# How does a system interact with environment in quantum mechanics? When would this interaction occur? What is it?

As title says, how does a system interact with environment? I realize that this interaction can lead to interference terms and non-diagonal terms in density matrix being reduced (quantum decoherence). But what exactly is this interaction of system and environment? What would be the example of this interaction and when does this interaction occur?

• This does not make much sense, because quantum mechanics is about very small dimensions, and "system" and "environment" are blanket words for large ensembles of particles of these small dimensions. The density matrix formalism has been developed for this purpose. What do you mean by "system" and "environment"? – anna v Jul 27 '14 at 5:28
• For example, Lubos Motl, in his blog motls.blogspot.kr/2009/09/…, talks about interaction. "In general, the photon states are not exactly orthogonal. But when you calculate how quickly the process destroys the off-diagonal elements of the density matrix, it is extremely fast. Even the interactions with the cosmic microwave background are enough for a very tiny speck of dust to decohere within a tiny fraction of a second." – user55624 Jul 27 '14 at 5:33
• If wavefunctions of two "systems"(well, let us set aside QFT for now) have been not connected before interaction, how do they really interact? Is there some sorts of wavefunction of whole universe (universal wavefunction) that how things occur together non-locally or locally is probabilistically known? Or is there any theory that talks about how these interactions will take place between separate wavefunctions? – user55624 Jul 27 '14 at 5:36
• At this level with photon exchanges, there is nothing else long distance acting and as strong, no? – anna v Jul 27 '14 at 7:59
• It is just the contrary: Decoherence destroys interference and non-diagonal terms in the reduced density matrix... – Trimok Jul 27 '14 at 12:16

## 2 Answers

The quantum evolution in open systems is non-unitary, and is effectively described, usually, by the Lindblad master equation. It provides a good description for e.g. modeling cavity loss in a system of atoms interacting with radiation (see this paper).

• Not quite usually! Lindblad requires several assumptions, including Born-Markov, rotating wave approximation, etc. – Bubble Aug 31 '14 at 12:45
• @Bubble If you want the evolution of a quantum state to be trace-preserving and always positive (two reasonable assumptions to give a probabilistic interpretation to states), then it has to obey a Lindblad type equation, as showed by Lindblad in its original paper (at least for bounded generators). I was not talking about partial trace procedures but about describing the dynamics of an open system. – yuggib Aug 31 '14 at 15:24
• yes a $\bf{Markovian}$ and time local master equation for a CPT map has to be Lindblad form, however to actually derive Lindblad from the underlying microscopic physics (tracing over is you how you do it) to study open systems with it you have to make several assumptions which are not generic for open systems. One is usually left with Redfield equation. – Bubble Sep 1 '14 at 10:45

The interaction between the system and environment is really just any plain old interaction you like. For instance, if you can have electron-EM coupling, or spin-spin interaction or whatever. What is key to decoherence is that once you write the Hamiltonian for the total system+environment you trace over the environment degrees of freedom - this corresponds to ignorance about the microscopic properties of the environment. @yuggib said that the Lindblad master equation usually describes open quantum systems, which is not quite true. Lindblad is very special and nice (it is defines a completely positive trace preserving map and is Markovian), but decoherence (and thermalization!) is quite a generic process and does not occur only under very special circumstances.

EDIT: Now I see from your comments that you're confused about locality of interaction. The interaction between the system and the environment can be perfectly local, e.g., you have a spin chain coupled only at one site to the environment. The system need not interact with the all (or even many) degrees of freedom of the whole environment for decoherence What you need is the environment to be very large compared to the system.