Effects of cross correlations between 1D and 3D inhomogeneities on the high-frequency susceptibility of superlattices
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SORDER, AND PHASE TRANSITIONS IN CONDENSED SYSTEMS
Effects of Cross Correlations between 1D and 3D Inhomogeneities on the High-Frequency Susceptibility of Superlattices V. A. Ignatchenko and Yu. I. Mankov Kirenskiœ Institute of Physics, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036 Russia e-mail: [email protected] Received August 1, 2005
Abstract—Cross correlations between components of a mixture of one-dimensional (1D) and three-dimensional (3D) inhomogeneities are described by introducing a distribution function taking into account correlations between absolute values of two random variables in the absence of correlations between the variables themselves. This distribution function is used for derivation and analysis of the superlattice correlation function containing a mixture of cross-correlated 1D and 3D inhomogeneities. The effect of such inhomogeneities on the high-frequency susceptibility at the edge of the first Brillouin zone of the superlattice is investigated. It is shown that positive cross correlations partly suppress the effect of a mixture of 1D and 3D inhomogeneities on the wave spectrum: the gap at the boundary of the Brillouin zone increases, and wave damping decreases as compared to the effect produced by a mixture of 1D and 3D inhomogeneities in the absence of cross correlations. Negative cross correlations lead to the opposite effect: the gap decreases and wave damping increases. Cross correlations also lead to the emergence of new resonance effects: a narrow dip or a narrow peak at the center of the band gap (depending on the sign of the correlation factor). PACS numbers: 68.65.-k, 75.30.Ds DOI: 10.1134/S106377610604011X
1. INTRODUCTION Wave spectra in partly stochastic superlattices have been intensely studied in recent years in view of wide application of such materials in various high-tech devices. In addition, these materials are convenient models for developing new methods in theoretical physics for studying media without translational symmetry. Several theoretical approaches have been developed to investigate such superlattices, including the introduction of a 1D random phase [1, 2], modeling of violation of ordering in the sequence of layers of two different materials [3–9], numerical simulation of random deviations of the interfaces between the layers from their initial periodic arrangement [10–12], postulation of the form of the correlation function of the superlattice with inhomogeneities [13, 14], application of geometrical optics approximations [15], and development of a dynamic theory of composite elastic media [16]. One more method for investigating the effect of inhomogeneities in a superlattice on the wave spectrum, which was proposed in our earlier publication [17], is known as the method of random spatial modulation (RSM) of the superlattice period. It can be briefly described as follows. The method of averaged Green functions is known to be the most consistent approach for describing the spectral properties of any inhomogeneous medi
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