Decoherence: What is a Robust Correlation

[dlgoff]

While reading Zurek paper Decoherence and the transition from quantum to classical -- REVISITED, he makes the statement:

When correlations are robust enough, or the record is sufficiently indelible, familiar classical
“objective reality” emerges from the quantum substrate. Moreover, even a minute interaction
with the environment, practically inevitable for any macroscopic object, will establish such a
correlation: ...

What exactly is a "robust enough" correlation (from a interaction with the environment)?

 

[jfizzix]

I think the robust correlations are those which are established between the system and environment through interaction (i.e. measurement). Measuring a second time the same way doesn't alter the system a second time because it is in a measurement eigenstate. In that sense, the correlations would be robust.

Looks like a good paper, I'll have to read it.

 

[dlgoff]

Still pondering... A minute interaction with the environment causes a correlation that's "robust enough" to lead to the preferred state? Does that sound right? "robust enough" sounds like there are degrees of "interactioness".

 

[jfizzix]

Another way of looking at it would be that interaction leaves the system in a state that doesn't change appreciably with further interaction. We see this with the spontaneous emission of light from excited atoms. The atoms interact coherently with the environment, which in this case would be the quantum electromagnetic vacuum, and over time it becomes overwhelmingly likely that the vacuum has the energy that the atom used to have. Over more time, this is the equilibrium state since there are infinitely more ways for the energy of a photon to be in the electromagnetic field than in the atom.

 

[dlgoff]

Thanks. Examples are nice.

So it's not "degrees of interactioness" but the "number of interactions"; which gets into time evolution of Decoherence?

 

[jfizzix]

I see two factors that enter the process. One is the degree of coupling between the system and the environment, and the other is the relative dimensionality of the environment compared to the system.

As the coupliing grows (all other things being constant) the decoherence will happen more quickly.

If the environment is much larger than the system, the decoherence will tend to happen in one direction.

You can imagine if the system and environment were two quantum systems of the same dimension (provided that dimension is finite), that eventually the system plus environment will evolve until it reaches the exact same state it started with. (this is how the solutions to the Schrodinger equation behave)
In such a case the system will decohere and "recohere" over time.

Unfortunately, I'm not an expert in decoherence, though I'm a grad student doing quantum optics at the U of R.

 

[dlgoff]

Thank you so much jfizzix. That makes perfect sense. I'll still be pondering decoherence but for now ... :thumbs:

 

[jfizzix]

glad to help :)