Marzlin Karl-Peter, Sanders Barry C
Institute for Quantum Information Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada.
Phys Rev Lett. 2004 Oct 15;93(16):160408. doi: 10.1103/PhysRevLett.93.160408.
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.
绝热定理指出，缓慢变化的哈密顿量的初始本征态在稍后时刻仍接近该哈密顿量的瞬时本征态。我们表明，如果本征态的变化显著，那么对这一表述的敷衍应用是有问题的，无论演化多么接近满足绝热定理的要求。我们还引入了一个具有精确可解演化的两能级系统的例子，以证明绝热近似对于特定缓慢变化的哈密顿量不适用。
