Physics:Scar

In physics, and especially quantum chaos, a wavefunction scar is an enhancement (i.e. increased norm squared) of an eigenfunction along unstable classical periodic orbits in classically chaotic systems .They were discovered and explained in 1984 by E.J. Heller and are part of the large field of quantum chaos. Scars are unexpected in the sense that stationary classical distributions at the same energy are completely uniform in space with no special concentrations along periodic orbits, and quantum chaos theory of energy spectra gave no hint of their existence. Scars stand out to the eye in some eigenstates of classically chaotic systems, but are quantified by projection of the eigenstates onto certain test states, often Gaussians, having both average position and average momentum along the periodic orbit. These test states give a provably structured spectrum that reveals the necessity of scars, especially for the shorter and least unstable periodic orbits. Scars have been found and are important in membranes, wave mechanics, optics, microwave systems, water waves, and electronic motion in microstructures.