摘要The dimensionless universal coefficient ξ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be ξ=4/9. The energy gap is △=5/18kf2/(2m).
Abstract:The dimensionless universal coefficient ξ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be ξ=4/9. The energy gap is △=5/18kf2/(2m).
CHEN Ji-Sheng. Ground State Energy of Unitary Fermion Gas with the Thomson Problem Approach[J]. 中国物理快报, 2007, 24(7): 1825-1828.
CHEN Ji-Sheng. Ground State Energy of Unitary Fermion Gas with the Thomson Problem Approach. Chin. Phys. Lett., 2007, 24(7): 1825-1828.
[1] DeMarco B and Jin D S 1999 Science 285 1703 [2] Bishop R A 2001 Int. J. Mod. Phys. B 15 iii [3] Baker G A 2001 Int. J. Mod. Phys. B 15 {1314 [4]Heiselberg H 2001 Phys. Rev. A 63 {043606 [5]Carlson J, Chang S Y, Pandharipande V R and Schmidt K E2003 Phys. Rev. Lett. 91 050401 Carlson J, Chang S Y, Pandharipande V R and Schmidt K E 2004 Phys. Rev. A 70 043602 [6]Ho T L 2004 Phys. Rev. Lett. 92 090402 [7]Astrakharchik G E, Boronat J, Casulleras J and Giorgini S 2004 Phys. Rev. Lett. 93 200404 [8] Astrakharchik G E, Combescot R, Leyronas X and Stringari S2005 Phys. Rev. Lett. 95 030404 [9]Schwenk A and Pethick C J {2005 Phys. Rev. Lett. 95 {160401 [10]Carlson J and Reddy S 2005 Phys. Rev. Lett. 95 060401 [11]Cohen T D 2005 Phys. Rev. Lett. 95 120403 [12] Lee D and Schaefer T 2006 Phys. Rev. C 73 015201 Lee D and Schaefer T 2006 Phys. Rev. C 73 015202 [13] Chevy F 2006 Phys. Rev. Lett. 96 130401 [14] Hu H, Liu X J and Drummond P D 2006 Europhys. Lett. 74 574 [15] Nishida Y and Son D T 2006 Phys. Rev. Lett. 97 050403 [16] Bhattacharyya A and Papenbrock T 2006 Phys. Rev. A 74 041602(R) [17] Rupak G 2007 Phys. Rev. Lett. 98 090403 [18]Bulgac A and Bertsch G F 2005 Phys. Rev. Lett. 94 070401 [19]Bulgac A, Drut J E, and Magierski P 2006 Phys. Rev.Lett. 96 090404 [20]Gehm M E, Hemmer S L, Granade S R, O'Hara K M andThomas J E 2003 Phys. Rev. A 68 011401(R) [21] Bourdel T, Cubizolles J, Khaykovich L, Magalh\"aes K M F,Kokkelmans S J J M F, Shlyapnikov G V and Salomon C 2003 Phys. Rev. Lett. 91 020402 [22]Bartenstein M, Altmeyer A, Riedl S, Jochim S, Chin C,Denschlag J H and Grimm R 2004 Phys. Rev. Lett. 92 120401 [23]Kinast J, Turlapov A, Thomas J E, Chen Q, Stajic J and Levin K2005 Science 307 1296 [24]Partridge G B, Li W, Kamar R I, Liao Y A andHulet R G 2006 Science 311 503 [25] Stewart J T, Gaebler J P, Regal C A and Jin D S {2006 Phys.Rev. Lett. 97 220406 [26]Lee D 2006 Phys. Rev. B 73 115112 [27]Chen J S, Li J R and Jin M 2005 Phys. Lett. B 608 39 Chen J S 2005 Preprint nucl-th/0509038 [28] Thomson J J 1904 Philos. Mag. 7 237 [29]Bowick M, Cacciuto A, Nelson D R and Travesset A2002 Phys. Rev. Lett. 89 185502 [30]Luca J D, Rodrigues S B and Levin Yan 2005 Europhys.Lett. 71 84 [31]Proca A 1936 J. Phys. Radium 7 347 [32]Jackson J D 1999 Classical Electrodynamics 3rd edn (NewYork: John Wiley \& Sons) [33]Peskin M E and Schroeder D V 1995 An Introduction toQuantum Field Theory (New York: Addison-Wesley) [34]Dvali G, Papucci M and Schwartz M D 2005 Phys. Rev.Lett. 94 191602 [35]Walecka J D 1974 Ann. Phys. (N.Y.) 83 491 [36]Serot B D and Walecka J D 1986 Adv. Nucl. Phys. 16 1 [37]Kapusta J I 1989 Finite Temperature Field Theory(Cambridge: Cambridge University Press) [38]Kohn W and Sham L J 1965 Phys. Rev. A 140 1133 [39] Chomaz P, Gulminelli F, Ducoin C, Napolitani P and Hasnaoui KH O 2005 Preprint astro-ph/0507633 [40] Chen J S, Li J R and Zhuang P F 2003 Phys. Rev. C 67 068202 Chen J S, Zhuang P F and Li J R 2003 Phys. Rev. C 68 045209 Chen J S, Li J R and Zhuang P F 2004 Phys. Lett. B 585 85 [41]Steele J V 2000 Preprint nucl-th/0010066 [42]Burovski E, Prokof'ev N, Svistunov B and Troyer M 2006 Phys.Rev. Lett. 96 160402 [43]Luo L, Clancy B, Joseph J, Kinast J and Thomas J E2007 Phys. Rev. Lett. 98 080402 [44]Heiselberg H 2004 Phys. Rev. Lett. 93 040402 [45]Chen J S 2006 Preprint nucl-th/0608063 Chen J S 2007 Commun. Theor. Phys. (in press) Chen J S, Cheng C M, Li J R and Wang Y P 2007 Preprintcond-mat/0702569