Time propagation

Yaer Aharon Haddad Fennech

ALVARO DE SOUZA DUTRA, Bin Kang Cheng

Through a sequence of time-dependent transformations and time substitution, we evaluate the propagator of a harmonically bound charged particle with time-dependent mass in a time-varying electromagnetic field by relating it to those of free particles. From this propagator we derive the wave functions. The propagators beyond and at caustics are then investigated, respectively, by including the Maslov phase factor and by using the modified semigroup property. Finally, we calculate explicitly the propagator for the constant-damping case.

Maxim Secor, Alexander V. Soudackov, Sharon Hammes‐Schiffer

The utilization of artificial neural networks (ANNs) provides strategies for accelerating molecular simulations. Herein, ANNs are implemented as propagators of the time-dependent Schrödinger equation to simulate the quantum dynamics of systems with time-dependent potentials. These ANN propagators are trained to map nonstationary wavepackets from a given time to a future time within the discrete variable representation. Each propagator is trained for a specified time step, and iterative application of the propagator enables the propagation of wavepackets over long time scales. Such ANN propagators are developed and applied to one- and two-dimensional proton transfer systems, which exhibit nuclear quantum effects such as hydrogen tunneling. These ANN propagators are trained for either a specific time-independent potential or general potentials that can be time-dependent. Hierarchical, multiple time step algorithms enable parallelization, and the extension to higher dimensions is straightforward. This strategy is applicable to quantum dynamical simulations of diverse chemical and biological processes.

Yaer Aharon Haddad Fennech

Bancha Kirdmanee, Surarit Pepore, Bodinchat Sukbot

We demonstrate that the use of a space-time transformation in path integral can simplify the calculation of the propagator for a harmonic oscillator with time-dependent mass and frequency. We show that such a propagator can be easily obtained from the unit mass and frequency propagator in the new space-time coordinate systems. Two cases of harmonic oscillator with time-dependent mass, which exact propagator can be evaluated, are investigated.

Yaer Aharon Haddad Fennech