Non-Markovian vibrational relaxation dynamics at surfaces.

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.

A hierarchical effective mode approach to phonon-driven multilevel vibrational relaxation dynamics at surfaces.

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.

Exact open quantum system dynamics: Optimal frequency vs time representation of bath correlations.

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.

Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation.

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.