Phys. Rev. D 73, 114012 (2006) [14 pages]
Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity
Abstract
References (46)
Citing Articles
Massimo Mannarelli, 1 Krishna Rajagopal, 1,2 and Rishi Sharma11Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2Nuclear Science Division, MS 70R319, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
Received 17 March 2006; published 9 June 2006
It is an open challenge to analyze the crystalline color superconducting phases that may arise in cold dense, but not asymptotically dense, three-flavor quark matter. At present the only approximation within which it seems possible to compare the free energies of the myriad possible crystal structures is the Ginzburg-Landau approximation. Here, we test this approximation on a particularly simple "crystal" structure in which there are only two condensates <us>~Deltaexp(iq2·r) and <ud>~Deltaexp(iq3·r) whose position-space dependence is that of two plane waves with wave vectors q2 and q3 at arbitrary angles. For this case, we are able to solve the mean-field gap equation without making a Ginzburg-Landau approximation. We find that the Ginzburg-Landau approximation works in the Delta-->0 limit as expected, find that it correctly predicts that Delta decreases with increasing angle between q2 and q3 meaning that the phase with q2||q3 has the lowest free energy, and find that the Ginzburg-Landau approximation is conservative in the sense that it underestimates Delta at all values of the angle between q2 and q3.
©2006 The American Physical Society
| URL: |
http://link.aps.org/doi/10.1103/PhysRevD.73.114012
|
| DOI: |
10.1103/PhysRevD.73.114012 |
| PACS: |
12.38.Mh;
24.85.+p
|
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