Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

Area of Science:

• Quantum dynamics
• Statistical mechanics
• Computational chemistry

Background:

• The linearized semiclassical-initial value representation (LSC-IVR) is a widely used approximation for quantum time-correlation functions.
• Standard LSC-IVR is derived by taking the limit of a ring-polymer path integral, but it does not conserve the quantum Boltzmann distribution.
• Accurate quantum dynamics simulations are crucial for understanding chemical reactions and material properties.

Purpose of the Study:

• To develop a modified classical dynamics that conserves the quantum Boltzmann distribution.
• To improve the accuracy of semiclassical approximations for quantum time-correlation functions.
• To explore new avenues for computationally tractable quantum dynamics.

Main Methods:

• The study rederives the LSC-IVR by considering the normal modes of a free ring-polymer.
• A key modification involves truncating the quantum Liouvillian at specific Matsubara frequencies, rather than in powers of ħ(2).
• The resulting "Matsubara" dynamics is inherently classical and conserves the quantum Boltzmann distribution due to Hamiltonian symmetry.

Main Results:

• The proposed Matsubara dynamics conserves the quantum Boltzmann distribution.
• Numerical tests demonstrate that the Matsubara approximation converges with respect to the number of modes.
• The Matsubara approximation shows better agreement with exact quantum results compared to the standard LSC-IVR.

Conclusions:

• A single modification in the LSC-IVR derivation leads to a classical dynamics that preserves the quantum Boltzmann distribution.
• The Matsubara dynamics offers a more accurate approximation to quantum time-correlation functions than standard LSC-IVR.
• While computationally expensive for large systems, further approximations of Matsubara dynamics could yield practical methods for quantum simulations.