What does the quantum butterfly effect tell us?

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Discussion Overview

The discussion revolves around the concept of the quantum butterfly effect, particularly its implications and interpretations in relation to classical chaos theory and quantum mechanics. Participants explore the differences between classical and quantum perspectives on sensitivity to initial conditions, referencing experimental demonstrations and theoretical frameworks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how the Hamiltonian can change while keeping initial conditions fixed, questioning the implications for linear superposition principles in quantum mechanics.
  • Another participant cites a Wikipedia article discussing how small perturbations in entangled quantum states can lead to significant changes in observable values, suggesting a connection to the quantum butterfly effect.
  • There is a request for clarification regarding the specific article referenced in the Wikipedia snippet, indicating uncertainty about the source of the claims made.
  • Participants discuss the experimental demonstration of entangled quantum states amplifying perturbations, with some interpreting this as potentially distinct from the claims made in the Wikipedia article.
  • One participant identifies a specific reference from the Wikipedia article that relates to the discussion, but there is still ambiguity about its interpretation and relevance.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the quantum butterfly effect or the specific claims made in the Wikipedia article. Multiple competing views and uncertainties remain regarding the relationship between entangled states and observable changes.

Contextual Notes

There are limitations in understanding the definitions and implications of the quantum butterfly effect, particularly regarding the role of Hamiltonians and the nature of perturbations in quantum systems. The discussion reflects varying interpretations of the cited literature.

Naty1
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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.
 
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Naty1 said:
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.
 
A quote from the article cited on Wikipedia:

What article is that? I can't find that statement in the article I linked.
 
Naty1 said:
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.
 
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.
 
It's the ref. [16] in the Wikipedia article, and which appears in the citation in your first post.
 

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