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Taking specifically the case of the chaotic "scrambling" of quantum information, there is a famous conjecture, currently the subject of much study, that the fastest possible scrambler is a black hole. As an amateur on this subject, perhaps the best I can do is to quote the title and abstract of one of the relevant papers: A bound on chaos We ...


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In this context how does the Heisenberg Uncertanity Principle Physics is the discipline that uses mathematical models, called Physics Theories, to describe observations and data, and, very important to predict future behavior. (A model that only fits existing data is a map, not a theory). So quantum mechanics, the theory developed from observations and ...


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The Heisenberg uncertainty principle reflects the fact that, according to quantum mechanics, certain combinations of the observable properties of particles are fundamentally incompatible (the technical term is 'non-commuting'), so that the particle cannot posses both properties at once. If a particle has a definite position say, its momentum is undefined. ...


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The HUP is fully compatible with determinism. Quantum mechanics without any special role for measurement (i.e. with the Schrodinger equation as the only law of motion) is deterministic, for example.


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Not every quantum-mechanical model has an immediate, unique classical counterpart. That said, classical counterparts for the Bose-Hubbard model have been proposed, for instance, in Kolovsky's paper, "Bose-Hubbard Hamiltonian: Quantum Chaos approach", and in Graefe's thesis, "Quantum-Classical Correspondence for a Bose-Hubbard dimer and its non-Hermitian ...


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An interesting question that unfortunately might not have a clear answer and/or be off topic (see this discussion on big list questions). Why is it hard to answer? First, Lyapunov exponents $\lambda$ have unit of frequency, i.e., 1/time and systems have intrinsic time scales $\tau$, so a normalized Lyapunov exponent $$\lambda_\tau=\lambda/\tau$$ would ...


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There are a number of ways of quantifying chaos. For instance: Lyapunov exponents - Sandberg's answer covers the intensity of chaos in a chaotic system as measured by its Lyapunov exponents, which is certainly the main way of quantifying chaos. Summary: larger positive exponents and larger numbers of positive exponents correspond to stronger chaos. Relative ...


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Lyapunov exponents are the standard method. If the dynamics is $\mathbf{x}'(t)=\mathbf{f}(\mathbf{x})$ and we follow a particular trajectory $\mathbf{x}_0(t)$ starting at $\mathbf{x}_0$, then a small ball of other starting points $\mathbf{x}_0+\mathbf{\epsilon}$ gives rise to a deformed ball (an ellipsoid) $\mathbf{x}_\epsilon(t)$ at later times. The axes of ...


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By checking the relevant reference (and iterating once) you arrive at the paper by Qi Ouyang, Harry L. Swinney, and Ge Li, "Transition from Spirals to Defect-Mediated Turbulence Driven by a Doppler Instability" (Phys. Rev. Lett. 84, 1047; e-print 1, 2), which describes: The observed spiral instability occurs whent he spiral tip meanders and the Doppler ...


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I don't know if I can state a clear single "definition", but hopefully I will be able to sort out some of the concepts and the confusion. integrability is sometimes associated with having a closed form solution This, I think, is categorically not true. At least in the usual sense of 'closed form'. If you take the Lieb-Liniger model, which is I believe ...


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After doing some studies on this subject for months now I did received the answer to the question that I've been looking out for(I'm really Shameful for myself now).Ok then, here it goes as the phenomena of Chaos is Unpredictable so one can NEVER determine the exact values of Chaotic System Parameters for which the system exhibit Sensitive dependence on ...


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As long as large-scale global circulation is stable, the weather patterns do not change too much and it is possible to calculate averages. For example of the total heat balance. Many models exclude potentially important feedback mechanisms, like the effect of melting Arctic sea ice on albedo. And it is of course impossible to model feedback mechanisms that ...


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Chaotic dynamics typically occurs on an attractor state. At large times where on the attractor the system ends up is unpredictable - but it is highly predictable that it will be on the attractor. So short term unpredictability is not a problem for long term predictability.


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After some debugging I have come to the conclusion that those jumps are longitudinal mode jumps created by the interaction of the VCSEL with a parasitic external cavity, created by the end connector of the optical fiber pigtailed to the VCSEL. This fits to the expected fiber cavity length of the 51 MHz jumps: $$z_{cavity}=\frac{c}{2 \nu n}=1.96\textrm{ m}$$


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