Efficiency of different numerical methods for solving Redfield equations

The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different implementations as well as methods especially developed for time propagation: the Short Iterative Arnoldi, Chebyshev and Newtonian propagators. In addition, an implementation of a symplectic integrator has been studied. For a simple example of a two-center electron transfer system we discuss some aspects of the efficiency of these methods to integrate the equations of motion. Overall for time-independent potentials the Newtonian method is recommended. For time-dependent potentials implementations of the Runge-Kutta algorithm are very efficient

Polynomial propagators for classical molecular dynamics

Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular dynamics is introduced based on an expansion of the time evolution operator in series of Chebyshev and Newton polynomials. The suggested propagators have, in principle, arbitrary order of accuracy which can be controlled by the choice of expansion order after that the series is truncated. However, the expansion converges only after a minimum number of terms is included in the expansion and this number increases linearly with the time step size. Measurements of the energy drift demonstrate the acceptable long-time stability of the polynomial propagators. It is shown that a system of interacting Lennard-Jones particles is tractable by the proposed technique and that the scaling with the expansion order is only polynomial while the scaling with the number of particles is the same as with the conventional velocity Verlet. The proposed method is, in principle, extendable for further interaction force fields and for integration with a thermostat, and can be parallelized to speed up the computation of every time step

A density matrix approach to photoinduced electron injection

Electron injection from an adsorbed molecule to the substrate (heterogeneous electron transfer) is studied. One reaction coordinate is used to model this process. The surface phonons and/or the electron-hole pairs together with the internal degrees of freedom of the adsorbed molecule as well as possibly a liquid surrounding the molecule provide a dissipative environment, which may lead to dephasing, relaxation, and sometimes excitation of the relevant system. In the process studied the adsorbed molecule is excited by a light pulse. This is followed by an electron transfer from the excited donor state to the quasi-continuum of the substrate. It is assumed that the substrate is a semiconductor. The effects of dissipation on electron injection are investigated

Stochastic unraveling of Redfield master equations and its application to electron transfer problems

A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e. are not positive semidefinite by definition. The unraveling can be achieved by allowing for trajectories with negative weights. Such a property is necessary, e.g. to unravel the Redfield QME and to treat various related problems with high numerical efficiency. The method is successfully tested on the damped harmonic oscillator and on electron transfer models including one and two reaction coordinates. The obtained results are compared to those from a direct propagation of the reduced density matrix (RDM) as well as from the standard quantum jump method. Comparison of the numerical efficiency is performed considering both the population dynamics and the RDM in the Wigner phase space representation.Comment: accepted in J. Chem. Phys.; 26 pages, 6 figures; the order of authors' names on the title page correcte

Phase separation and pair condensation in a spin-imbalanced 2D Fermi gas

We study a two-component quasi-two-dimensional Fermi gas with imbalanced spin populations. We probe the gas at different interaction strengths and polarizations by measuring the density of each spin component in the trap and the pair momentum distribution after time of flight. For a wide range of experimental parameters, we observe in-trap phase separation characterized by the appearance of a spin-balanced condensate surrounded by a polarized gas. Our momentum space measurements indicate pair condensation in the imbalanced gas even for large polarizations where phase separation vanishes, pointing to the presence of a polarized pair condensate. Our observation of zero momentum pair condensates in 2D spin-imbalanced gases opens the way to explorations of more exotic superfluid phases that occupy a large part of the phase diagram in lower dimensions