Discrete breathers: classical and quantum

Discrete breathers are time-periodic spatially localised motions in networks of oscillators. Their occurrence in three principal contexts is reviewed: (i) autonomous Hamiltonian or reversible systems, (ii) autonomous forced damped systems, and (iii) time-periodically forced systems. The main proposed area of application, however, is to molecular crystals, where quantum effects must be taken into account. Thus an idea for a theory of quantum discrete breathers is also presented, though some details remain to be worked out.