The Moving Born-Oppenheimer Approximation

TL;DR

The paper introduces the Moving Born-Oppenheimer Approximation (MBOA), a new mixed quantum-classical framework that accounts for the influence of slow degrees of freedom's momenta on fast degrees, revealing complex dynamics and state modifications.

Contribution

It extends the traditional BOA by incorporating momentum dependence, enabling the analysis of richer dynamical behaviors in coupled quantum-classical systems.

Findings

Reveals reflection, trapping, and mass renormalization effects in model systems.

Shows entanglement and squeezing in spins within the MBOA framework.

Demonstrates long-time gradient development in fast particles coupled to a piston.

Abstract

We develop a mixed quantum-classical framework, dubbed the Moving Born-Oppenheimer Approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer Approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.