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

Walking crystals may lead to new field of crystal robotics

February 23, 2018

Researchers have demonstrated that tiny micrometer-sized crystals—just barely visible to the human eye—can "walk" inchworm-style across the slide of a microscope. Other crystals are capable of different modes of locomotion ...

Seeing nanoscale details in mammalian cells

February 23, 2018

In 2014, W. E. Moerner, the Harry S. Mosher Professor of Chemistry at Stanford University, won the Nobel Prize in chemistry for co-developing a way of imaging shapes inside cells at very high resolution, called super-resolution ...

Recurrences in an isolated quantum many-body system

February 23, 2018

It is one of the most astonishing results of physics—when a complex system is left alone, it will return to its initial state with almost perfect precision. Gas particles, for example, chaotically swirling around in a container, ...

Researchers turn light upside down

February 23, 2018

Researchers from CIC nanoGUNE (San Sebastian, Spain) and collaborators have reported in Science the development of a so-called hyperbolic metasurface on which light propagates with completely reshaped wafefronts. This scientific ...

Hauling antiprotons around in a van

February 22, 2018

A team of researchers working on the antiProton Unstable Matter Annihilation (PUMA) project near CERN's particle laboratory, according to a report in Nature, plans to capture a billion antiprotons, put them in a shipping ...

0 comments

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.