The Floquet Wigner-Smith Operator for Time-Periodic Systems

Abstract

The manipulation of small objects with waves is of great interest in various fields of science including, e.g., medicine and biology. Recently a theory based on the generalized Wigner-Smith (GWS) operator was developed, where the knowledge of the scattering matrix of a static system is enough to find optimal states for micromanipulation. In the present thesis, we extend this concept to time-periodic Floquet-setups. For such systems a unitary scattering matrix can be found, too, which we use to introduce the Floquet Wigner-Smith (FWS) operator. To illustrate the operative principle of our theory, we apply this new operator to four different potentials. We start with the simple case of a Dirac delta potential oscillating in strength or position. Due to the pointlike interaction region, such potentials are convenient to handle. We then look at more realistic setups of an extended rectangular barrier. We study a rectangular potential barrier also oscillating in strength or position. The eigenstates of the FWS operators in all of the above cases develop properties, which are favourable for the micromanipulation of periodically moving objects. We can interpret the specific behaviour of those eigenstates since they share a strong connection to their static GWS counterparts.