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Using the example of graphene, we have extended the classic ripple tank experiment to illustrate the behavior of waves in periodic lattices. A loudspeaker driving air through a periodically perforated plate onto the tank's water surface creates wave patterns that are in agreement with numerical simulations and are explained in terms of solid state theory. From an educational point of view, the experiment provides an illustrative example of the concepts of reciprocal space and symmetry.

We study an ideal Bose gas of N atoms contained in a box formed by two identical planar and parallel surfaces S, enclosed by a mantle of height a perpendicular to them. Calling r0 the mean atomic distance, we assume S >> r0^2 while a may be comparable to r0. In the bidimensional limit (a/r0 << 1) we find a macroscopic number of atoms in the condensate at temperatures T ~1/log(N); therefore, condensation cannot be described in terms of intensive quantities; in addition, it occurs at temperatures not too low in comparison to the tridimensional case. When condensation is present we also find a macroscopic occupation of the low--lying excited states. In addition, the condensation phenomenon is sensitive to the shape of S. The former two effects are significant for a nanoscopic system. The tridimensional limit is slowly attained for increasing (a/r0), roughly at (a/r0) ~ 10^{2}-10^{3}., Comment: 19 pages, including 4 figures and one table. Latex source file

We perform a fully quantum mechanical numerical calculation for the problem of a single electron (or excitation) propagating in a N-site one-dimensional chain in the presence of a single Holstein impurity. We compute the long-time averaged probability for finding the electron on the impurity site as a function of the nonlinearity parameter, defined in terms of the electron-phonon coupling strength and the oscillator frequency. The results, in the intermediate nonlinearity parameter range, differ substantially from the ones obtained through the use of the discrete nonlinear Schroedinger equation, even in the high-frequency regime., Comment: 8 pages, 4 figures