Andreas Markmann

Time-Sliced Thawed Gaussian Propagation Method for Simulations of Quantum Dynamics

A rigorous method for simulations of quantum dynamics is introduced on the basis of concatenation of semiclassical thawed Gaussian propagation steps. The time-evolving state is represented as a linear superposition of closely overlapping Gaussians that evolve in time according to their characteristic equations of motion, integrated by fourth-order Runge-Kutta or velocity Verlet. The expansion coefficients of the initial superposition are updated after each semiclassical propagation period by implementing the Husimi Transform analytically in the basis of closely overlapping Gaussians. An advantage of the resulting time-sliced thawed Gaussian (TSTG) method is that it allows for full-quantum dynamics propagation without any kind of multidimensional integral calculation, or inversion of overlap matrices. The accuracy of the TSTG method is demonstrated as applied to simulations of quantum tunneling, showing quantitative agreement with benchmark calculations based on the split-operator Fourier transform method.

Tunneling through Coulombic barriers: quantum control of nuclear fusion

A general coherent control scheme for speeding up quantum tunneling of proton transfer through Coulombic barriers is analysed. The quantum control scenario is based on repetitive electron impact ionization pulses that affect the ensuing interference phenomena responsible for quantum dynamics and force the proton to tunnel into classically forbidden regions of configuration space. The scheme is demonstrated for the simplest model of nuclear fusion, hinting at the possible enhancement of reactive scattering based on low energy collisions.

Kepler Predictor–Corrector Algorithm: Scattering Dynamics with One-Over-R Singular Potentials

An accurate and efficient algorithm for dynamics simulations of particles with attractive 1/r singular potentials is introduced. The method is applied to semiclassical dynamics simulations of electron-proton scattering processes in the Wigner-transform time-dependent picture, showing excellent agreement with full quantum dynamics calculations. Rather than avoiding the singularity problem by using a pseudopotential, the algorithm predicts the outcome of close-encounter two-body collisions for the true 1/r potential by solving the Kepler problem analytically and corrects the trajectory for multiscattering with other particles in the system by using standard numerical techniques (e.g., velocity Verlet, or Gear Predictor corrector algorithms). The resulting integration is time-reversal symmetric and can be applied to the general multibody dynamics problem featuring close encounters as occur in electron-ion scattering events, in particle-antiparticle dynamics, as well as in classical simulations of charged interstellar gas dynamics and gravitational celestial mechanics.

Steered Quantum Dynamics for Energy Minimization

We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimized to find an effective Hamiltonian that steers the dynamics of the system into the global minimum without getting trapped into local minima. The algorithm is illustrated as applied to energy minimization on rugged surfaces and golf potentials comparable to those previously explored for testing quantum annealing methodologies.