Adiabatic theorem

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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.

The adiabatic theorem does not state that there is a finite lower bound for the duration over which a perturbation must be performed on the system in order to keep it in its instantaneous eigenstate. It does state 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.

[edit] External links and references

• J. E. Avron, A. Elgart: Adiabatic Theorem without a Gap Condition Full paper ArXiv preprint