Coordinate transformations and matter waves cloaking. (English) Zbl 1364.35300
Summary: The transformation method provides an efficient tool to control wave propagation inside materials. Using the coordinate transformation approach, we study invisibility cloaks with sphere, cylinder and ellipsoid structures for electronic waves propagation. The underlying physics behind this investigation is the fact that a Schrödinger equation with position dependent mass tensor and potentials has a covariant form which follows the coordinate transformation. Using this technique, we obtain the exact spatial form of the mass tensor and potentials for a variety of cloaks with different shapes.
MSC:
| 35Q40 | PDEs in connection with quantum mechanics |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35L05 | Wave equation |
| 78A48 | Composite media; random media in optics and electromagnetic theory |
Keywords:
matter waves; metamaterials; cloaking; coordinate transformation; invisibility; effective massReferences:
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