Non-Markovian Vibrational Relaxation Dynamics at Surfaces

Abstract

Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as model lab for studying fundamental problems of open quantum systems. We employ a previously developed model for the relaxation of a D-Si-Si bending mode at a D:Si(100)-(2$\times$1) surface, induced by a "bath" of more than $2000$ phonon modes [U. Lorenz, P. Saalfrank, Chem. Phys. {\bf 482}, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [E.W. Fischer, F. Bouakline, M. Werther, P. Saalfrank, J. Chem. Phys. {\bf 153}, 064704 (2020)] to study relaxation of higher excited vibrational states than hitherto done, by solving a high-dimensional system-bath time-dependent Schrödinger equation (TDSE). In the HEM approach, (many) real bath modes are replaced by (much less) effective bath modes. Accordingly, we are able to examine scaling laws for vibrational relaxation lifetimes for a realistic surface science problem. Second, we compare the performance of the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) approach with the recently developed coherent-state based multi-Davydov D2 {\it ansatz} [N. Zhou, Z. Huang, J. Zhu, V. Chernyak, Y. Zhao, {J. Chem. Phys.} {\bf 143}, 014113 (2015)]. Both approaches work well, with some computational advantages for the latter in the presented context. Third, we apply open-system density matrix theory in comparison with basically "exact" solutions of the multi-mode TDSEs. Specifically, we use an open-system Liouville-von Neumann (LvN) equation treating vibration-phonon coupling as Markovian dissipation in Lindblad form to quantify effects beyond the Born-Markov approximation.

16 pages, 8 figures, v2: minor changes in abstract, v3: small changes after peer-review

References in corpus (7)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
• Foundations and Measures of Quantum Non-Markovianity
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• Polaron dynamics with a multitude of Davydov D${}_2$ trial states
• Symmetry and the critical phase of the two-bath spin-boson model: Ground-state properties
• Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians

Cited by in corpus (1)

• Simulating spin measurement with a finite heat bath model for the environment