مقایسه آنتروپی و گرمای ویژه در سیم های کوانتومی با سطح مقطع متوازی الاضلاع و مثلثی با استفاده از آمار تی سالیس

نوع مقاله : مقاله پژوهشی کامل

نویسندگان

1 هیات علمی, گروه فیزیک، دانشکده علوم، دانشگاه یاسوج، یاسوج، ایران

2 دانشجوی دکترا گروه فیزیک، دانشکده علوم، دانشگاه یاسوج، یاسوج، ایران

چکیده

در این مقاله، آنتروپی و گرمای ویژه یک سیم کوانتومیGaAs بادو سطح مقطع متوازی الاضلاع و مثلثی بررسی می شود. در ابتدا، ویژه مقادیر انرژی و ویژه توابع سیستم با استفاده از حل معادله شرودینگر محاسبه می شوند. سپس، با استفاده از فرمول بندی تی-سالیس، آنتروپی و گرمای ویژه هر دو سیم کوانتومی را به دست می آوریم. نتایج به دست آمده نشان می دهد که آنتروپی و گرمای ویژه توابع پیوسته ای هستند. در این سیستمها، بر خلاف ترمودینامیک کلاسیک، آنترپی و گرمای ویژه هر مقداری نخواهد داشت و توسط یک شر ط (شرط قطع) تعیین می شود. در هر دو سیستم، با افزایش اندازه سیم کوانتومی، تعداد قله ها و اندازه قله ها در گرمای ویژه هر دو سیستم تغییر می کند. هر چقدر محدودیت کوانتومی قویتر می شود، طبیعت گسسته خواص ترمودینامیکی بیشتر آشکار می شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Comparison of entropy and specific heat in quantum wires with cross sections of parallelograms and triangles using Tsallis statistics

نویسندگان [English]

  • Reza Khordad 1
  • Bahareh Mirhoseini 2
1 Department of Physics, College of Science, Yasouj University, Yasouj, Iran
2 Department of Physics, College of Science, Yasouj University, Yasouj, Iran
چکیده [English]

In this paper, entropy and specific heat of a GaAs quantum wire with two different cross sections is studied. First, using the solution of Schrodinger equation, the eigenvalues and eigenfunctions are calculated analytically. Then, we have obtained entropy and specific heat of two quantum wires using Tsallis formalism. The results show that entropy and specific heat are continnus functions. Unlike classical thermodynamics, entropy and specific heat will not have any value and by a condition (cut off) is determined. For both wire, with increasing wire size the peak numbers in specific heat are changed. The stronger the quantum confinement, the thermodynamic properties of the discrete nature becomes more apparent.

کلیدواژه‌ها [English]

  • Quantum wire
  • Entropy
  • specific heat
[1] D. Bimberg, M. Grudmann, N.N. Ledentsov, Quantum Dot Heterostructures, John Wiley, New York, (1999).
[2] S. Adachi, GaAs and Related Materials: Bulk Semiconducting and Superlattices Properties, World Scientific, Singapore, (1994).
[3] D. Ferry, S. Goodnick, Transport in Nanostructures, Cambridge University press Cambridge, (1997). 

[4] L. Guo, Structural, energetic, and electronic properties of hydrogenated aluminum arsenide clusters, Journal of Nanoparticle Research 13 (2011) 2029-2039.

