What is Quantum chaos: Definition and 14 Discussions

Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of Planck's constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos (although this may not be a fruitful way of examining classical chaos). If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics?In seeking to address the basic question of quantum chaos, several approaches have been employed:

Development of methods for solving quantum problems where the perturbation cannot be considered small in perturbation theory and where quantum numbers are large.
Correlating statistical descriptions of eigenvalues (energy levels) with the classical behavior of the same Hamiltonian (system).
Semiclassical methods such as periodic-orbit theory connecting the classical trajectories of the dynamical system with quantum features.
Direct application of the correspondence principle.

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  1. Demystifier

    A Discussing the Sachdev–Ye–Kitaev Model

    Currently it's a very hot topic, so it would be nice to have a thread on this. Those who never heard of it may start from https://en.wikipedia.org/wiki/Sachdev–Ye–Kitaev_model A good review is https://arxiv.org/abs/1711.08482
  2. MathematicalPhysicist

    A Quantum Chaos: Expert Discussion and Q&A

    I might have a few questions about this topic in the future. So I am just asking if there are any experts on this topic here? Thanks in advance! BTW I asked also in physics stackexchange why they don't have a tag of QC, but you know how that site is...
  3. P

    I Calculating Hamiltonian matrix elements in a chaotic system

    The system in which I tried to calculate the Hamiltonian matrix was a particle in a stadium (Billiard stadium). And I used the principle where we take a rectangle around the stadium in which the parts outside the stadium have a very high potential V0. We know the wave function of a rectangular...
  4. C

    A Exploring Quantum Chaos: Is it Truly Random or Deterministic?

    Hi, I was curious to know what the perception of quantum chaos is. It seems a bit on the fringe, but at the same time it seems interesting. An adviser I'm considering working for works on both solid state physics applications and does some theoretical work in quantum chaos, so I'm wondering if...
  5. C

    What are current research directions in Quantum Chaos?

    What are the topics which are been perceived by researchers around the World on the topic of Quantum Chaos? I know my questions is not specific, but I do not have any idea to ask about anything specific.
  6. DeathbyGreen

    Quantum fluctuations and order

    Is there a good explanation for how we can explain an ordered universe arising from an inherently uncertain quantum world? I'm aware of the conflict between special relativity and quantum vacuum fluctuations, but is this the only issue? The correspondence principle would seem to imply that...
  7. S

    Quantum Chaos, Level spacing distr. in integrable system

    Hello all, For an undergraduate essay, I am studying the development of quantum chaos in a 1D spin 1/2 chain (my main source paper can be found here:http://scitation.aip.org/content/aapt/journal/ajp/80/3/10.1119/1.3671068). One of the main tools used to distinguish chaotic from non chaotic...
  8. M

    Bohm Mechanics and Quantum Chaos

    Hello everyone, I would like to know if Bohm Mechanics (and weak measurement) could be useful in understanding Quantum Chaos theories? I'm currently in search of a PhD in Foundation of QM and I would like to know if doing a project that combine the trajectories coming from Bohm Mechanics with...
  9. W

    Can Quantum Chaos Theory Unravel the Mysteries of Biology?

    http://www.technologyreview.com/blog/arxiv/27628/?p1=blogs For those who might not know of the theory the goal of quantum chaos theory is to explain all of classical physics including classical chaos as emerging from quantum systems. They've had some experimental success in the past, but this...
  10. A

    Quantum Chaos: Existence and Stability

    what is quantum chaos? dose it exist realy? the original definition of classical chaos is a system with exponential sensitivity to initial conditions. however in quantum mechanics because of the linear property of the schrodinger equation, variation on initial condition of the wave function...
  11. MathematicalPhysicist

    Synthesis between Quantum Chaos and QFT.

    Are there any attempts to synthesize between these two theories? I mean are there methods from QFT being used in QC and vice versa? I asked one professor from my univ if I were to research under his belt in QC, would I need some QFT knowledge and he said not. So I wonder are they really...
  12. F

    Dimensions of the logistic map state space and quantum chaos.

    Apologies if this is the wrong forum, but I have a pair of thematically connected questions that I can't really fit anywhere else. Please move if this is better suited to the quantum physics forums. My first question being: The Poincare-Bendixon theorem states that chaos can only occur for...
  13. Q

    Is Quantum Chaos Real Despite Contradictions in Physics?

    According to Prof. Sir M. Berry's argument, the Quantum Mechanics transition to Classical Mechanics (when the Planck constant approaches 0) is a singular process. So there is a lot of new physics here. Let's consider the Schrodinger Equation. If the wave function at t=0 has a small error...
  14. MathematicalPhysicist

    Understanding Quantum Chaos: A Beginner's Guide

    can someone please explain me in a layman (or even in elaborative manner) way, what is quantum chaos?