What does the quantum butterfly effect tell us?

[Naty1]

I'm interested in interpretations and comments regarding this Wikipedia snippet:http://en.wikipedia.org/wiki/Butterfly_effect#Examples

... Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity. This quantum butterfly effect has been demonstrated experimentally.[16] Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.[

This idea is new to me. My limited understanding is that the macroscopic butterfly effect is related to non linear system effects...and slightly different initial conditions...but here it seems the initial condition is fixed, so how does the Hamiltonian change...what does that mean?? Is this 'quantum butterfly' effect saying anything about our linear [superposition] principles in QM?

thanks.

 

[DrClaude]

My limited understanding is that the macroscopic butterfly effect is related to non linear system effects...and slightly different initial conditions...but here it seems the initial condition is fixed, so how does the Hamiltonian change...what does that mean?? Is this 'quantum butterfly' effect saying anything about our linear [superposition] principles in QM?

A quote from the article cited on Wikipedia:

However, quantum mechanics offers another alternative of converting a small perturbation into a big change in observable values. It is based on using special entangled states of a composite quantum system. For such states, perturbation acting on a small part of a system changes a state of the whole system in a coherent way and produces changes of ‘‘macroscopic’’ observables.

 

[Naty1]

A quote from the article cited on Wikipedia:

What article is that? I can't find that statement in the article I linked.

 

[DrClaude]

Jae-Seung Lee and A. K. Khitrin, Quantum amplifier: Measurement with entangled spins, J. Chem. Phys. 121, 3949 (2004). http://dx.doi.org/10.1063/1.1788661

 

[Nugatory]

What article is that? I can't find that statement in the article I linked.

It's in one of the references linked to from the wikipedia article.

 

[Naty1]

Nugatory:

It's in one of the references linked to from the wikipedia article.

but which one? I interpret the reference as different from what Wikipedia states.

DrClaude:

It is experimentally demonstrated that entangled quantum states can be used to amplify perturbations and to increase changes in observable values.

This, too, I interpret as likely distinct from the case Wikipedia claims.

 

[DrClaude]

It's the ref. [16] in the Wikipedia article, and which appears in the citation in your first post.