Salvador Miret-Artés

A trajectory-based understanding of quantum interference

Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical perspective and the Bohmian one. From this analysis, clear and insightful pictures of the physics involved in these kind of processes are obtained, which are of general validity (i.e., regardless of the type of wave packets considered) in the understanding of more complex cases where interference is crucial (e.g., scattering problems, slit diffraction, quantum control scenarios or, even, multipartite interactions). In particular, we show how problems involving wave-packet interference can be mapped onto problems of wave packets scattered off potential barriers.

Comparative configurational study for He, Ne, and Ar trimers

Helium trimer bound states are calculated by means of a variational method described in terms of atom pair coordinates and distributed Gaussian basis functions for zero total angular momentum. To show the feasibility of this method, we also apply it to the calculation of the first vibrational levels of the Ar3 and Ne3 clusters. Special emphasis is made on the study of the possible Efimov behavior of the first excited state found in the 4He3 trimer. Geometrical configurations of the ground and first excited states of these rare gas trimers have been exhaustively studied owing to the proper symmetry of the coordinates chosen.

A wave packet Golden Rule treatment of vibrational predissociation

The time‐dependent wave packet technique is applied to the Golden Rule treatment of vibrational predissociation. The wave packet at time zero is taken as the product of the quasibound wave function and the coupling inducing predissociation. The rate for vibrational predissociation can then be obtained by Fourier transform into the energy domain of the time‐dependent wave packet autocorrelation function. The method has been applied to a model triatomic van der Waals molecule. It is shown that when the bound‐state components of the wave packet are projected out, the time‐dependent version of the Golden Rule approximation provides an alternative efficient technique to treat intramolecular decay.

Hydrodynamic View of Wave-Packet Interference: Quantum Caves

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display counterclockwise helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. The string of alternating stagnation and vortical tubes is sufficient to generate divergent trajectories. Moreover, the average wrapping time for trajectories and the rotational rate of the nodal line in the complex plane can be used to define the lifetime for interference features.

Interplay of causticity and vorticality within the complex quantum Hamilton-Jacobi formalism

Interference dynamics is analyzed in the light of the complex quantum Hamilton-Jacobi formalism, using as a working model the collision of two Gaussian wave packets. Though simple, this model nicely shows that interference in quantum scattering processes gives rise to rich dynamics and trajectory topologies in the complex plane, both ruled by two types of singularities: caustics and vortices, where the former are associated with the regime of free wave-packet propagation, and the latter with the collision (interference) process. Furthermore, an unambiguous picture connecting the complex and real frameworks is also provided and discussed.

Matrix elements for anharmonic potentials: Application to I2 morse oscillator

Many authors have contributed expressions for obtaining analytical matrix elements for Morse oscillators. In this work, we discuss the advantages of using these expressions. At the same time, we propose a full numerical method to calculate these matrix elements and we compare, for the I2 system, the different results given by Gallas, Vasan, and Cross, and the variational method.

Line shape broadening in surface diffusion of interacting adsorbates with quasielastic He atom scattering

The experimental line shape broadening observed in adsorbate diffusion on metal surfaces with increasing coverage is usually related to the nature of the adsorbate-adsorbate interaction. Here we show that this broadening can also be understood in terms of a fully stochastic model just considering two noise sources: (i) a Gaussian white noise accounting for the surface friction, and (ii) a shot noise replacing the physical adsorbate-adsorbate interaction potential. Furthermore, contrary to what could be expected, for relatively weak adsorbate-substrate interactions the opposite effect is predicted: line shapes get narrower with increasing coverage.

Double continuum fragmentation in the vibrational predissociation X⋅⋅⋅BC(v)⋅⋅⋅Y→BC(v’<v)+X+Y of van der Waals complexes: A perturbative treatment

We present an approximate quantal model to study the double continuum problem arising in the complete fragmentation of X⋅⋅⋅BC(v)⋅⋅⋅Y van der Waals(vdW) complexes, where BC is a conventional diatomic molecule vibrationally excited and X and Y are rare gas atoms, through vibrational predissociation (VP). Assuming a near equilibrium geometry of the complex and using an adiabatic approximation for describing the oscillation in the angle formed by the BC⋅⋅⋅X and BC⋅⋅⋅Y weak bonds, the rates for complete fragmentation are expressed in the frame of Fermi’s ‘‘Golden Rule’’. Double continuum wave functions may be obtained by a perturbative treatment that allows one to take properly into account the symmetry of the problem in the particular and very frequent case X≡Y.

Understanding interference experiments with polarized light through photon trajectories

Abstract Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago–Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago–Fresnel laws for the interference of polarized light.

A close‐coupling infinite order sudden approximation (IOSA) to study vibrational predissociation of the HeI2 van der Waals molecule

We apply in this paper a model related to the ‘‘infinite order sudden approximation’’ to treat the vibrational predissociation of the HeI2 van der Waals molecule. For each configuration, the stretching motions within the complex are exactly solved in the close‐coupling formalism. The bending motion is then considered in an approximate way and averaged predissociation rates are obtained. Our results are compared with the experiment and also with previous models.