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限制在一维谐振势下的三维自由电子气的一些热力学性质

邵宗乾 陈金望 李玉奇 潘孝胤

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限制在一维谐振势下的三维自由电子气的一些热力学性质

邵宗乾, 陈金望, 李玉奇, 潘孝胤

Thermodynamical properties of a three-dimensional free electron gas confined in a one-dimensional harmonical potential

Shao Zong-Qian, Chen Jin-Wang, Li Yu-Qi, Pan Xiao-Yin
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  • 利用围路积分表达的计算系统热力学势的一个公式, 得到被一维谐振子势限制、有垂直磁场作用的三维自由电子气的在任意温度下的热力学势的精确解析表达式. 然后利用其研究了不同温度和尺度区域内磁化强度、磁化率和比热随磁场强度的变化情况. 研究表明,低温下磁化强度、磁化率和比热随磁场强度变化出现振荡现象, 其中比热还会出现两种不同的振荡模式.
    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.
    • 基金项目: 国家自然科学基金(批准号: 11275100)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11275100).
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    Landau L D 1930 Z. Phys. 64 629

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    Childers D, Pinkus P 1969 Phys. Rev. 117 1036

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    [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 物理学报 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

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    Wendler L, Grigoryan V G 1996 Phys. Rev. B 54 8652

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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 物理学报 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

计量
  • 文章访问数:  2272
  • PDF下载量:  420
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-06-11
  • 修回日期:  2014-08-18
  • 刊出日期:  2014-12-05

限制在一维谐振势下的三维自由电子气的一些热力学性质

  • 1. 宁波大学理学院, 宁波 315211
    基金项目: 

    国家自然科学基金(批准号: 11275100)资助的课题.

摘要: 利用围路积分表达的计算系统热力学势的一个公式, 得到被一维谐振子势限制、有垂直磁场作用的三维自由电子气的在任意温度下的热力学势的精确解析表达式. 然后利用其研究了不同温度和尺度区域内磁化强度、磁化率和比热随磁场强度的变化情况. 研究表明,低温下磁化强度、磁化率和比热随磁场强度变化出现振荡现象, 其中比热还会出现两种不同的振荡模式.

English Abstract

参考文献 (28)

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