Bayesian optimization for inverse problems in time-dependent quantum dynamics.

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schrödinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schrödinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with the Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduces the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO2 and propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.

Tracer diffusion in hard sphere fluids from molecular to hydrodynamic regimes.

Molecular dynamics is employed to investigate tracer diffusion in hard sphere fluids. Reduced densities (rho*=rhosigma(3), sigma is the diameter of bath fluid particles) ranging from 0.02 to 0.52 and tracers ranging in diameter from 0.125sigma to 16sigma are considered. Finite-size effects are found to pose a significant problem and can lead to seriously underestimated tracer diffusion constants even in systems that are very large by simulation standards. It is shown that this can be overcome by applying a simple extrapolation formula that is linear in the reciprocal cell length L(-1), allowing us to obtain infinite-volume estimates of the diffusion constant for all tracer sizes. For higher densities, the range of tracer diameters considered spans diffusion behavior from molecular to hydrodynamic regimes. In the hydrodynamic limit our extrapolated results are clearly consistent with the theoretically expected slip boundary conditions, whereas the underestimated values obtained without extrapolation could easily be interpreted as approaching the stick limit. It is shown that simply adding the Enskog and hydrodynamic contributions gives a reasonable qualitative description of the diffusion behavior but tends to overestimate the diffusion constant. We propose another expression that fits the simulation results for all densities and tracer diameters.

Collision-induced alignment of H2O+ drifting in helium.

The collision-induced alignment of H(2)O(+) drifting in helium is studied with a molecular dynamics method that has been extended to treat nonlinear rigid ions. Rotational distribution functions and averaged quantities are presented in terms of the rho formalism [M. Thachuk, Phys. Rev. A 72, 032722 (2005)], and it is shown that this description gives a very good agreement with simulation results. In addition to velocity and angular velocity autocorrelation functions, a velocity-angular velocity cross correlation function is introduced. This cross correlation function provides insight into the dynamical nature of the alignment mechanism.