Equation reveals the characteristics of quantum chaos

September 4, 2017, Lund University

Researchers have now succeeded in formulating a mathematical result that provides an exact answer to the question of how chaos actually behaves. The researchers have analysed chaotic states at the atomic level.

What does look like in the smallest of worlds that we can imagine – inside atoms? The world in there behaves a lot differently to the world that we experience; the protons and neutrons in the nucleus are waves. In this microcosmos, the so-called quantum world, the normal rules of nature do not apply, but in terms of the state called chaos, there are universal features that are present, regardless of the level of existence.

In a new study, a research group including researchers from Lund University, has therefore set out to tackle the theory of quantum chaos, i.e. they have studied the chaotic state at quantum level. The theory of quantum chaos is about explaining the irregular movements of both electrons and nuclei, as well as the irregular movements of, for example, rays of light in optical instruments with complex geometries, or sound waves in a furnished room.

The researchers have analysed statistical properties at different in a quantum chaos state. Although the research is theoretical, it has practical applications. Chaos theory and the associated concept of random matrices are used in different contexts where there is an attempt to describe and analyse chaotic . These contexts include financial instruments, brain surgery and even the string for the universe.

"In chaotic quantum systems, the energy levels repel each other, and they affect each other even if they are far apart," states Vladimir Osipov, a researcher at Lund University's Faculty of Science and one of the authors of the new study.

He notes that it is difficult to make computer calculations for a specific chaos state, as chaotic systems are extremely sensitive to the initial numbers entered in calculations. Small differences in initial values can produce large diviations in the final result of the calculation. However, due to the results of the new study, it is possible from now on to use an exact, mathematical equation to predict the characteristics of chaos without such extensive number-crunching.

"Yes, we now have an exact equation. Personally, I am actually surprised that it was possible at all," says Vladimir Osipov.

Explore further: Quantum chaos in ultracold gas discovered

More information: Roman Riser et al. Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems, Physical Review Letters (2017). DOI: 10.1103/PhysRevLett.118.204101

Related Stories

Quantum chaos in ultracold gas discovered

March 12, 2014

A team of University of Innsbruck researchers discovered that even simple systems, such as neutral atoms, can possess chaotic behavior, which can be revealed using the tools of quantum mechanics. The ground-breaking research, ...

Probing the edge of chaos

February 27, 2014

The edge of chaos—right before chaos sets in—is a unique place. It is found in many dynamical systems that cross the boundary between a well-behaved dynamics and a chaotic one. Now, physicists have shown that the distribution—or ...

Testing Weyl's law at optical frequencies

April 13, 2016

Stable states (or resonances) are always of importance in understanding reactions and collision processes of all energy scales, but they often prove difficult to detect in experiments, particularly when a system exhibits ...

Recommended for you

Coffee-based colloids for direct solar absorption

March 22, 2019

Solar energy is one of the most promising resources to help reduce fossil fuel consumption and mitigate greenhouse gas emissions to power a sustainable future. Devices presently in use to convert solar energy into thermal ...

Physicists reveal why matter dominates universe

March 21, 2019

Physicists in the College of Arts and Sciences at Syracuse University have confirmed that matter and antimatter decay differently for elementary particles containing charmed quarks.

ATLAS experiment observes light scattering off light

March 20, 2019

Light-by-light scattering is a very rare phenomenon in which two photons interact, producing another pair of photons. This process was among the earliest predictions of quantum electrodynamics (QED), the quantum theory of ...

How heavy elements come about in the universe

March 19, 2019

Heavy elements are produced during stellar explosion or on the surfaces of neutron stars through the capture of hydrogen nuclei (protons). This occurs at extremely high temperatures, but at relatively low energies. An international ...


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.