Comparison between explicit and implicit discretization strategies for a dissipative thermal environment.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• Simulating open quantum systems is crucial for understanding complex molecular processes.
• Dissipative baths significantly influence quantum system dynamics.
• Accurate simulation methods are needed to capture these effects.

Purpose of the Study:

• To compare the efficiency and accuracy of explicit (ML-MCTDH) and implicit (TTN-HEOM) methods for simulating open quantum systems.
• To identify the most suitable method for different types of dissipative baths and quantum dynamics.
• To evaluate the performance of the TENSO package in implementing these simulation strategies.

Main Methods:

• Explicit wave function-based discretization using multi-layer multi-configuration time-dependent Hartree (ML-MCTDH).
• Implicit density matrix-based master equation method using tree tensor network hierarchical equations of motion (TTN-HEOM).
• Implementation and comparison within the TENSO computational package.

Main Results:

• TTN-HEOM demonstrates superior efficiency for dissipative baths with exponentially decaying correlation functions.
• Explicit methods like ML-MCTDH require extensive discretization for continuum baths, causing computational bottlenecks.
• TTN-HEOM accurately captures dissipative dynamics with fewer auxiliary modes, while ML-MCTDH is accurate in pure dephasing regimes.

Conclusions:

• The implicit TTN-HEOM approach is more computationally efficient than explicit ML-MCTDH for simulating open quantum systems coupled to certain dissipative baths.
• The choice of simulation method depends on the bath characteristics and the specific quantum dynamics being investigated.
• The TENSO package provides a unified framework for implementing and comparing these advanced simulation techniques.