Interaction with the environment

Abstract

The closed Hamiltonian system discussed in Chapters 5–10 is an idealization of the real systems in nature. Even the simplest two-particle system in the world, the hydrogen atom, cannot be treated as an isolated system. The first evidence of its interaction with an environment comes from an investigation of the spectral lines. The spectral lines have a finite width (the natural line width) no matter how isolated the atom is. This stands in contradiction with the quantum mechanics of a finite number of particles which predicts infinitely sharp spectral lines. It has been realized a long time ago [385] that an infinite environment of light quanta can explain the finite line width. The spectral line has a finite width because of dissipation resulting from an irreversible loss of energy transferred to the reservoir (if the reservoir consists of a chaotic system then a small number of particles can be sufficient for an irreversible statistical behaviour, see [389] [229]). Models of an interaction of a quantum particle with a reservoir consisting of an infinite number of oscillators have been discussed in many textbooks on quantum optics [272] [3] [339]. A dissipation in nonlinear models is often discussed in terms of quantum Langevin equations. However, as some authors point out [3][339], it is difficult to determine the form of the quantum noise from a given Hamiltonian. Usually only an additive noise is discussed. In general systems there is an additive as well as a multiplicative noise. A linear dissipation and additive noise constitute the Ornstein-Uhlenbeck theory of the Brownian motion [300].