Time-periodic quantum point interactions

We consider one-dimensional quantum motion of a particle under potential with time periodic strength. It is shown that in the case of Dirac's delta potential, the problem can be mapped to the scattering process in a star graph with infinite number of edges and non-conventional node couplings. The Schr\"odinger equation is solved by suitable finite truncation of number of edges. The solution exhibits oscillating patterns near threshold resonances. Asymptotic expressions for transmission and reflection probabilities are derived for the special case of time periodic delta potential.

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