2018
DOI: 10.1088/2399-6528/aad221
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Abstract: We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin equation, with exponential memory friction. Numerical simulations based on an extended phase space method confirm the analytical results. The simulated trajectories provide qualitative insight into the effect that introducing a finite memory timescale has on the analytical line shapes. The relative amplitude of the long-time exponential tail of the line shape is suppresse… Show more

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Cited by 9 publications
(14 citation statements)
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“…In the present work we are concerned with the calculation of scattering from the adsorbates and, for that purpose, the Langevin, or Generalised-Langevin framework provides a convenient and well established method to understand the motion. [25][26][27][28][29] Here, the dynamical coordinates of the adsorbates are treated explicitly while the substrate interactions are represented by an adiabatic potential-energy surface. Thermal excitation is represented by a combination of random forces and an appropriate frictional force and it is possible to include an explicit description of inter-adsorbate interactions.…”
Section: Numerical Simulations Of Coherent and Incoherent Scatteringmentioning
confidence: 99%
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“…In the present work we are concerned with the calculation of scattering from the adsorbates and, for that purpose, the Langevin, or Generalised-Langevin framework provides a convenient and well established method to understand the motion. [25][26][27][28][29] Here, the dynamical coordinates of the adsorbates are treated explicitly while the substrate interactions are represented by an adiabatic potential-energy surface. Thermal excitation is represented by a combination of random forces and an appropriate frictional force and it is possible to include an explicit description of inter-adsorbate interactions.…”
Section: Numerical Simulations Of Coherent and Incoherent Scatteringmentioning
confidence: 99%
“…Differences in the calculated intensity correlations using the Langevin or Generalised-Langevin equations depend on the frequency spectrum of the thermal noise; however, those differences disappear as the correlation-time extends beyond any correlations in the noise spectrum. 28 For these reasons we adopt the computationally more efficient Langevin approach. The equation of motion for the dynamical coordinates, r j , is…”
Section: Numerical Simulations Of Coherent and Incoherent Scatteringmentioning
confidence: 99%
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“…The VACF and the friction kernel are compactly related in Laplace space. Defining Ψ(s) and Γ(s) as the Laplace transforms of ψ(t) and γ(t) respectively, the transforms are related by [29,30]…”
Section: Analytic Isfs 611 Translational Glementioning
confidence: 99%
“…which can be analytically inverted to obtain ψ(t) for sufficiently simple forms of Γ(s). When γ(t) is a mono-exponential function γ(t) = γω c exp(−ω c t), the inversion to obtain ψ(t), and the subsequent integration of ψ(t) to obtain the exponent of Equation 10 produces [30]…”
Section: Analytic Isfs 611 Translational Glementioning
confidence: 99%