摘要A Fock--Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of ω/ωc and certain algebra realization (SU(2)and SU(1,1)), and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.
Abstract：A Fock--Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of ω/ωc and certain algebra realization (SU(2)and SU(1,1)), and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.
YU Xiao-Min;LI Kang. Non-Commutative Fock--Darwin System and Magnetic Field Limits[J]. 中国物理快报, 2008, 25(6): 1980-1983.
YU Xiao-Min, LI Kang. Non-Commutative Fock--Darwin System and Magnetic Field Limits. Chin. Phys. Lett., 2008, 25(6): 1980-1983.
[1] Seiberg N et al 1999 J. High Energy Phys. 0329909 [2] Connes A et al 1998 J. High Energy Phys. 0039802 Douglas M R et al 1998 J. High Energy Phys. 0089802 Douglas M R et al 2001 Rev. Mod. Phys. 73 977 [3] Ardalan F et al 1999 J. High Energy Phys. 0169902 [4]Curtright T et al 1998 Phys. Rev. D 58 25002 Mezincescu L hep-th/0007046 [5] Chu S C and Ho P M 1999 Nucl. Phys. B 550 151 Chu S C and Ho P M 2000 Nucl. Phys. B 568 447 [6] Schomerus V 1999 J. High Energy Phys. 030 9906 [7] Filk T 1996 Phys. Lett. B 376 53 [8] Castellani L 2000 Class. Quant. Grav. 17 3377 [9] Konechny A and Schwarz A 2002 Phys. Rept. 360353 [10]Dunne G et al 1990 Phys. Rev. D 41 661 [11] Demetrian M and Kochan D hep-th/0102050 Zhang J Z 2004 Phys. Lett. B 584 204 [12] Li K et al 2005 Mod. Phys. Lett. A 20 2165 [13] Nair V P 2001 Phys. Lett. B 505 249 Nair V P et al 2001 Phys. Lett. B 505 267 [14] Morariu B et al 2001 Nucl. Phys. B 610 531 Morariu B et al 2002 Nucl. Phys. B 634 326 [15]Chaichian M et al 2001 Phys. Rev. Lett. 862716 Chaichian M et al 2001 Nucl.Phys. B 611 383 [16]Li K and CHAMOUN N 2006 Chin. Phys. Lett. 231122 [17]Chaichian M et al 2002 Phys. Lett. B 527 149 Falomir H et al 2002 Phys. Rev. D 66 045018 Dayi O F and Jellal A 2002 J. Math. Phys. 434592 [18]Wang J H and Li K 2007 Chin. Phys. Lett. 24 5 Li K and Chamoun N 2007 Chin. Phys. Lett. 241183 [19]Mirza B and Zarei M 2004 Eur. Phys. J. C 32583 [20]Chambers R G 1960 Phys. Rev. Lett. 5 3 [21] Karabali D et al 2002 Nucl. Phys. B 627 565 [22]See, for examples, Dayi \"{O F and Jellal A 2001 Phys. Lett. A 287 349 Basu B and Ghosh S 2005 Phys. Lett. A 346 133 Susskind L hep-tp/0101029 Lee B H, Moon K and Rim C 2001 Phys. Rev. D 64085014 [23]Banerjee R 2002 Mod. Phys. Lett. A 17 631 [24]Ghosh S hep-th/0405177 Jellal A hep-th/0105303. [25]Fock V 1928 Z. Phys. 47 446 Darwin C G 1930 Proc. Cambridge Phil. Soc. 2786 Dune G V et al 1990 Phys. Rev. D 41 661 [26]Landau L D 1930 Z. Phys. 64 629
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