Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations

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.

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• Fast global spectral methods for three-dimensional partial differential equations
• Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets
• Approximation in the extended functional tensor train format
• Optimization of the Femtosecond Laser Impulse for Excitation and the Spin-Orbit Mediated Dissociation in the NaRb Dimer
• Pseudospectral method for solving PDEs using Matrix Product States