Extending the Adiabatic Theorem
Jerk the support from which a swinging pendulum hangs, and you will change the pendulum’s motion. But move the support very gradually, and the system will adapt so that the pendulum’s motion relative to its support remains unchanged. A similar principle holds true for quantum systems. The quantum adiabatic theorem says that a system, when perturbed sufficiently slowly, remains in its instantaneous ground state. Sarah Damerow and Stefan Kehrein of the University of Göttingen in Germany now show that aspects of this principle remain true even for the opposite limit: The ground state remains the single most likely state even for a quantum system subjected to an instantaneous perturbation [1].
Formally, the quantum adiabatic theorem describes how a perturbed system’s Hamiltonian evolves in time. It shows that, for a slow perturbation, the system transitions from its initial ground state to the time-evolved Hamiltonian’s ground state with a probability greater than the combined probabilities of all the excited states.
Damerow and Kehrein used analytical and numerical tools to examine a quantum system undergoing rapid perturbation. They considered a quantum Ising model—a lattice of interacting magnetic spins—subjected to a rapidly changing external field. They found that the system was more likely to evolve from its initial ground state to the time-evolved Hamiltonian’s ground state than to any given excited state—provided that the lattice was in the same magnetic phase (paramagnetic or ferromagnetic) in both ground states.
The result could provide insight into the dynamics of other quantum systems under rapid, nonadiabatic transitions—for example, in thermalization and many-body localization problems. In future work, the researchers will investigate whether the result can be generalized to such systems, or whether it applies only to the model studied.
–Rachel Berkowitz
Rachel Berkowitz is a Corresponding Editor for Physics Magazine based in Vancouver, Canada.
References
- S. Damerow and S. Kehrein, “Extension of the adiabatic theorem,” Phys. Rev. B 113, 165102 (2026).