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Scientists at Brookhaven National Laboratory have used two-dimensional condensed matter physics to understand the interactions of quarks in neutron stars, simplifying the study of these densest cosmic entities. This work helps to describe low-energy excitations in dense nuclear matter and may unveil new phenomena at extreme densities, driving advances in the study of neutron stars and comparing heavy- ion collisions.

#### The science

Understanding the behavior of nuclear matter—including the quarks and gluons that make up the protons and neutrons of atomic nuclei—is extremely complex. This is particularly true in our world, which is three dimensional. Mathematical techniques from condensed matter physics that consider interactions in one spatial dimension (including time) greatly simplify the challenge. Using this two-dimensional approach, scientists have solved the complex equations that describe how low-energy excitations travel through a system of dense nuclear matter. This work indicates that the center of neutron stars, where such dense nuclear matter exists in nature, can be described by an unexpected form.

#### The Effect

The ability to understand quark interactions in two dimensions opens a new window into understanding neutron stars, the densest form of matter in the universe. The approach could help advance the current “golden age” for the study of exotic stars. This surge in research success was triggered by the recent discoveries of[{” attribute=””>gravitational waves and electromagnetic emissions in the cosmos. This work shows that for low-energy excitations, all of the complications of the three-dimensional quark interactions fall away. These low-energy excitations are slight disturbances triggered as a neutron star emits radiation or by its own spinning magnetic fields. This approach might also enable new comparisons with quark interactions in less dense but much hotter nuclear matter generated in heavy-ion collisions.

#### Summary

The modern theory of nuclei, known as quantum chromodynamics, involves quarks bound by the strong nuclear force. This force, carried by gluons, confines quarks into nucleons (protons and neutrons). When the density of nuclear matter increases, as it does inside neutron stars, the dense system behaves more like a mass of quarks, without sharp boundaries between individual nucleons. In this state, quarks at the edge of the system are still confined by the strong force, as quarks on one side of the spherical system interact strongly with quarks on the opposite side.

This work by researchers at Brookhaven National Laboratory uses the one-dimensional nature of this strong interaction, plus the dimension of time, to solve for the behavior of excitations with low energy near the edge of the system. These low energy modes are just like those of a free, massless boson—which is known in condensed matter as a “Luttinger liquid.” This method allows scientists to compute the parameters of a Luttinger liquid at any given density. It will advance their ability to explore qualitatively new phenomena expected to occur at the extreme densities within neutron stars, where nuclear matter behaves quite differently than it does in ordinary nuclei, and compare it with much hotter (trillion-degree) dense nuclear matter generated in heavy-ion collisions.

Reference: “When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid” by Marton Lajer, Robert M. Konik, Robert D. Pisarski and Alexei M. Tsvelik, 30 March 2022, *Physical Review D*.

DOI: 10.1103/PhysRevD.105.054035

This research was funded by the Department of Energy Office of Science.

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