Quantum kinetic expansion in the spin-boson model: Matrix formulation and system-bath factorized initial state

Area of Science:

• Quantum dynamics
• Condensed matter physics
• Theoretical chemistry

Background:

• The hierarchy equation of motion (HEOM) is a powerful framework for studying open quantum systems.
• The quantum kinetic expansion (QKE) offers an alternative approach to describing quantum dynamics.
• Understanding system-bath interactions is crucial for various quantum phenomena.

Purpose of the Study:

• To reformulate the QKE method for the spin-boson model in a matrix representation.
• To extend the matrix formulation of QKE to system-bath factorized initial states.
• To investigate the impact of initial conditions on quantum population transfer.

Main Methods:

• Reformulation of the QKE method within the HEOM framework using matrix representations.
• Numerical verification of equivalence between matrix and quantum operator formulations.
• Extension to system-bath factorized initial states and rederivation of quantum kinetic equations.

Main Results:

• Numerical equivalence established between HEOM matrices and quantum operators for QKE rates.
• A modified QKE is derived with an extra term in the rate kernel, dependent on site-site coupling.
• Significant differences in population transfer observed for system-bath factorized initial states compared to local equilibrium, especially under strong dissipation.

Conclusions:

• The matrix formulation of QKE provides a robust alternative within the HEOM framework.
• The modified QKE accurately captures non-Markovian dynamics and initial state effects.
• Initial state preparation critically influences quantum transport in dissipative systems.