-wave system Bi(114) and the layered pnictogen chalcogenides. The electron-phonon coupling, as determined for several topological insulators belonging to the class of bismuth chalcogenides, suggests a dominant contribution of the surface quantum well states over the Dirac electrons in terms of λ.

Electron-Phonon Coupling Constant of Metallic Overlayers from Specular He Atom Scattering.

He atom scattering has been shown to be a sensitive probe of electron-phonon interaction properties at surfaces. Here it is shown that measurements of the thermal attenuation of the specular He atom diffraction peak (the Debye-Waller effect) can determine the electron-phonon coupling constant, λ, for ultrathin films of metal overlayers on various close-packed metal substrates. Values of λ obtained for single and multiple monolayers of alkali metals, and for Pb layers on Cu(111), extrapolated to large thicknesses, agree favorably with known bulk values. This demonstrates that He atom scattering can measure the electron-phonon coupling strength as a function of film thickness on a layer-by-layer basis.

Scattering of He Atoms from a Microstructured Grating: Quantum Reflection Probabilities and Diffraction Patterns.

The quantum reflection measured previously by Zhao et al. ( Phys. Rev. A 2008 , 78 , 010902(R) ) for the scattering of He atoms off of a microstructured grating is described and analyzed theoretically. Using the close-coupling formalism with a complex absorbing potential and describing the long-range interaction in terms of the Casimir-van der Waals potential, we find probabilities and diffraction patterns that are in fairly good agreement with the experimental results. The central outcomes of this study are two-fold. First is the theoretical confirmation that, indeed, the phenomenon of quantum reflection may be detected not only through the elastic peak but also in terms of a quantum reflected diffraction pattern. Second, we demonstrate that the phenomenon of quantum reflection is the result of a coherent process where all of the potential regions are involved on an equal footing. It is a nonlocal property and cannot be related only to the long-range badlands region of the potential of interaction.

Ballistic Diffusion in Polyaromatic Hydrocarbons on Graphite.

This work presents an experimental picture of molecular ballistic diffusion on a surface, a process that is difficult to pinpoint because it generally occurs on very short length scales. By combining neutron time-of-flight data with molecular dynamics simulations and density functional theory calculations, we provide a complete description of the ballistic translations and rotations of a polyaromatic hydrocarbon (PAH) adsorbed on the basal plane of graphite. Pyrene, C16H10, adsorbed on graphite is a unique system, where at relative surface coverages of about 10-20% its mean free path matches the experimentally accessible time/space scale of neutron time-of-flight spectroscopy (IN6 at the Institut Laue-Langevin). The comparison between the diffusive behavior of large and small PAHs such as pyrene and benzene adsorbed on graphite brings a strong experimental indication that the interaction between molecules is the dominating mechanism in the surface diffusion of polyaromatic hydrocarbons adsorbed on graphite.

Electron-Phonon Coupling Strength at Metal Surfaces Directly Determined from the Helium Atom Scattering Debye-Waller Factor.

A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He atoms from a metal surface, where the energy and momentum exchange with the phonon gas can occur only through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant λ. The comparison between the values of λ extracted from existing data on the Debye-Waller factor for various metal surfaces and the λ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic helium atom scattering intensities.

A langevin canonical approach to the dynamics of chiral systems: thermal averages and heat capacity.

A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators was developed within a coupling scheme different from the well-known spin-boson model. Thermal equilibrium values were reached at asymptotic times by solving the corresponding set of nonlinear coupled equations in a Markovian regime. In particular, phase difference thermal values (or, equivalently, the so-called coherence factor) and heat capacity through energy fluctuations were obtained and are discussed in terms of tunneling rates and asymmetries.

Second order classical perturbation theory for atom surface scattering: analysis of asymmetry in the angular distribution.

A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to "soft" corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.