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Journal of Physics Conference Series

Low temperature motion of hydrogen on metal surfaces signals breakdown of quantum mechanics in 3+1 dimensions

D. Drakova, G. Doyen

Published Jun 10, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/442/1/012049

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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.
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.
A particle switching between two sites of a symmetric system in weak interaction with an environmental continuum of high density of states exhibits a telegraph-signal-like time development without the need of the Born-Bohr principle of reduction on eigenstates of the measuring equipment. The origin of the telegraph signal is a very weak local coupling of the particle to the continuum of gravitons which is connected with an enormous slow down of the particle motion. The proposed mechanism envisages entanglement to gravitons in high dimensional spacetime, which, in accord with Gauss law, gives rise to a local and much stronger gravitational law compared to classical gravitation. The physics behind the quantum jumps and the telegraph-signal-like time development is elucidated. The model might be useful for studying environmental decoherence effects on adsorbate localization and quantum diffusion on solid surface.
Abstract The so-called quantum-to-classical transition is studied in the surface diffusion dynamics. This continuous and smooth transition is carried out from the Liouville-von Neumann equation by scaling Planck’s constant. As an application, the Brownian motion of an adsorbate on a flat surface is analyzed within the Caldeira–Leggett master equation formalism for the reduced density matrix and the two extreme time behaviors, the ballistic and diffusive motions. In the ballistic time regime, the intermediate scattering function displays a Gaussian function which is governed by the thermal velocity in the classical regime, whereas in the quantum regime, by the initial spreading velocity of the wave packet. Adsorbates behave as a classical or quantum ideal gas. Finally, in the diffusive regime, and starting from the Chudley–Elliott model, the well-known H-function is calculated for three different surface temperatures in the diffusion of H and D on a Pt(111) surface. The main goal of this analysis is whether one can discriminate the irreversibility coming from tunneling or thermal activation diffusion.
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]
We develop a deterministic theory which accounts for the coupling of a high dimensional continuum of environmental excitations (called gravonons) to massive particle in a very localized and very weak fashion. For the model presented Schrödinger's equation can be solved practically exactly in 11 spacetime dimensions and the result demonstrates that as a function of time an incoming matter wave incident on a screen extinguishes, except at a single interaction center on the detection screen. This transition is reminiscent of the wave - particle duality arising from the ''collapse" (also called ''process one") postulated in the Copenhagen-von Neumann interpretation. In our theory it is replaced by a sticking process of the particle from the vacuum to the surface of the detection screen. This situation was verified in experiments by using massive molecules. In our theory this "wave-particle transition" is connected to the different dimensionalities of the space for particle motion and the gravonon dynamics, the latter propagating in the hidden dimensions of 11 dimensional spacetime. The fact that the particle is detected at apparently statistically determined points on the screen is traced back to the weakness and locality of the interaction with the gravonons which allows coupling on the energy shell alone. Although the theory exhibits a completely deterministic "chooser" mechanism for single site sticking, an apparent statistical character results, as it is found in the experiments, due to small heterogeneities in the atomic and gravonon structures.
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.