Energy absorption and dissipation in quantum systems

Stemming from the time-dependent Schrِdinger equation, it is noted that any Hermitian form representing work done on a system yields a bounded expectation of energy. This expectation can be periodic, quasiperiodic or even chaotic. Such boundedness is unrealistic because energy may be added to or removed from the system. Thus, a complex non-Hermitian form is introduced into the Hamiltonian of a system which, when positive represents work being done on the system and gives an increasing energy expectation, and when negative represents a dissipation of energy from the system and gives a decreasing energy expectation. Two cases are studied. In the first, the perturbative term is purely time-dependent. In the second, it is also space-dependent. This latter case is applied to the kicked quantum rotor. A number of other applications of this formalism to systems of experimental and theoretical interest are noted.