Formation of bound states in the continuum for a quantum dot with variable width

We consider mechanisms of formation of the bound states in the continuum in open rectangular quantum dots with variable width. Because of symmetry there might be bound states in the continuum (BSCs) embedded into one, two, and three continua because of the symmetry of system. These BSCs arise for selected values of the width. We show numerically that the BSCs can be excited for transmission of wave packets if the quantum dot width is varied in time and reaches these selected values of dot width. Moreover, we consider numerically a decay process of different eigenstates in the closed quantum dot to show that some of them trap in the BSC after the quantum dot is opened.