Motivation

The goal of dissipative quantum mechanics or `quantum dissipation theory' is to formulate microscopic theories of irreversible behaviour of quantum systems. Simply speaking, one would like to understand processes like, e.g., friction or `damping' on a microscopic level. This requires at least two things: `friction' means that physical objects interact with each other, i.e., we need to talk about interactions. Furthermore, this occurs as a function of time for systems which are usually out of equilibrium, i.e., we need to talk about dynamics.

A further, more ambitious goal is to better understand the relation between microscopic and macroscopic theories, e.g., the relation between mechanics (classical or quantum) and statistical mechanics (again classical or quantum).

Already in classical (Newtonian) mechanics, the description of irreversible behaviour is a non-trivial problem. One can often introduce dissipation into microscopic equations by adding phenomenological terms, such as the velocity-dependent damping term $\gamma \dot{x}(t)$ ($\gamma>0$) in the damped (forced) harmonic oscillator,

$$\ddot{x}(t) + \gamma \dot{x}(t) + \omega^2 x(t) = f(t).$$ (1)

In this example, one of the goals would be to derive this equation and to actually calculate $\gamma$ from an underlying microscopic theory.

Other examples (some of these are very tough, some not so tough problems):

• What is the spontaneous photon emission rate of an atom in vacuum?
• What is the electrical resistance of a (small or large) piece of metal at very low temperatures?
• How does a Laser work?
• What is the typical time after which a given realisation of a qubit (a quantum two-level system as realised in, e.g., a linear ion trap, the charge or magnetic flux in superconducting junctions, the electron charge or spin in semiconductor quantum dots, the nuclear spin etc.) fails to operate in the desired manner?