Adiabatic Theorem without a Gap Condition
نویسنده
چکیده
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.
منابع مشابه
An Adiabatic Theorem without a Gap Condition
The basic adiabatic theorems of classical and quantum mechanics are overviewed and an adiabatic theorem in quantum mechanics without a gap condition is described. 1 Classical Adiabatic Invariants Consider a (mathematical) pendulum whose period is slowly modulated, for example by shortening the length of the pendulum, fig 1, [1, 18]. Figure 1: An adiabatic pendulum The Hamiltonian describing the...
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