Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations

TL;DR

The paper introduces the functional tensor-train Chebyshev (FTTC) method, a novel approach for efficient and rigorous multidimensional quantum dynamics simulations, demonstrated on a 50-dimensional DNA base pair model.

Contribution

The FTTC method applies Chebyshev propagation to continuous tensor-train representations, enabling high-dimensional quantum simulations with improved efficiency and accuracy.

Findings

Successfully simulated proton quantum dynamics in 50 dimensions

Demonstrated the method's efficiency for complex chemical systems

Validated FTTC's accuracy against known benchmarks

Abstract

Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state, represented in continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.