Symmetry breaking and current patterns due to a weak imperfection

The influence of a very weak impurity on the conduction pattern is discussed. It is shown that when the incoming particles’ energy is close to (Formula presented) (where w is the width of the wire and n is an integer number) even the most negligible imperfection may break the symmetry of the conduction pattern. When the impurity is very close to the wire’s boundaries the resultant pattern is independent of the impurity’s characteristics. In general, small variations in the incoming energy may be responsible for large modifications in the conduction pattern.