# Effects of local periodic driving on transport and generation of bound states

## TL;DR

This paper investigates how local periodic driving in a one-dimensional lattice can control wave transmission and generate bound states, revealing tunable transmission and Floquet bound states through Green's function analysis.

## Contribution

It introduces a method to control transmission and generate bound states via local periodic driving, extending understanding of Floquet states and their interaction with local sites.

## Key findings

- Transmission can be tuned to zero using driving parameters.
- Floquet bound states exist in certain parameter ranges.
- Decreasing driving frequency delocalizes bound states into resonances.

## Abstract

We periodically kick a local region in a one-dimensional lattice and demonstrate, by studying wave packet dynamics, that the strength and the time period of the kicking can be used as tuning parameters to control the transmission probability across the region. Interestingly, we can tune the transmission to zero which is otherwise impossible to do in a time-independent system. We adapt the non-equilibrium Green's function method to take into account the effects of periodic driving; the results obtained by this method agree with those found by wave packet dynamics if the time period is small. We discover that Floquet bound states can exist in certain ranges of parameters; when the driving frequency is decreased, these states get delocalized and turn into resonances by mixing with the Floquet bulk states. We extend these results to incorporate the effects of local interactions at the driven site, and we find some interesting features in the transmission and the bound states.