Recent Applications of the Quantum Trajectory Method

Courtney L. Lopreore

Corey Jason Trahan

Alexey Liniov, Valentin Volokitin, Iosif B. Meyerov +2 more

Kisam Park, Bill Poirier, Gérard Parlant

Quantum trajectory methods (QTMs) hold great promise as a potential means of obtaining dynamical insight and computational scaling similar to classical trajectory simulations but in an exact quantum dynamical context. To date, the development of QTMs has been stymied by the "node problem"--highly nonclassical and numerically unstable trajectories that arise when the wavepacket density |psi|2 exhibits substantial interference oscillations. In a recent paper, however [B. Poirier, J. Chem. Phys. 128, 164115 (2008)], a "bipolar decomposition," psi=psi+(+)(psi)psi(-), was introduced for one-dimensional (1D) wavepacket dynamics calculations such that the component densities |psi(+)(-)|2 are slowly varying and otherwise interference-free, even when |psi|2 itself is highly oscillatory. The bipolar approach is thus ideally suited to a QTM implementation, as is demonstrated explicitly in this paper. Two model 1D benchmark systems exhibiting substantial interference are considered--one with more "quantum" system parameters and the other more classical-like. For the latter, more challenging application, synthetic QTM results are obtained and found to be extremely accurate, as compared to a corresponding fixed-grid calculation. Ramifications of the bipolar QTM approach for the classical limit and also for multidimensional applications, are discussed.

Yohann Scribano, Gérard Parlant

In this contribution, we expose a new mixed quantum-classical reaction dynamics method whosenovelty is that it is entirely based on trajectories. Our approach rests on the concept of quantumtrajectory, which has been long been considered a philosophical and interpretative tool for quantummechanics [1]. Recently, quantum trajectories have been “rediscovered” with the goal of developinga totally new and unconventional computational method for doing quantum reaction dynamics [2,3].The most recent formulation, due to Bill Poirier and coworkers [4-6], sums up as a system ofcoupled ordinary differential equations (ODEs), that can be propagated in an extremely stable andaccurate manner. Potential advantages of this method are easily seen: (i) accurate propagation canbe extended to very large internuclear distances at low temperature; (ii) the propagation of onequantum degree of freedom together with several—possibly many—classical degrees of freedomsimply amounts to solving a “cheap” classical-like ODE system.Here we elaborate on our companion communication “Quantum trajectory capture at low and ultralowtemperature”. The above quantum trajectory approach is introduced and its physical as well ascomputational advantages are detailed, with special emphasis on the capture process.

Perry R. Rice