Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation.

A full quantum-mechanical (QM) description of large amplitude nuclear motion, associated with chemical reactions or isomerization of high-dimensional molecular systems, is inherently challenging due to the exponential scaling of the QM complexity with system size. To ameliorate the scaling bottleneck in studies of realistic systems, typically modeled in the configuration space, the nuclear wave functions are represented in terms of time-dependent basis functions. Such bases are expected to give an accurate description with a modest number of basis functions employed, by adapting them to the wave function solving the time-dependent Schrödinger equation.

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.

Schrödinger-Cat States in Landau-Zener-Stückelberg-Majorana Interferometry: A Multiple Davydov Ansatz Approach.

Employing the time-dependent variational principle combined with the multiple Davydov D Ansatz, we investigate Landau-Zener (LZ) transitions in a qubit coupled to a photon mode with various initial photon states at zero temperature. Thanks to the multiple Davydov trial states, exact photonic dynamics taking place in the course of the LZ transition is also studied efficiently. With the qubit driven by a linear external field and the photon mode initialized with Schrödinger-cat states, asymptotic behavior of the transition probability beyond the rotating-wave approximation is uncovered for a variety of initial states.

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.

Simplified approach to the mixed time-averaging semiclassical initial value representation for the calculation of dense vibrational spectra.

We present and test an approximate method for the semiclassical calculation of vibrational spectra. The approach is based on the mixed time-averaging semiclassical initial value representation method, which is simplified to a form that contains a filter to remove contributions from approximately harmonic environmental degrees of freedom. This filter comes at no additional numerical cost, and it has no negative effect on the accuracy of peaks from the anharmonic system of interest.

Application of the mixed time-averaging semiclassical initial value representation method to complex molecular spectra.

The recently introduced mixed time-averaging semiclassical initial value representation of the molecular dynamics method for spectroscopic calculations [M. Buchholz, F. Grossmann, and M.

Polaron dynamics with off-diagonal coupling: beyond the Ehrenfest approximation.

Treated traditionally by the Ehrenfest approximation, the dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-DAnsatz. It is shown that the Ehrenfest method is equivalent to our variational method with the single DAnsatz, and with the multi-DAnsatz, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-DAnsatz is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation.

Mixed semiclassical initial value representation time-averaging propagator for spectroscopic calculations.

A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based propagation methods. A separable approximation is then introduced that greatly reduces (about an order of magnitude) the computational cost compared with a full Herman-Kluk time-averaging semiclassical calculation for the same systems.

Semiclassical hybrid approach to condensed phase molecular dynamics: application to the I2Kr17 cluster.

We study the vibrational decoherence dynamics of an iodine molecule in a finite krypton cluster comprising the first solvation shell. A normal mode analysis allows us to successively increase the complexity of the description. For the ground state dynamics, comparison with experimental matrix results shows that already four degrees of freedom are sufficient to capture the main decoherence mechanism.

Trajectory based non-markovian dissipative tunneling.

The influence of a dissipative environment on scattering of a particle by a barrier is investigated by using the recently introduced bohmian mechanics with complex action [J. Chem. Phys.

Coherent and incoherent effects on the imaging and scattering process in transmission electron microscopy and off-axis electron holography.

The standard treatment for the different plane wave components of incoming electrons in transmission electron microscope imaging is an incoherent superposition. However, projectile electrons in transmission electron microscopes are localized in space, and therefore have to be described as coherent wave-packets. Moreover, recent developments towards ultrafast electron microscopy and dynamic transmission electron microscopy require a description using highly localized wave-packets.

Investigating quantum transport with an initial value representation of the semiclassical propagator.

Quantized systems whose underlying classical dynamics possess an elaborate mixture of regular and chaotic motion can exhibit rather subtle long-time quantum transport phenomena. In a short wavelength regime where semiclassical theories are most relevant, such transport phenomena, being quintessentially interference based, are difficult to understand with the system's specific long-time classical dynamics. Fortunately, semiclassical methods applied to wave packet propagation can provide a natural approach to understanding the connections, even though they are known to break down progressively as time increases.

Decoherence and dissipation in a molecular system coupled to an environment: an application of semiclassical hybrid dynamics.

Applying the recently developed semiclassical hybrid dynamics [Grossmann, J. Chem. Phys.

A finite-difference implementation of the Caldeira-Leggett master equation.

The Caldeira-Leggett master equation for dissipative quantum dynamics has predominantly been implemented in phase space, where it plays the role of a quantum Fokker-Planck equation. Here we demonstrate the feasibility of a pure coordinate space implementation in the case of intermediate damping strength and temperature, for times long enough to observe thermal equilibration. After a thorough numerical investigation of the analytically solvable harmonic oscillator case, a Morse oscillator model is studied.

Non-Markovian dissipative semiclassical dynamics.

The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low temperatures, where non-Markovian effects are substantial, this approach allows for the accurate description of dissipative dynamics in anharmonic potentials over many oscillation periods until thermalization is reached. The problem of convergence of the stochastic average at long times, which plagues full quantum mechanical implementations, is avoided through a joint sampling of the stochastic noise and the semiclassical phase-space distribution.

A semiclassical hybrid approach to many particle quantum dynamics.

We analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys. 91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J.

Conductance calculations for real systems on the nanoscale.

Electron transport across molecular junctions is a rapidly growing topic at the borderline between physics and chemistry. We review calculations which were done in the Landauer transport formalism for monovalent systems, ranging from clusters to fullerenes. A realistic description of molecular conductance can be achieved by a density functional based approach to the calculation of the electronic transport properties.