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arXiv · 1802.10148

Time-dependent treatment of tunneling and Time's Arrow problem

Shmuel Gurvitz
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Abstract

New time-dependent treatment of tunneling from localized state to continuum is proposed. It does not use the Laplace transform (Green's function's method) and can be applied for time-dependent potentials, as well. This approach results in simple expressions describing dynamics of tunneling to Markovian and non-Markovian reservoirs in the time-interval $-\infty<t<\infty$. It can provide a new outlook for tunneling in the negative time region, illuminating the origin of the time's arrow problem in quantum mechanics. We also concentrate on singularity at $t=0$, which affects the perturbative expansion of the evolution operator. In addition, the decay to continuum in periodically modulated tunneling Hamiltonian is investigated. Using our results, we extend the Tien-Gordon approach for periodically driven transport, to oscillating tunneling barriers.

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Shmuel Gurvitz. 2018-02-27. Time-dependent treatment of tunneling and Time's Arrow problem. https://arxiv.org/abs/1802.10148

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