Sözde manyetik alan altında bulunan iki bacaklı merdivenin dinamiği

Especially in the last two decades, there have been intensive theoretical and experimental studies on the periodically driven quantum systems. The reasons for these intensive studies are the emergence of new topological effects and to be able to control these systems by periodic forcing. Another important reason is that systems governed by time-periodic Hamiltonian can be also described byan infinite-dimensional time-independent Hamiltonian in the Floquet formalism. Reducing this time-independent Hamiltonian into an effectiveN×NdimensionalHamiltonian provides great convenience to analyze the periodic quantum systems. We study the dynamics of a particle in a two-leg ladder subject to a time-dependent artificial magnetic flux for two cases. In the first case, we consider that artificial magnetic flux varying linearly with time, and in the second case, artificial magnetic flux oscillates in time. In both cases, we obtain a time-periodic Hamiltonian in k-space at each k-point. Therefore, we use Floquet formalism to get eigensolutions of the Hamiltonian in k-space numerically, and then we construct the wave function of the particle in real space as a superposition of the Floquet states. We first analyze the quasi-energy bands for different values of the driving frequency and examine the effect of the field amplitude on the quasi-energy bands for the oscillating magnetic field. Secondly, we examine the behaviorof the particle in the real space for the different values of the driving frequencyand the field amplitude.