A long standing unsolved puzzle is the wide range of experimentally determined frequency factors for adsorbate diffusion spanning twelve orders of magnitude which are only poorly explained by modern quantum theories of surface diffusion (QTSD) based on ab initio potential energy surfaces (refs. [1]-[4]). This contribution investigates whether decoherence mechanisms, neglected in QTSD, can shed some light on these discrepancies. We suggest a quantum-mechanical theory treating the entanglement of adsorbates with their environment (phonons, electron-hole pairs, plasmons, gravitons) [5]. Time dependent wave packet evolution and quantum Zeno effect (permenant “measurement” by specific environmental excitations) are investigated. [DOI: 10.1380/ejssnt.2010.6]
A long standing unsolved puzzle is the wide range of experimentally determined frequency factors for adsorbate diffusion spanning twelve orders of magnitude which are only poorly explained by modern quantum theories of surface diffusion (QTSD) based on ab initio potential energy surfaces (refs. [1]-[4]). This contribution investigates whether decoherence mechanisms, neglected in QTSD, can shed some light on these discrepancies. We suggest a quantum-mechanical theory treating the entanglement of adsorbates with their environment (phonons, electron-hole pairs, plasmons, gravitons) [5]. Time dependent wave packet evolution and quantum Zeno effect (permenant “measurement” by specific environmental excitations) are investigated. [DOI: 10.1380/ejssnt.2010.6]
A long standing unsolved puzzle is the very small rate of surface diffusion of ad-sorbates in the low temperature STM in the regime of quantum diffusion, differing by orders of magnitude from the results of modern quantum theories of surface diffusion (QTSD) based on ab initio potential energy surfaces (refs. [1]-[5]). We investigate whether decoherence mechanisms, neglected in QTSD, can shed some light on these discrepancies. A quantum-mechanical theory is presented treating the entanglement of adsorbates with their environment (phonons, electron-hole pairs, gravitons) [6]. Time dependent wave packet evolution including the environmental modes indicates possible paths towards an explanation of the observed discrepancies and gives an insight into phenomenological descriptions like adsorbate localization, quantum Zeno effect (permenant "measurement" by specific environmental excitations) and wave function collapse.
Surface diffusion of interacting adsorbates is here analyzed within the context of two fundamental phenomena of quantum dynamics, namely the quantum Zeno effect and the anti-Zeno effect. The physical implications of these effects are introduced here in a rather simple and general manner within the framework of non-selective measurements and for two (surface) temperature regimes: high and very low (including zero temperature). The quantum intermediate scattering function describing the adsorbate diffusion process is then evaluated for flat surfaces, since it is fully analytical in this case. Finally, a generalization to corrugated surfaces is also discussed. In this regard, it is found that, considering a Markovian framework and high surface temperatures, the anti-Zeno effect has already been observed, though not recognized as such.
The low temperature motion of hydrogen on solid metal surfaces displays some unexplained experimental features: in the quantum diffusion regime more than nine orders of magnitude difference between the diffusion rates on different metal surfaces have been measured, the lowest diffusion rates being established in the low temperature scanning tunnelling microscope. Furthermore telegraph-signal-like adsorption site change, rather than Rabi oscillations predicted by Schrodinger equation in 3+1 dimensions, is observed, signaling the breakdown of quantum mechanics in 3+1 dimensions. A theory is presented to resolve these problems, involving the entanglement of the adsorbate motion to gravitons in high-dimensional spacetime. Soft local massive gravonons, induced in the presence of the adsorbate, determine the time scale for surface diffusion. The γη-model is used for the evaluation of the soft gravonon modes. Weak and local entanglement of the adsorbate motion with a nearly degenerate graviton continuum of high density of states are the conditions for the telegraph-signal-like time development of adsorption site change. In contrast to the Copenhagen interpretation of quantum mechanics, this apparent classical behaviour of the adsorbate in 3+1 dimensional spacetime is the result of the solution of Schrodinger's time dependent equation in high-dimensional spacetime.
Metals can sustain traveling electromagnetic waves at their surfaces supported by the collective oscillations of their free electrons in unison. Remarkably, classical electromagnetism captures the essential physics of these 'surface plasma' waves using simple models with only macroscopic features, accounting for microscopic electron–electron and electron–phonon interactions with a single, semi-empirical damping parameter. Nevertheless, in quantum theory these microscopic interactions could be important, as any substantial environmental interactions could decohere quantum superpositions of surface plasmons, the quanta of these waves. Here we report a measurement of path entanglement between surface plasmons with 95% contrast, confirming that a path-entangled state can indeed survive without measurable decoherence. Our measurement suggests that elastic scattering mechanisms of the type that might cause pure dephasing in plasmonic systems must be weak enough not to significantly perturb the state of the metal under the experimental conditions we investigated.
Particles (electrons, atoms, molecules) in interaction with large ensembles of atoms, e.g. solids and surfaces, often display properties, which are unexpected, based on experimental and theoretical investigations of small ensembles. A frequently cited phrase has been coined by P.W. Anderson to focus on this problem: "More is different" . Theoretical descriptions of the unexpected properties commonly use ad hoc assumptions, justified by referring to the vogue word "emergence" . In this contribution some striking examples of behaviour changes are outlined with the transition from "few" to "more" . It is suggested that entanglement between the observable local system and unobservable continua of the environment (phonons, electron-hole pairs, gravitons) can contribute much to the understanding of the relationship between the behaviour of "few" and "more" . Solving the time dependent Schrödinger equation for coherent model worlds, comprising both the local system and the entangled continua of the environment, adsorbate motion at surfaces at low temperature is examined. In the time-dependent formalism the entanglement of the core movement of a gas atom to the high dimensional continuum of substrate environs leads to a qualitative behaviour as it is observed experimentally. The focus in the present article is the emergence of classical appearance of a local quantum system entangled with the excitations of the environment. The dynamical evolution of the quantum system is coherent and according to the time dependent Schrödinger equation. The environmental excitations can be phonons, tomonagons, gravitons, either observable or not observable in experiment.
Surface diffusion of small adsorbates is analyzed in terms of the so-called intermediate scattering function and dynamic structure factor, observables in experiments using the well-known quasielastic Helium atom scattering and Helium spin echo techniques. The linear theory applied is an extension of the neutron scattering due to van Hove and considers the time evolution of the position of the adsorbates in the surface. This approach allows us to use a stochastic trajectory description following the classical, quantum and Bohmian frameworks. Three different regimes of motion are clearly identified in the diffusion process: ballistic, Brownian and intermediate which are well characterized, for the first two regimes, through the mean square displacements and Einstein relation for the diffusion constant. The Langevin formalism is used by considering Ohmic friction, moderate surface temperatures and small coverages. In the Bohmian framework, analyzed here, the starting point is the so-called Schrödinger-Langevin equation which is a nonlinear, logarithmic differential equation. By assuming a Gaussian function for the probability density, the corresponding quantum stochastic trajectories are given by a dressing scheme consisting of a classical stochastic trajectory followed by the center of the Gaussian wave packet, and issued from solving the Langevin equation (particle property), plus the time evolution of its width governed by the damped Pinney differential equation (wave property). The Bohmian velocity autocorrelation function is the same as the classical one when the initial spread rate is assumed to be zero. If not, in the diffusion regime, the Brownian-Bohmian motion shows a weak anomalous diffusion.