F. Borondo

Particle diffraction studied using quantum trajectories

Diffraction and interference of matter waves are key phenomena in quantum mechanics. Here we present some results on particle diffraction in a wide variety of situations, ranging from simple slit experiments to more complicated cases such as atom scattering by corrugated metal surfaces and metal surfaces with simple and isolated adsorbates. The principal novelty of our study is the use of the so-called Bohmian formalism of quantum trajectories. These trajectories are able to satisfactorily reproduce the main features of the experimental results and, more importantly, they provide a causal intuitive interpretation of the underlying dynamics. In particular, we will focus our attention on: (a) a revision of the concepts of near and far field in undulatory optics; (b) the transition to the classical limit, where it is found that although the quantum and classical diffraction patterns tend to be quite similar, some quantum features are maintained even when the quantum potential goes to zero; and (c) a qualitative description of the scattering of atoms by metal surfaces in the presence of a single adsorbate.

Quantum trajectories in atom–surface scattering with single adsorbates: The role of quantum vortices

In this work, a full quantum study of the scattering of He atoms off single CO molecules, adsorbed onto the Pt(111) surface, is presented within the formalism of quantum trajectories provided by Bohmian mechanics. By means of this theory, it is shown that the underlying dynamics is strongly dominated by the existence of a transient vortitial trapping with measurable effects on the whole diffraction pattern. This kind of trapping emphasizes the key role played by quantum vortices in this scattering. Moreover, an analysis of the surface rainbow effect caused by the local corrugation that the CO molecule induces on the surface, and its manifestation in the corresponding intensity pattern, is also presented and discussed.

A quantum trajectory description of decoherence

Abstract.A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of degrees of freedom, this making the problem numerically intractable from a purely quantum-mechanical point of view. To overcome this drawback, a new class of quantum trajectories is proposed. These trajectories, based on the same grounds as Bohmian ones, are solely associated to the system reduced density matrix, since the evolution of the environment degrees of freedom is not considered explicitly. Within this approach, environment effects come into play through a time-dependent damping factor that appears in the system equations of motion. Apart from their evident computational advantage, this type of trajectories also results very insightful to understand the system decoherence. In particular, here we show the usefulness of these trajectories analyzing decoherence effects in interference phenomena, taking as a working model the well-known double-slit experiment.

A periodic orbit analysis of the vibrationally highly excited LiNC/LiCN: A comparison with quantum mechanics

By constructing continuation/bifurcation diagrams of families of periodic orbits of LiNC/LiCN system the spectroscopy and dynamics for this species are deduced and compared with accurate quantum mechanical calculations up to 13 000 cm−1. The interesting phenomenon of the appearance of gaps in the continuation diagram of the principal family that corresponds to the bend motion is shown to occur in both isomers, LiNC and LiCN. Through semiclassical quantization a one to one correspondence of specific periodic orbits to certain eigenstates is demonstrated. One interesting example is the case of periodic orbits that are generated from a saddle‐node bifurcation and describe rotations of the Li+ ion around the CN− fragment. The correspondence of these periodic orbits to regular rotating type eigenfunctions is shown, thus, demonstrating in a clear way the importance of the saddle‐node bifurcations in locating localized wavefunctions in highly energized molecules.

Local frequency analysis and the structure of classical phase space of the LiNC/LiCN molecular system

The phase space structure of a generic Hamiltonian model, describing the vibrational dynamics of the LiNC/LiCN molecular system, is studied using a frequency analysis method. The results obtained for the regular region constitute a true parametrization of the corresponding invariant tori on which the trajectories are located. By performing the frequency analysis locally, much richer information about chaotic trajectories is obtained, since it clearly reveals the dynamical characteristics of trajectory fragments hidden behind the t→∞ ergodic property.

Contextuality, decoherence and quantum trajectories

Abstract Here we analyze the relationship between quantum contextuality and decoherence in interference experiments with matter particles by means of a simple reduced quantum-trajectory model, which attempts to simulate the behavior of the projections of multi-dimensional, system-plus-environment Bohmian trajectories onto the subspace of the reduced system. This model allows us to understand the crossing of the subsystem trajectories as a combined effect of interference quenching and erasure of ‘which-way’ information, which can be of utility to interpret decoherence effects in many-dimensional systems where full Bohmian treatments become prohibitive computationally.

Adiabatic energies and radial couplings of the 3Σ+u states of H2

We present a calculation of the potential energy curves of the 3Σ+u states of the H2 molecule in the region R=1–30 a.u. The features of the correlation diagram are discussed, and a new series of avoided crossings in the region of R<5 a.u. is predicted. We calculate and analyze the radial couplings which are of interest in the study of the excitation process H(1s)+H(1s)→H(2s,2p)+H(1s). Finally, we introduce a simple analytical model which accounts for the 2 3Σ+u−3 3Σ+u interaction.

Signatures of homoclinic motion in quantum chaos.

Homoclinic motion plays a key role in the organization of classical chaos in Hamiltonian systems. In this Letter, we show that it also imprints a clear signature in the corresponding quantum spectra. By numerically studying the fluctuations of the widths of wave functions localized along periodic orbits we reveal the existence of an oscillatory behavior that is explained solely in terms of the primary homoclinic motion. Furthermore, our results indicate that it survives the semiclassical limit.

Quantum manifestations of saddle-node bifurcations

Abstract We show that the periodic orbits originating from a saddle-node bifurcation have a profound influence on the topology of the vibrational wavefunctions of the LiNC/LiCN molecular system described by a realistic and complex potential energy surface. The underlying classical structures (manifolds) are examined in detail.

SADDLE-NODE BIFURCATIONS IN THE LINC/LICN MOLECULAR SYSTEM : CLASSICAL ASPECTS AND QUANTUM MANIFESTATIONS

A classical‐quantum correspondence study of a saddle‐node bifurcation in a realistic molecular system is presented. The relevant classical structures (periodic orbits and manifolds) and its origin are examined in detail. The most important conclusion of this study is that, below the bifurcation point, there exists an infinite sequence of precursor orbits, which mimic for a significant period of time the (future) saddle‐node orbits. These structures have a profound influence in the quantum mechanics of the molecule and several vibrational wave functions of the system present a strong localization along the saddle‐node periodic orbits. A striking result is that this scarring effect also takes place well below the bifurcation energy, which constitutes a manifestation of the so‐called ‘‘ghost’’ orbits in configuration and phase space. This localization effect has been further investigated using wave packet dynamics.