Problem-free time-dependent variational principle for open quantum systems.

Area of Science:

• Quantum chemistry
• Theoretical chemistry
• Computational physics

Background:

• Time-dependent variational principle (TDVP) is efficient for simulating quantum nuclear wave-function dynamics in isolated systems.
• Extending TDVP to density matrix methods for open systems leads to unphysical energy and population dissipation due to basis set incompleteness.
• This issue is particularly problematic for mixed states and incomplete basis approximations in practical calculations.

Purpose of the Study:

• To develop a robust method for simulating open quantum systems that overcomes the limitations of standard TDVP extensions.
• To introduce a formulation that conserves energy and population in quantum dynamics simulations, even with incomplete basis sets.

Main Methods:

• Introduced a constrained Lagrangian formulation of TDVP applied to a non-stochastic open system Schrödinger equation.
• The formulation is applicable to any variational ansatz for the system density matrix.
• Working equations and numerical assessments were performed using the variational multiconfiguration Gaussian approach for a model system.

Main Results:

• The constrained Lagrangian TDVP formulation successfully prevents unphysical energy and population dissipation in open quantum systems.
• Demonstrated the method's validity and effectiveness using a two-dimensional linear vibronic coupling model interacting with a harmonic bath.
• The approach ensures accurate simulations by mitigating artifacts arising from basis set incompleteness.

Conclusions:

• The constrained Lagrangian TDVP offers a reliable and accurate approach for simulating quantum nuclear dynamics in open systems.
• This method overcomes critical limitations of previous TDVP extensions, enabling more trustworthy computational studies.
• The formulation provides a significant advancement for theoretical studies involving open quantum systems and environmental interactions.