Hierarchical Equations-of-Motion Method for Momentum System-Bath Coupling

Area of Science:

• Quantum mechanics
• Quantum dynamics
• Condensed matter physics

Background:

• Nonlinear system-bath couplings are common in quantum models.
• Analyzing these nonlinear couplings is computationally challenging.
• Existing methods struggle with complex nonlinear quantum dynamics.

Purpose of the Study:

• To develop a new theoretical framework for analyzing nonlinear quantum systems.
• To enable the application of the hierarchical equations-of-motion (HEOM) method to a broader class of quantum models.
• To provide a computationally tractable approach for nonlinear quantum dynamics.

Main Methods:

• Equivalently mapping nonlinear system-bath coordinate coupling to bilinear system-bath momentum coupling.
• Utilizing the hierarchical equations-of-motion (HEOM) method for analysis.
• Performing proof-of-principle simulations to validate the approach.

Main Results:

• Demonstrated an exact mapping for a broad class of nonlinear quantum models.
• Showed that the mapped bilinear system-bath momentum coupling is amenable to HEOM treatment.
• Presented successful proof-of-principle simulations using the developed methodology.

Conclusions:

• The developed mapping provides a powerful new tool for studying nonlinear quantum systems.
• The HEOM method can now be applied to a new family of quantum models.
• This work opens avenues for accurate numerical simulations of complex quantum dynamics.