English

Taming the divergent terms that occur during adiabatic switching in perturbation theory

Quantum Physics 2016-08-31 v3

Abstract

A potential problem with adiabatic switching in perturbation theory is that divergent terms appear in the series solution. An example of this was presented by C. Brouder et al [4] for a simple 2 state system where the evolution of system in the presence of a time dependent perturbation was considered. One of their results is that the evolution operator has no well-defined limit for adiabatic switching. We will rework this problem to show that for adiabatic switching the evolved states are well-defined with any divergences being absorbed in a time independent phase factor which can be removed. These results will then be applied to the more general problem of a system with an arbitrary number of states. It will be shown that for this case, also, the potentially divergent terms all appear in a time-independent phase factor.

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Cite

@article{arxiv.1606.07021,
  title  = {Taming the divergent terms that occur during adiabatic switching in perturbation theory},
  author = {Dan Solomon},
  journal= {arXiv preprint arXiv:1606.07021},
  year   = {2016}
}

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