Adiabatic theorem

The adiabatic theorem is an important theorem in quantum mechanics which provides the foundation for perturbative quantum field theory.

There are different versions of this theorem. Max Born and V. A. Fock proved the original version in 1928:

A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.

To be more precise, the adiabatic theorem does not tell us that there is any finite lower bound for the duration over which we have to perform a perturbation on the system in order to keep it in its instantaneous eigenstate. It just tells that this is the case if the rate of change approaches zero!

In 1990 J. E. Evron and A. Elgart found a new version of the adiabatic theorem that does not require gaps.

External links and references

• J. E. Evron, A. Elgart: Adiabatic Theorem without a Gap Condition