## Jens Oluf Andersen

Jens Oluf Andersen is a professor at the Department of Physics at NTNU. He is the head of divison for theoretical physics.

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# Understanding fundamental particles in strong magnetic fields Jens Oluf Andersen       22   22 April, 2016 When the universe was created, strong magnetic fields existed. The same type of magnetic fields can be created in experiments when heavy ions are made to collide. We study how elementary particles behave in these fields. The theoretical understanding of this is important in order to explain the experiments as well the history of the universe.

Elementary particles, such as protons, neutrons, and pions are composed of different types of quarks and anti-quarks. For example, a proton is composed of two u-quarks and one d-quark, while a pion is built out of a u-quark and an anti d-quark.(see Figure 1). Elementary particles that consist of quarks and/or antiquarks are called hadrons. Figure 1: Protons are composed of three quarks (left) and pions are built out of a quark and an antiquark

Extreme temperatures
When a hadron gas is heated to extreme temperatures, the hadrons “melt”. This means that the quarks and antiquarks are no longer bound together, but can move freely around. This is called
a phase transition from the hadronic phase to a so-called quark-gluon plasma phase.
The temperature required for this phase transition is approximately 4 trillion degrees Celsius, which is many orders of magnitude higher than the temperature in the core of the Sun, which
approximately 15 million degrees Celsius.

Temperature drop after the Big Bang
The opposite of the melting process mentioned above, took place shortly after the Big Bang.
Immediately after the Big Bang, the temperature was so high that a quark-gluon
plasma existed. As the universe expanded, the temperature dropped rapidly, and approximately 10 microseconds after the Big Bang it was so “cold” that hadrons were formed.
This is schematically illustrated in Figure 2.

Heavy-ion collision experiments at CERN
A quark-gluon plasma can be created in the lab by colliding two heavy ions, for example
gold or lead ions. This kind of experiments are carried out at the Large Hadron Collider at CERN, Geneva. The energy of the particles in these experiments is so high that the associated temperature created in the collision is sufficient for the hadrons to melt (see Figure 2). Figure 2. Quark-gluon plasma in the early universe and heavy-ion collisions

It is known that very strong magnetic field existed in the early universe. Strong magnetic fields are also created in some of the heavy-ion collision experiments. The theoretical understanding of how hadrons behave in these fields, is therefore important in order to explain the experiment as well the history of the universe.

Elementary particles in strong magnetic fields
In a recently published paper, we have discussed in detail the properties of elementary particles in strong magnetic fields at temperatures in the vicinity of the phase transition. The material that we have covered includes the contributions from a large number of authors. It also includes the PhD work of William Naylor in collaboration with Anders Tranberg (UiS) and Jens O. Andersen.

This new knowledge is a step of the way towards understanding what happened in the early universe. Figure 3: The melting temperature for a gas of pions as a function of the magnetic field measured in units of the pion mass

Figure 3 shows how the melting temperature of a pion gas varies with the temperature. In this model calculation, the melting temperature increases as the magnetic fields grows. The green curve corresponds to massless pions while the blue curve corresponds to pions with the mass found in nature.

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# Understanding Quark Matter Jens Oluf Andersen       22   22 December, 2015  We are looking into the very deep of the stars resulting from supernova explosions. Through our work, we have found a new way of understanding the interaction between quarks – the atoms’ smallest building blocks.

Atoms are the building blocks of matter. They consist of a nucleus with electrons moving around. The nucleus is built out of neutrons and protons (nucleons), which again are built out of quarks, see Figure 1. Quarks can have three different color charges (analogous to electric charge), red, green, and blue.

### Quark matter in neutron stars

When a giant star explodes, its core collapses. The protons and electrons essentially melt into each other, and a neutron star consisting mainly of nucleons is formed. Nucleons are extremely densely packed: A neutron star has a mass of 1-2 solar masses and a radius of only about 10km.
Or put differently, if a cricket ball were made of neutron star material it would weigh about 40 times the estimated weight of the entire human population.

Normally, quarks are bound in nucleons. However, when nucleons are squeezed hard enough together, the individual nuclei lose their identity, and the quarks move freely around. This is called quark matter.

As a result of the total collapse the neutron star has undergone, quark matter can possibly be found deep inside them. The properties of neutron stars depend heavily on whether quark matter is present in the core of the star or not.

### How to understand quark matter

The quarks and their interactions are described by a theory called Quantum Chromodynamics (QCD). In practice, a direct application of QCD to calculate the properties of three-color quark matter is technically not yet feasible. Hence one must resort to models to simplify the problem.

### From three colors to two

It turns out that we can use QCD directly to calculate the properties of quark matter, if we imagine a world where quarks only come in two colors. This technique is a numerical method and is called lattice simulations.

In a world of two-color QCD, we can compare quark-matter properties from lattice simulations with those from model calculations. In our recent paper (lenke) we have done exactly this. Generally, we obtain good agreement between the lattice results and our results.

Figure 2 shows one of the properties that we have calculated, namely the so-called Polyakov loop. This is a measure of how free the quarks are. Depending on the temperature, the Polyakov loop varies between zero for bound quarks and one for completely free quarks. The blue crosses are the data points from lattice simulations and the red curve shows the result from the model calculations, with uncertainty (yellow).

### New insights in quark matter

It is straightforward to translate our model from two colors to three colors, and therefore we believe that our results ultimately will give us additional insight into quark matter in the real world and perhaps increase our understanding of neutron stars. Figure 2. Polyakov loop as a function of the temperature from lattice simuations (blue crosses) and model calculation (red curve) with uncertainty band (yellow).

Our work is published in Physical Review D: Confronting effective models for deconfinement in dense quark matter with lattice data Authors: Jens O. Andersen (NTNU), Tomáš Brauner (UiS), and William R. Naylor (NTNU).

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