Berry's Phase
Berry's Phase
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DOI：
10.1007/978-3-540-70626-7_12
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发表时间：
2007-08
期刊：
影响因子：
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通讯作者：
D. Rohrlich
中科院分区：
文献类型：
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作者：
D. Rohrlich
Berry's phase [1] is a quantum phase effect arising in systems that undergo a slow, cyclic evolution. It is a remarkable correction to the quantum adiabatic theorem and to the closely related Born-Oppenheimer approximation [2]. Berry's elegant and general analysis has found application to such diverse fields as atomic, condensed matter, nuclear and elementary ► particle physics, and optics. In this brief review, we first derive Berry's phase in the context of the quantum adiabatic theorem and then in the context of the Born-Oppenheimer approximation. We mention generalizations of Berry's phase and analyze its relation to the ► Aharonov-Bohm effect.Consider a HamiltonianHf(R) that depends on parametersR1,R2, …,Rn, components of a vectorR. Let us assume thatHf(R) has at least one discrete and nondegenerate eigenvalueEi(R) with | Ψi(R)⟩ its eigenstate;Ei(R) and | Ψi(R)⟩ inherit their dependence onRfromH(R). If the vectorRchanges in time, then | Ψi(R)⟩ is not an exact solution to the time-dependent ► Schrödinger equation. But ifRchanges slowly enough, the system does not ► quantum jump to another eigenstate. Instead, it adjusts itself to the changing Hamiltonian. A heavy weight hanging on a string illustrates such adiabaticity. Pull the string quickly — it snaps and the weight falls. Pull the string slowly — the weight comes up with it.
