## Research Abstracts Online

January
2008 - March 2009

### University of Minnesota Twin Cities

Institute of Technology

School of Physics and Astronomy

Department of Physics

Theoretical Physics Institute

## PI: Philippe de Forcrand, Adjunct Fellow

### Quantum Chromodynamics at Finite Density

Quantum chromodynamics (QCD) predicts that quarks are confined at low temperature and low density. But the theory predicts that confinement is lost under extreme conditions: at high temperature, a plasma of quarks and gluons forms; at high densities and low temperatures, Cooper pairs of two quarks condense and color superconductivity takes place. In addition to these three regimes, other phases are likely to exist.

At non-zero quark density, the numerical simulations have to face the "sign problem”: the integral to sample is over an oscillatory function, and importance sampling fails. Information can only be obtained on small volumes and for small densities.

While continuing their very successful investigation based on an imaginary chemical potential followed by analytic continuation, these researchers have started the study of a "corner” of the phase diagram. At this location, the sign problem is absent, interesting physics takes place, and some theoretical predictions are available: that is, the case of finite isospin density, where two quark species have opposite (non-zero) densities. In this case, the corresponding chemical potential *mu[sub]I* is coupled to charged pions *mu[sub]pi*. These are bosons, which condense at low temperature when *mu[sub]I* > *mu[sub]pi*. This Bose condensation occurs in addition to the usual, temperature-driven, confinement-deconfinement transition, making the (*mu[sub]I*, T) phase diagram rich and difficult to predict.

The researchers have determined the (*mu[sub]I*, T) phase diagram of QCD for isospin *mu[sub]I* on a small lattice. Ongoing crosschecks on a larger lattice, however, reveal significant finite-size effects on the Bose condensation. These effects require a careful extrapolation to infinite volume, which is the next step in this research.

### Group Members

Urs Wenger, Insitute for Theoretical Physics, ETZ Zürich, Zürich, Switzerland

Owe Philipsen, Institute for Theoretical Physics, Westfaelische Wilhelms-Universität, Münster, Germany