An Adiabatic Theorem without a Gap Condition
نویسنده
چکیده
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 system is H(s) = 1 2 ( p + ω(s)x )
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