Trajectory approach to dissipative quantum phase space dynamics: Application to barrier scattering

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Computational physics

Background:

• The Caldeira-Leggett master equation describes quantum systems interacting with thermal environments.
• Simulating quantum dynamics in thermal baths is computationally challenging.
• Understanding decoherence is crucial for quantum information processing.

Purpose of the Study:

• To numerically study the effect of a thermal environment on wave packet scattering.
• To investigate the dynamics of quantum systems using phase space trajectories.
• To assess the efficiency of the derivative propagation method (DPM) for such simulations.

Main Methods:

• Utilized the Caldeira-Leggett master equation in Lindblad form.
• Employed phase space trajectories of the distribution function W(q,p,t).
• Applied the derivative propagation method (DPM) for individual trajectory propagation.

Main Results:

• Demonstrated decoherence via trajectory swelling in momentum space on short timescales.
• Calculated transmission probabilities for scattering from a repulsive Eckart barrier.
• Compared DPM results with exact calculations for nondissipative systems.

Conclusions:

• The DPM offers an efficient method for simulating quantum dynamics in thermal environments.
• Decoherence significantly impacts wave packet scattering dynamics.
• Numerical simulations provide valuable insights into quantum dissipation and scattering phenomena.