Some properties of Eck-like steps in 2D underdamped Josephson junctions arrays

Two-dimensional (2D) Josephson Junctions arrays have been studied largely in the overdamped case. Only recently some experimental, numerical and theoretical results have been obtained in the underdamped case. The nature of dynamical states of an array when placed in a magnetic field is again not fully explained and only approximate (linear) models have been proposed. On the other hand, the comprehension of such dynamics is of great importance for understanding the behavior of such arrays. In this work, we study numerically some of the dynamical states in 2D arrays using a full inductance matrix in the array equations. The results show that the response of the array to the magnetic field is governed at large by the parameter β_L. Moreover we study the underlying dynamics which is dominated by so-called checkerboard solutions. The properties of such arrays are investigated in view of applications