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We study the thermodynamical properties of a noninteracting electron gas confined in one dimension by a harmonic-oscillator potential. The exact analytical expression for the thermodynamical potential is obtained by using a formula of contour integration. The magnetizations, magnetic susceptibilities, and the specific heats are then studied each as a function of the strength of the magnetic field in different regimes of the temperature and effective thickness. It is shown at low temperature, the magnetization, magnetic susceptibility, and the specific heat oscillate as the strength of the magnetic field increases. Especially, there exist two modes of oscillations for the specific heat in certain regimes of low temperature and effective thickness.
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Keywords:
- thermodynamical potential /
- magnetization /
- magnetic susceptibility /
- specific heat
[1] Halperin W P 1986 Rev. Mod. Phys. 58 533
[2] Landau L D 1930 Z. Phys. 64 629
[3] Papapetro A 1939 Z. Phys. 112 587
[4] Dingle R B 1952 Proc. Roy. Soc. (London) A 212 38
[5] Ham F S 1953 Phys. Rev. 92 1113
[6] Friedman L 1964 Phys. Rev. 134 A336
[7] Childers D, Pinkus P 1969 Phys. Rev. 117 1036
[8] Thomas R B 1973 Phys. Rev. B 7 4399
[9] Denton R V 1973 Z. Phys. 265 119
[10] Meier F, Wyder P 1973 Phys. Rev. Lett. 30 181
[11] Jennings B K, Bhaduri R K 1976 Phys. Rev. B 14 1202
[12] Wang L, O'Connell R F 1986 Phys. Rev. B 34 5160
[13] Horing N J M, Gumbs G, Kamen E, Glasser M L 1990 Phys. Rev. B 41 10453
[14] Grzesik J A 2012 AIP Advances 2 012105
[15] van Leeuwen J H 1921 J. Phys. 2 361
[16] van Vleck J H 1932 The Theory of Electric and Magnetic Susceptibility (Oxford: Clarendon Press)
[17] Chen J W, Pan X Y 2013 Chin. Phys. B 22 117501
[18] Meir Y, Entin-Wohlman O, Gefen Y 1990 Phys. Rev. B 42 8351
[19] Geyler V A, Margulis V A 1997 Phys. Rev. B 55 2543
[20] Wang Z J, L G L, Zhu C H, Huo W S 2012 Acta Phys. Sin. 61 179701 (in Chinese) [王兆军, 吕国梁, 朱春花, 霍文生 2012 61 179701]
[21] Li Z B, Shen B G, Niu E, Liu R M, Zhang M, Sun J R 2013 Chin. Phys. B 22 117503
[22] Tian H Y, Wang J 2012 Chin. Phys. B 21 017203
[23] Gazeau J P, Hsiao P Y, Jellal A 2002 Phys. Rev. B 65 094427
[24] Champel T 2001 Phys. Rev. B 64 054407
[25] Kuzmenko N K, Mikhajlov V M 2003 Phys. Lett. A 311 403
[26] Wendler L, Grigoryan V G 1996 Phys. Rev. B 54 8652
[27] Alexandrov A S, Bratkovsky A M 1996 Phys. Rev. Lett. 76 1308
[28] Sullivan P F, Seidel G 1968 Phys. Rev. 173 679
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[1] Halperin W P 1986 Rev. Mod. Phys. 58 533
[2] Landau L D 1930 Z. Phys. 64 629
[3] Papapetro A 1939 Z. Phys. 112 587
[4] Dingle R B 1952 Proc. Roy. Soc. (London) A 212 38
[5] Ham F S 1953 Phys. Rev. 92 1113
[6] Friedman L 1964 Phys. Rev. 134 A336
[7] Childers D, Pinkus P 1969 Phys. Rev. 117 1036
[8] Thomas R B 1973 Phys. Rev. B 7 4399
[9] Denton R V 1973 Z. Phys. 265 119
[10] Meier F, Wyder P 1973 Phys. Rev. Lett. 30 181
[11] Jennings B K, Bhaduri R K 1976 Phys. Rev. B 14 1202
[12] Wang L, O'Connell R F 1986 Phys. Rev. B 34 5160
[13] Horing N J M, Gumbs G, Kamen E, Glasser M L 1990 Phys. Rev. B 41 10453
[14] Grzesik J A 2012 AIP Advances 2 012105
[15] van Leeuwen J H 1921 J. Phys. 2 361
[16] van Vleck J H 1932 The Theory of Electric and Magnetic Susceptibility (Oxford: Clarendon Press)
[17] Chen J W, Pan X Y 2013 Chin. Phys. B 22 117501
[18] Meir Y, Entin-Wohlman O, Gefen Y 1990 Phys. Rev. B 42 8351
[19] Geyler V A, Margulis V A 1997 Phys. Rev. B 55 2543
[20] Wang Z J, L G L, Zhu C H, Huo W S 2012 Acta Phys. Sin. 61 179701 (in Chinese) [王兆军, 吕国梁, 朱春花, 霍文生 2012 61 179701]
[21] Li Z B, Shen B G, Niu E, Liu R M, Zhang M, Sun J R 2013 Chin. Phys. B 22 117503
[22] Tian H Y, Wang J 2012 Chin. Phys. B 21 017203
[23] Gazeau J P, Hsiao P Y, Jellal A 2002 Phys. Rev. B 65 094427
[24] Champel T 2001 Phys. Rev. B 64 054407
[25] Kuzmenko N K, Mikhajlov V M 2003 Phys. Lett. A 311 403
[26] Wendler L, Grigoryan V G 1996 Phys. Rev. B 54 8652
[27] Alexandrov A S, Bratkovsky A M 1996 Phys. Rev. Lett. 76 1308
[28] Sullivan P F, Seidel G 1968 Phys. Rev. 173 679
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