Mathematical and Numerical Aspects of Quantum Dynamics

Tensor-Train Split-Operator Fourier Transform (TT-SOFT) method: multidimensional nonadiabatic quantum dynamics  

Victor Batista

Yale University


We introduce the “tensor-train split-operator Fourier transform” (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S1/S2 interconversion dynamics of pyrazine after UV photoexcitation to the S2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.