Time-Dependent Gaussian Basis Sets for Many-Body Systems Using Rothe's Method: A Mean-Field Study

Area of Science:

• Computational physics
• Quantum chemistry
• Strong-field physics

Background:

• Modeling time-dependent strong-field processes, such as high-harmonic generation, in many-body systems is computationally demanding.
• Representing the electronic continuum accurately is a key challenge in these simulations.

Purpose of the Study:

• To develop an efficient and accurate method for modeling time-dependent strong-field processes.
• To reformulate time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) equations as an optimization problem.

Main Methods:

• Application of Rothe's method to TDHF and TDDFT equations of motion for orbitals.
• Utilizing thawed, complex-valued Gaussian basis sets for efficient propagation, eliminating the need for grids.
• Investigating the use of a few flexible Gaussians to describe unbound dynamics.

Main Results:

• Demonstrated efficient propagation of Gaussian basis sets for orbital-based TDHF and TDDFT approaches.
• Showcased that qualitatively correct results for unbound dynamics can be achieved with minimal flexible Gaussians.
• Achieved quantitative agreement with grid calculations using 30-100 Gaussians for intensities up to 4 × 10^14 W/cm^2 in 1D systems.

Conclusions:

• Rothe's method combined with Gaussian basis sets provides an efficient alternative to grid-based methods for strong-field process modeling.
• This approach simplifies the representation of the electronic continuum, enabling accurate simulations of high-harmonic generation.
• The method shows promise for studying complex many-body systems under intense laser fields.