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A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states entirely in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin-1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wavepacket in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory or semiclassical approaches.
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Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally-measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here we review recent progress in the field with the development of methods including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD) and Thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from `Matsubara dynamics, a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also rederive t->0+ quantum transition-state theory (QTST) in the Matsubara dynamics formalism showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.
WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213, 223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagations to WavePacket. In those simulations 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 surfaces. To model these transitions, two classes of stochastic algorithms have been implemented: (1) J. C. Tullys 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 non-adiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.0.2 which is essentially an object-oriented rewrite of previo
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the measurement outcomes. We then describe the structure of the corresponding particle quantum filters for estimating constant parameter and we prove their stability. In the continuous-time (diffusive) case, we propose a new formulation of these particle quantum filters. The interest of this new formulation is first to prove stability, and also to provide an efficient algorithm preserving, for any discretization step-size, positivity of the quantum states and parameter classical probabilities. This algorithm is tested on experimental data to estimate the detection efficiency for a superconducting qubit whose fluorescence field is measured using a heterodyne detector.
We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively describe this mechanism in two different ways: the explicit description of transition probabilities in terms of interfering trajectories, and an hierarchical integration over fluctuations in the classical phase space of the array cavities.
We analyze the attosecond electron dynamics in hydrogen molecular ion driven by an external intense laser field using ab-initio numerical simulations of the corresponding time-dependent Schr{{o}}dinger equation and Bohmian trajectories. To this end, we employ a one-dimensional model of the molecular ion in which the motion of the protons is frozen. The results of the Bohmian trajectory calculations do agree well with those of the ab-initio simulations and clearly visualize the electron transfer between the two protons in the field. In particular, the Bohmian trajectory calculations confirm the recently predicted attosecond transient localization of the electron at one of the protons and the related multiple bunches of the ionization current within a half cycle of the laser field. Further analysis based on the quantum trajectories shows that the electron dynamics in the molecular ion can be understood via the phase difference accumulated between the Coulomb wells at the two protons. Modeling of the dynamics using a simple two-state system leads us to an explanation for the sometimes counter-intuitive dynamics of an electron opposing the classical force of the electric field on the electron.
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