What does the quantum butterfly effect tell us?

In summary, the butterfly effect can occur in both classical and quantum systems, with the latter being known as the quantum butterfly effect. This effect deals with the sensitivity of a system's observable values to small changes in the Hamiltonian with a fixed initial condition. This has been demonstrated experimentally using entangled quantum states and has implications for our understanding of linear principles in quantum mechanics.
  • #1
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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  • #2
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.
 
  • #3
A quote from the article cited on Wikipedia:

What article is that? I can't find that statement in the article I linked.
 
  • #5
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.
 
  • #6
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.
 
  • #7
It's the ref. [16] in the Wikipedia article, and which appears in the citation in your first post.
 

1. What is the quantum butterfly effect?

The quantum butterfly effect is a concept in quantum physics that suggests that small changes in one part of a system can have a significant impact on the entire system in the long run.

2. How does the quantum butterfly effect differ from the classical butterfly effect?

The classical butterfly effect, based on chaos theory, states that a small change in initial conditions can lead to drastically different outcomes. In contrast, the quantum butterfly effect takes into account the inherent uncertainty and randomness in quantum systems, making its effects less predictable.

3. What does the quantum butterfly effect tell us about determinism?

The quantum butterfly effect challenges the concept of determinism, which states that all events are caused by previous events and therefore, can be predicted. The uncertainty and randomness in quantum systems suggest that the future is not entirely determined by the past.

4. How is the quantum butterfly effect relevant in everyday life?

The quantum butterfly effect is relevant in understanding complex systems, such as weather patterns, stock market fluctuations, and even the human brain. It reminds us that small changes in our actions or decisions can have a significant impact on the world around us.

5. Can the quantum butterfly effect be harnessed for practical applications?

While the quantum butterfly effect is still a theoretical concept, it has been studied and applied in fields such as quantum computing, cryptography, and communication. However, its full potential and practical applications are still being explored.

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