Dividing Line between Quantum and Classical Trajectories: Bohmian Time Constant

This work proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schr\"odinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant which should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8 10^{-15} m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i. e., ${\tau_{B\max}} = {10^{- 26}}s$

Bohmian Trajectories of Airy Packets

The discovery of Berry and Balazs in 1979 that the free-particle Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schr\"odinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space-time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject's theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schr\"odinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams depends significantly on initial parameters and configurations of the experimental set-up.Comment: 8 page

Communication: Semiclassical perturbation theory for the quantum diffractive scattering of atoms on thermal surfaces

Inspired by the semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)10.1063/1.446609], we derive explicit expressions for the angular distribution of particles scattered from thermal surfaces. At very low surface temperature, the observed experimental background scattering is proportional to the spectral density of the phonons. The angular distribution is a sum of diffraction peaks and a broad background reflecting the spectral density. The theory is applied to measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. © 2012 American Institute of Physics.This work has been graciously supported by grants from the Israel Science Foundation and the German-Israel Foundation for Basic Research, FIS2011-29596-C01-02 (Spain) and COST action MP1006.Peer Reviewe

A new approach to atom scattering from conducting surfaces: The effective electron-phonon Debye-Waller factor

Photodynamics conference; Mendoza, Argentina. 9th-13st of May 2016 ; http://photodynamics9.wixsite.com/phd9Peer Reviewe

Quantum manifestations of chaos in elastic atom-surface scattering

Quantum manifestations of chaos in the diffraction of atoms from corrugated surfaces, for a range of initial conditions easily attainable in scattering experiments, are presented and discussed. The appearance of strong oscillations in diffraction patterns is shown to be directly related to the presence of classical chaos and threshold effects. We also show that the autocorrelation function for some of the collision S-matrix elements over incident angles is sensitive to the character, hyperbolic or nonhyperbolic, of the underlying chaotic dynamics, in agreement with general semiclassical arguments for unbound chaotic systems. © 2001 The American Physical SocietyThis work was supported by DGES (Spain) under Contract Nos. PB95-71 and PB98-115 and the European Contract No. HPRN-CT-1999-00005. R.G. acknowledges financial support from CAM (Spain).Peer Reviewe

Observation of rotationally mediated focused inelastic resonances in D2 scattering from Cu(001)

6 págs.; 4 figs.; 1 tab.Rotationally mediated focused inelastic resonances (RMFIR's) in the angular distributions of D2 scattered from Cu(001) are observed. The FIR effect involves a phonon-assisted focusing of an incident beam of arbitrary energy and direction into a final channel of one single well-defined energy and direction. Surprisingly for an incident energy Ei = 27 meV the RMFIR conditions for the scattered beam coincide with the kinematic conditions required for a further elastic selective adsorption mechanism called the rotationally mediated critical kinematic (RMCK) effect. By taking advantage of the RMFIR and elastic RMCK effects, three effective bound states of energy ¿n,J = -21.5 meV, -12.4 meV, and -10.3 meV are determined. They are attributed to the lowest bound states ¿0 = -28.9 meV and ¿1 = -19.8 meV combined with the rotational excitation energy for J = 1 to be BrotJ(J + 1) = 7.41 meV, respectively, and ¿3 = -10.3 meV combined with the rotational ground state (J = 0). While the ¿1 and ¿3 states appear as maxima in the angular distribution at RMFIR conditions, the ¿0 yields a striking minimum which represents the first evidence of what we call an anti-FIR feature. Theoretical arguments to explain the different FIR signatures observed are provided. A fit of a phenomenological interaction potential to the experimental bound-state values yields a value for the well depth D = 32.5 meV which is somewhat deeper than that found previously. © 1997 The American Physical SocietyS.M.A. acknowledges the Alexander von Humboldt Stiftung for support. G.B. was supported by Max-Planck Grant No. V-3.MPF-1028848. M.F.B. was supported by the ‘‘Training and Mobility of Researchers’’ Program of the European Union ~Grant No. ERB4001GT952431!. This work was started within the framework of Acciones Integradas Hispano-Alemanas Grant No. 165 A.Peer Reviewe

Kramers' turnover theory for diffusion of Na atoms on a Cu(001) surface measured by He scattering

12 pages, 7 figures.The diffusion of adatoms and molecules on a surface at low coverage can be measured by helium scattering. The experimental observable is the dynamic structure factor. In this article, we show how Kramers' turnover theory can be used to infer physical properties of the diffusing particle from the experiment. Previously, Chudley and Elliot showed, under reasonable assumptions, that the dynamic structure factor is determined by the hopping distribution of the adsorbed particle. Kramers' theory determines the hopping distribution in terms of two parameters only. These are an effective frequency and the energy loss of the particle to the bath as it traverses from one barrier to the next. Kramers' theory, including finite barrier corrections, is tested successfully against numerical Langevin equation simulations, using both separable and nonseparable interaction potentials. Kramers' approach, which really is a steepest descent estimate for the rate, based on the Langevin equation, involves closed analytical expressions and so is relatively easy to implement. Diffusion of Na atoms on a Cu(001) surface has been chosen as an example to illustrate the application of Kramers' theory.This work has been supported in part by DGICYT (Spain) under Contract No. BFM2001-2179. R.G. and J.L.V. thank the Minister of Science and Technology (Spain) for a Ramón y Cajal Contract and a predoctoral F.P.I. grant. This work has also been supported by grants from the Israel Science Foundation, the Minerva Foundation (Munich), and the Volkswagen Foundation.Peer reviewe