Study of the elastic enhancement factor and nearest neighbor spacing distribution for partially chaotic and chaotic systems

We will present the results of experimental studies of the elastic enhancement factor W and the nearest neighbors spacing distribution P(s) for microwave rectangular and rough cavities simulating two-dimensional quantum billiards in a transient region between regular and chaotic dynamics [1] and in a pure chaotic dynamics region, respectively. The analogy between microwave cavities and quantum billiards is based upon the equivalency of the Helmholtz equation describing 2D microwave cavities and the Schrö̈dinger equation describing the quantum systems [2]. It holds for the excitation frequency below νmax = c/2d, where c is the speed of light in the vacuum and d is the height of the cavity, when only the transverse magnetic T M0 mode can be excited inside the cavity. The elastic enhancement factor W is the ratio of variances of diagonal elements of the two-port scattering matrix S to off-diagonal elements of this matrix. W is defined by the relationship [3, 4]: