The advancement of fabrication and lithography techniques of semiconductors have made it possible to study bi-layer systems made of two electronic layers separated by distances of several hundred Angstroms. In this situation the electrons in layer 1 are distinguishable from those in layer 2, and can communicate through the direct inter-layer Coulomb interaction. In particular, if a current is applied to one of the layers, the electrons in the second will be dragged giving rise to a transresistance ρ D . In this article we review recent theoretical and experimental developments in the understanding of this effect. At very low temperatures it turns out that phonons dominate the transresistance. The direct Coulomb interaction and plasmon excitations are important at temperatures T > 0.1T F , with T F the Fermi temperature. If a magnetic field is applied the transresistance is increased, in a very interesting interplay between ρ D and Landau quantization. The non-dissipative drag is also reviewed.

Femtosecond laser pulses and coherent two-phonon Raman scattering were used to excite KTaO3 into a squeezed state, nearly periodic in time, in which the variance of the atomic displacements dips below the standard quantum limit for half of a cycle. This nonclassical state involves a continuum of transverse acoustic modes that leads to oscillations in the refractive index associated with the frequency of a van Hove singularity in the phonon density of states.

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We present a model that explains the origin and predicts the statistical properties of columnar quasihexagonal crack patterns, as observed in the columnar jointing of basaltic lava flows. Induced by temperature gradients during cooling, irregular fractures appear at the surface of the material. At later times fractures penetrate into the material, and tend to form polygonal patterns. We show that this ordering can be described as a tendency to minimize an energy functional. Atomistic simulations confirm this interpretation. Numerical simulations based on a phenomenological implementation of this principle generate patterns that have remarkably good statistical agreement with real ones.

We consider the anisotropic quantum Heisenberg antiferromagnet (with anisotropy A) on a square lattice using a Chem-Simous (or Wigner-Jordan) approach. We show that the average field approximation (AFA) yields a phase diagram with two phases: a Neel state for A ) A, and a fiux phase for A & A, separated by a second-order transition at A, ( 1. We show that this phase diagram does not describe the XY regime of the antiferromagnet. Fluctuations around the AFA induce relevant operators which yield the correct phase diagram. We find an equivalence between the antiferromagnet and a relativistic field theory of two self-interacting Dirac fermions coupled to a Chem-Simons gauge field. The field theory has a phase diagram with the correct number of Goldstone modes in each regime and a phase transition at a critical coupling A' ) A, . We identify this transition with the isotropic Heisenberg point. It has a nonvanishing Neel order parameter, which drops to zero discontinuously for A ( A'.