# Physicists solve decade-old quantum mechanics problem

## Scientists are now able to calculate exactly how atoms will behave in the physical world.

Published

Danish scientists have solved the quantum mechanics problem that has been teasing them since the 1930s: how to calculate real life behaviour of atoms.

The formula helps them work out how to optimise the transport of information from one atom to another. This will be necessary if we are to one day construct quantum computers.

"The problem has been to calculate when atoms do one thing or another in the real world. We have been able to calculate this in theory, but when we experiment and insert data into existing models, they fall apart,” says co-author Nicolaj Thomas Zinner, associate professor at the Department of Physics and Astronomy at Aarhus University. “We have finally solved that problem."

The study was recently published in Nature Communications.

##### Why some iron is magnetic while other is not

The scientists’ discovery is best explained by an example:

Imagine a long row of atoms like beads on a string.

Every atom has what is known as a magnetic moment, that is to say a magnetic direction or 'spin' in either an upward or downward direction. This is a fundamental property of all atoms.

The atoms' overall magnetic moment determines whether the material constituted by the atoms is magnetic or not.

1. If all the atoms the same direction the material is ferromagnetic

2. If, on the other hand, every other atom points upwards and the other downwards, the material is antiferromagnetic (the atoms arrange themselves in a specific fashion so the material is not magnetic).

In this way, one piece of iron may be magnetic while another is not. The atoms' overall spin determines whether the iron is one type or the other.

##### Makes new calculations possible

Whether the atoms' magnetic moment points up or down is determined, among other things, by other atoms in the near vicinity.

Let us return to the example of the long string of atoms. In this case each atom's effect on each other determines the spin of neighbouring atoms.

This may for example be that if one atom has an upward spin, its neighbour to the left will have a downward spin. And this is where the scientists' problem arise.

Until now, scientists have been able to calculate how the entire string patterns will look if they turn the magnetic moment of one of the atoms from up to down.

They have been able to calculate how the information regarding the turned atom will spread to all the other assets and how they will then behave and in which direction they would turn -- in which direction all the atoms would turn if the scientists changed the direction of a single atom.

##### New formula includes the landscape

Performing the calculation is in itself quite some feat, and the formula used in the calculation dates back to Nobel prizewinner Hans Bethe, one of the grand old men of quantum mechanics.

The problem for scientists has been that they were only able to calculate the behaviour of atoms in an ideal world, in which the atoms lie in neat rows and are unaffected by their surroundings.

The surroundings do affect them, however, and it was not until the new Danish formula that scientists were able to include them in their calculations.

"For the first time, we're in a position to calculate the atoms' magnetic moment independently of each other in an atomic landscape. That's to say that our formula includes both local conditions or open 'landscapes' for each individual atom in the calculation. It makes no difference whether the atoms are sitting slightly up or slightly down or a bit closer to the atom to the right. Everything's included in our model," says Zinner.

##### Can optimise quantum computers

The interesting thing about scientists now being able to include the atoms' landscape in their calculations is that they can relatively easily alter the landscape experimentally, i.e. change the atoms' physical surroundings.

This means that scientists can now calculate how a landscape needs to look for the atoms to behave in a specific manner.

This may be when they want all the magnetic moments to point in one direction or if they want to optimise the transfer of the information passing from one end of the landscape to another when one atom is reversed.

"It's this kind of thing we are interested in being able to do with quantum computers. We'd like to be able to construct quantum mechanical systems in which information about the magnetic moment of atoms spreads rapidly and predictably to other atoms, ultimately ending up with a recipient of some form or other. Our formula shows how we can optimise the process," says Zinner.

##### Study makes scientists wiser

Anders S. Sørensen, professor of theoretical quantum optics at the Niels Bohr Institute was not involved in the new Danish study but has read it and finds it extremely interesting.

"It's interesting because it enables us to calculate something we’ve never previously been able to calculate. The study has made us wiser, and it solves a problem we have had great difficulty solving," says Sørensen.

He points out that we shouldn't expect the new research to result in new mobile phone technology or anything along those lines just yet.

"In the long run, though, it'll help us understand structure of materials in nature and helpers design new materials when out in the future," says Sørensen.

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Read the original story in Danish on Videnskab.dk

Translated by: Hugh Matthews