Sunday, August 24, 2008

Dense nuclear matter

New paper! Probably too technical to go into here, but it relates to our current inability to directly simulate dense nuclear matter (QCD at nonzero baryon density). When the number of quarks and antiquarks is equal, the functional integral representation of the partition function Z has good positivity properties and can be evaluated using importance sampling (lattice Monte Carlo methods). That is no longer true when the system has nonzero baryon number, as would be the case inside a neutron star or in nuclear matter.

We rewrite Z = Z+ - Z- , where Z+ and Z- have good positivity properties, and conjecture, based on arguments using the analytic properties of the free energy, that at most points of the phase diagram Z+ dominates Z-. At such points one can simulate the theory using Monte Carlo. (paper available after 5 pm pacific 8.24.08)

Sign problem? No problem -- a conjecture

Stephen D.H. Hsu, David Reeb

We investigate the Euclidean path integral formulation of QCD at finite baryon density. We show that the partition function Z can be written as the difference between two sums, each of which defines a partition function with positive weights. We argue that at most points on the phase diagram one will give an exponentially larger contribution than the other. At such points Z can be replaced by a more tractable path integral with positive definite measure, allowing for lattice simulation as well as the application of QCD inequalities. We also propose a test to control the accuracy of approximation in actual Monte Carlo simulations. Our analysis may be applicable to other systems with a sign problem, such as chiral gauge theory.

No comments:

Blog Archive