RESUMEN
Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as a 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 × 1) surface, induced by a "bath" of more than 2000 phonon modes [Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [Fischer et al., J. Chem. Phys. 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 that of the recently developed coherent-state-based multi-Davydov-D2 Ansatz [Zhou et al., J. Chem. Phys. 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.
RESUMEN
We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrödinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tier-model. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath.
RESUMEN
We theoretically investigate transitions in a two-level system, which are induced by a sweep through an avoided crossing in the presence of coupling to a single, excited bosonic mode. This allows us to propose an initial number-state bosonic excitation as a new possible control parameter for the survival probability at long times. The expansion of number states in terms of coherent states centered around points on a circle in phase space makes a multi-Davydov-Ansatz the method of choice to perform the required numerical calculations. It is revealed that the starting time of the transition greatly affects the final transition probabilities. In addition, we found that the mixing angle, which is tuning between the diagonal and off-diagonal coupling, is decisive for the ability to control the transition via number state excitation. For a mixing angle of π/4, we found the maximal effect of number state excitation on the transition probability.
RESUMEN
Two different numerically exact methods for open quantum system dynamics, the hierarchy of pure states (HOPS) method, and the multi-Davydov-Ansatz are discussed. We focus on the suitability of the underlying representations of bath correlations. While in the HOPS case the correct description of the bath correlation function (BCF) in the time domain is decisive, it turns out that a windowed Fourier transform of the BCF is an appropriate indicator of the quality of the discretization in the multi-Davydov-Ansatz. For the spin-boson model with sub-Ohmic spectral density considered here, a discretization of the spectral density based on an exponential distribution, used previously, turns out to be most favorable.