Stochastic simulation of anharmonic dissipation. I. Linear response regime

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Theoretical chemistry

Background:

• Theoretical studies of quantum dissipative dynamics have historically relied on linear dissipation models.
• Simulating nonlinear dissipative dynamics in condensed phases, involving infinite bath modes, presents significant theoretical challenges.

Purpose of the Study:

• To develop a computationally tractable stochastic scheme for simulating nonlinear quantum dissipative dynamics.
• To investigate the influence of anharmonic baths on quantum system dynamics.

Main Methods:

• A stochastic simulation scheme is proposed for nonlinear dissipative dynamics.
• The second-order cumulant expansion is utilized, which becomes exact in the linear response regime.
• A Hermitian stochastic Liouville equation is derived without explicit bath treatment.

Main Results:

• The developed stochastic scheme enables the simulation of nonlinear dissipative dynamics.
• Stochastic simulations of an anharmonic model demonstrate that anharmonic bath dissipation differs significantly from the Caldeira-Leggett model.
• Temperature dependence of the dynamics shows substantial variations compared to linear models.

Conclusions:

• The proposed stochastic method provides a viable approach for studying complex nonlinear quantum dissipative systems.
• Anharmonic baths introduce distinct temperature-dependent behaviors in quantum dynamics not captured by linear models.