Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
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>{approx}{delta}exp(iq{sub 2}{center_dot}r) and <ud>{approx}{delta}exp(iq{sub 3}{center_dot}r) whose position-space dependence is that of two plane waves with wave vectors q{sub 2} and q{sub 3} 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}{yields}0 limit as expected, find that it correctly predicts that {delta} decreases with increasing angle between q{sub 2} and q{sub 3} meaning that the phase with q{sub 2} parallel q{sub 3} 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 q{sub 2} and q{sub 3}.
- OSTI ID:
- 20774799
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 73, Issue 11; Other Information: DOI: 10.1103/PhysRevD.73.114012; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Is the term "type-1.5 superconductivity" warranted by Ginzburg-Landau theory?
Statistical studies of spinning black-hole binaries