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 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 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]
Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds, which is much shorter than the time required to carry out a computation on the timescale of seconds. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrödinger's time dependent equation in four dimensional spacetime. Compared to Schrödinger's time development, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 108 discrepancy between decoherence time and quantum computation time. The observation and our explanation are in analogy to the 108 discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrödinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.
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.
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.
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.
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.