Quasiperiodic states in linear surface wave experiments

Abstract

A subtle procedure to confine quasiperiodic hydrodynamic modes within an isolated region on the free surface of a fluid is presented. The experiment consists of a square vessel with an immersed concentric square well vibrating vertically, so that the surface waves generated by the meniscus at the vessel boundary interfere with the bound wave states of the well. This is a classical analogy of a double quantum well where some fundamental interference phenomena can be visualized and controlled. The described interference leads to a hydrodynamic transition from quasiperiodic to periodic patterns for the first time. As it will be shown, the quantum analogues of the present experiment suggest that our results could be transferred to design quantum confinements exhibiting quasiperiodic electronic states or their rational approximants.

Acknowledgments

Technical support from C. Zorrilla, S. Tehuacanero and C. Guerrero is gratefully acknowledged. This work has been partially supported by the Spanish MCYT (BFM2001-0202 and MAT2002-04429), the Mexican DGAPA-UNAM (IN-108502-3) and CONACyT (D40615-F), the Argentinean UBACYT (x210 and x447) and Fundación Antorchas, and the University of the Alicante.