WavePacket: A Matlab package for numerical quantum dynamics. III. Quantum‐classical simulations and surface hopping trajectories

Abstract

WavePacket is an open‐source program package for numerical simulations in quantum dynamics. Building on the previous Part I (Schmidt and Lorenz, Comput. Phys. Commun. 2017, 213, 223] and Part II (Schmidt and Hartmann, Comput. Phys. Commun. 2018, 228, 229] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum‐classical propagation techniques to WavePacket. There classical phase‐space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces, trajectories may switch between them. To model these transitions, two classes of stochastic algorithms have been implemented: (1) Tully's fewest switches surface hopping and (2) Landau–Zener‐based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring nonadiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.1.0, which is essentially an object‐oriented rewrite of previous versions, allowing to perform fully classical, quantum‐classical and quantum‐mechanical simulations on an equal footing, that is, for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki‐documentation as well as numerous worked‐out demonstration examples with animated graphics are available. © 2019 Wiley Periodicals, Inc.

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains

“…For small numbers of sites, N ≤ 5, our results, obtained with ExciDyn, are in excellent agreement with values obtained from conventional, grid-based solvers for general Hamiltonians available within the WavePacket software package [43][44][45].…”

Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions

“…The inset shows the labelling of the states as used in (5). The eigenenergies shown have been calculated using the WavePacket software package [56][57][58].…”

“…By means of both analytic and numerical methods (Split-Operator FFT method via WavePacket software package [56][57][58]), we were able to carry out the population analysis of the resulting wavepackets as well as of the time-evolution of the observables such as orientation and alignment cosines and the kinetic energy of the planar rotor. Our analysis revealed that these observables mirror the intersections -avoided and genuine -of the eigenenergy surfaces spanned by the orienting and aligning parameters whose loci are characterized by an integer termed the topological index.…”

Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter

“…The first eigenvalue λ R 1 = 0 correspond to the steady state of the system, where L 1 = 1 [5,21]. Also, the eigenvalues with k > 1 satisfy the condition λ R k < 0 leading to dissipation terms ∝ e λ R k t in the general solution defined in equation (15). The eigenvalue with the largest negative real part (λ R N ) defines the envelope e λ R N t of the experimental observables (see figure 1-(b)).…”

“…QuTIP library [10,11], the Quantum Mechanics Toolbox of Mathematica [12], and the Wave Packet open-source package of MATLAB [13,14,15], among others. In this work, we provide a simple tutorial to learn a route towards numerically solving a wide variety of complex quantum dynamics in MATLAB.…”