Extended non-Markovian stochastic Schrödinger equation with complex frequency modes for general basis functions.

Area of Science:

• Quantum mechanics
• Computational physics
• Chemical physics

Background:

• Simulating open quantum systems is crucial for understanding complex phenomena.
• Existing methods often rely on exponential approximations for spectral densities, limiting their applicability.
• Arbitrary spectral densities pose a significant challenge in quantum dynamics.

Purpose of the Study:

• Introduce an extended non-Markovian stochastic Schrödinger equation (extended cNMSSE) for open quantum systems.
• Enable simulation of quantum dynamics under arbitrary spectral densities, including those with higher-order poles.
• Overcome the limitations of exponential basis set expansions in previous models.

Main Methods:

• Developed an extended formulation of the non-Markovian stochastic Schrödinger equation (extended cNMSSE).
• Employed non-exponential basis sets to expand bath correlation functions, accommodating general spectral densities.
• Implemented the extended cNMSSE in pseudo-Fock space using ladder operators and solved with matrix product state techniques.

Main Results:

• The extended cNMSSE successfully simulates quantum dynamics for various spectral densities, including discrete, Ohmic, and Brownian types.
• Demonstrated excellent agreement between extended cNMSSE simulations and established methods like hierarchy equations.
• Validated the method's applicability beyond Debye-type spectral densities and for complex environments.

Conclusions:

• The extended cNMSSE offers a flexible and accurate approach for simulating open quantum systems with arbitrary spectral densities.
• The method preserves the efficiency and wavefunction-based nature of previous techniques.
• This advancement broadens the scope of quantum dynamics simulations for complex environmental couplings.