Numerical approaches to time evolution of complex quantum systems

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.     

Conformational dynamics of photoexcited conjugated molecules

Time-dependent photoexcitation and optical spectroscopy of pi-conjugated molecules is described using a new method for the simulation of excited state molecular dynamics in extended molecular systems with sizes up to hundreds of atoms. Applications are made to poly(p-phenylene vinylene) oligomers. Our analysis shows self-trapping of excitations on about six repeat units in the course of photoexcitation relaxation, identifies specific slow (torsion) and fast (bond-stretch) nuclear motions strongly coupled to the electronic degrees of freedom, and predicts spectroscopic signatures of molecular conformations.     

An analysis of domain wall ruckling initiated at the points of maximum shear-stress on a braket wall in (110)[001] SiFe

The eddy-current limited ruckling process by which a shaped “ket” domain wall in Goss oriented silicon iron transforms into a “bra” domain wall during magnetization reversal has been calculated from a new initial condition. It is now assumed that the re-oriented segments nucleate at the points of maximum shear stress on the domain wall and not at the surface as in a previous calculation. Both models are compared with experimental data obtained by Morgan and Overshott using Kerr magneto-optic microscopy. This suggests that ruckling is not initiated immediately d B/dT changes sign, but is delayed until the shearing stress is sufficient to nucleate re-oriented segments.     

Observation of quantum Hall "valley Skyrmions"

We report measurements of the interaction-induced quantum Hall effect in a spin-polarized AlAs two-dimensional electron system where the electrons occupy two in-plane conduction band valleys. Via the application of in-plane strain, we tune the energies of these valleys and measure the energy gap of the quantum Hall state at filling factor nu = 1. The gap has a finite value even at zero strain and, with strain, rises much faster than expected from a single-particle picture, suggesting that the lowest energy charged excitations at nu = 1 are "valley Skyrmions."     

Optical microrheology using rotating laser-trapped particles

We demonstrate an optical system that can apply and accurately measure the torque exerted by the trapping beam on a rotating birefringent probe particle. This allows the viscosity and surface effects within liquid media to be measured quantitatively on a micron-size scale using a trapped rotating spherical probe particle. We use the system to measure the viscosity inside a prototype cellular structure.