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The moving Born-Oppenheimer approximation.

Bernardo Barrera1, Daniel P Arovas2, Anushya Chandran1,3

  • 1Department of Physics, Boston University, Boston, MA 02215.

Proceedings of the National Academy of Sciences of the United States of America
|February 13, 2026
PubMed
Summary
This summary is machine-generated.

We introduce the moving Born-Oppenheimer approximation (MBOA), a new framework for simulating systems with coupled slow and fast dynamics. MBOA captures complex behaviors like entanglement and mass renormalization in quantum and classical systems.

Keywords:
Born–Oppenheimer approximationmixed quantum-classical dynamicsnonadiabatic dynamicsspin squeezingstate preparation

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Computational Chemistry

Background:

  • The Born-Oppenheimer approximation (BOA) is a cornerstone in quantum mechanics, simplifying molecular dynamics by separating electronic and nuclear motion.
  • Limitations of the standard BOA arise in systems where fast and slow degrees of freedom (DOFs) exhibit strong coupling, necessitating more advanced theoretical treatments.

Purpose of the Study:

  • To develop a novel quantum-classical framework, the moving Born-Oppenheimer approximation (MBOA), for accurately describing the dynamics of coupled slow and fast DOFs.
  • To extend the applicability of Born-Oppenheimer-like approximations to a broader range of physical systems, including those with significant momentum-dependent couplings.

Main Methods:

  • Development of the MBOA, a mixed quantum-classical approach where fast DOFs adiabatically follow a state dependent on both the positions and momenta of slow DOFs.
  • Application and testing of the MBOA on diverse model systems: a spin-1/2 particle in a magnetic field, a spinful molecule in a magnetic field, and a gas of fast particles interacting with a piston.

Main Results:

  • The MBOA reveals rich and complex dynamics for the slow DOFs, including phenomena such as reflection, dynamical trapping, and mass renormalization.
  • Significant modifications in the state of fast DOFs were observed, including entanglement and squeezing of molecular spins and synchronized gradient formation in a gas of fast particles.

Conclusions:

  • The MBOA provides a powerful and versatile framework for simulating the dynamics of systems with coupled slow and fast degrees of freedom.
  • The MBOA demonstrates potential for wide-ranging applications across quantum chemistry, condensed matter physics, atomic and molecular physics, and quantum sensing.