[5] J. Weiner, D. Chemla, D. Miller, H. Haus, A. Gossard, W. Wiegmann, C. Burrus, Highly anisotropic optical properties of single quantum well waveguides, Applied Physics Letters 47 (1985) 664-669.
 [6] L. Pfeiffer, K. West, H. Stormer, J. Eisenstein, K. Baldwin, D. Gershoni, J. Spector, Formation of high quality two-dimensional electron gas on cleaved GaAs,  Applied Physics Letters 56 (1990) 1697-1701.
[7] M. Yoshita, H. Akiyama, L. Pfeiffer, K. West, Quantum wells with atomically smooth interfaces, Applied Physics Letters 81 (2002) 49-56.
 [8] R. Khordad, Quantum wire with parallelogram cross section: optical properties, Journal of Theoretical and Applied Physics 6 (2012) 19-25.
[9] R. Khordad, Second and third-harmonic generation of parallelogram quantum wires: electric field, Indian Journal of Physics 88 (2014) 275-281.
[10] W. Xie, S. Liang, Optical properties of a donor impurity in a two-dimensional quantum pseudodot, Physica B 406 (2011) 4657-4660.
[11] Y. Hayamizu, M. Yoshita, S. Watanabe, H. Akiyama, L. Pfeiffer, K. West, Lasing from a single-quantum wire, Applied Physics Letters 81 (2002) 4937-4941.
[12] L. Mayants, The Enigma of Probability and Physics, Springer, (1984).
[13] Y. Okamoto, Nonextensive Statistical Mechanics, Application, Springer, (2001).
[14] A.H. Darooneh, Insurance pricing in small size markets, Physica A 380 (2007) 411-417.
[15] A.H. Darooneh, C. Dadashinia, Analysis of the spatial and temporal distributions between successive earthquakes: Nanextensive statistical mechanics viewpoint, Physica A 387 (2008) 3647-3654.
[16] C. Tsallis, Possible generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics 52 (1988) 479-487.
[17] B.H. Lavenda, J.D. Davies, Additive Entropies of degree-q and the Tsallis Entropy, Journal of Applied Sciences 5 (2005) 315-322.
[18] C. Beck, Generalised information and entropy measures in physics, Contemporary Physics 50 (2009) 495-510.

[19] T.S. Biro, G.G. Barnafoldi, P. V n, Quark-gluon plasma connected to finite heat bath, The European Physical Journal A 49 (2013) 110-116.

[20] N. Ito, C. Tsallis, Specific heat of the harmonic oscillator within generalized equilibrium statistics, Il Nuovo Cimento D 11 (1989) 907-911.

 

[21] L.S. Lucena, L.R. da Silva, C. Tsallis, Departure from Boltzmann-Gibbs statistics makes the hydrogen-atom specific heat a computable quantity, Physical Review E 51 (1995) 6247-6251.
[22] R. Khordad, Study of specific heat of quantum pseudodot under magnetic field, International Journal of Thermophysics 34 (2013) 1148-1157.
[23] R. Khordad, B. Mirhosseini, Internal energy and entropy of a quantum pseudodot, Physica B 420 (2013) 10-14.
[24] M. Barati, N. Moradi, Study of the specific heat of a hydrogenic donor impurity at the center of a spherical quantum dot in
contact with a heat reservoir, Journal of Computational and Theoretical Nanoscience 6 (2009) 1709-1713.
[25] R. Khordad, M.A. Sadeghzadeh, A. Mohamadian Jahan-Abad, Effect of magnetic field on internal energy and entropy of a parabolic cylindrical quantum dot, Communications in Theoretical Physics 59 (2013) 655-660.
[26] R. Khordad, M.A. Sadeghzadeh, A. Mohamadian Jahan-Abad, Specific heat of a parabolic cylindrical quantum dot in the presence of magnetic field, Superlattices and Microstructures 58 (2013) 11–19.
[27] V. Amar, M. Pauri, A. Scotti, Schrodinger equation for convex plane polygons: A tiling method for the derivation of eigenvalues and eigenfunctions, Journal of Mathematical Physics 32 (1991) 2442-2432.
[28] W.K. Li, S.M. Blinder, Solution of Schrodinger equation for a particle in an equilateral triangle, Journal of Mathematical Physics 26 (1985) 2784-2792.
[29] P.N. Gorley, Y.V. Vorobiev, J.G. Hern ndez, P.P. Horley, Analytical solution of the Schrodinger equation for an electron confined in a triangle-shaped quantum well, Microelectronic Engineering 66 (2003) 39-45.
[30] P.J. Richens, M.V. Berry, Pseudointegrable systems in classical and quantum mechanics, Physica D 2 (1981) 495-512.
[31] V.I. Arnold, A. Avez, Ergodic Problems of Classical Mechanics, Benjamin, New York, (1968).
[32] R. Khordad, Continuum Mechanics and Thermodynamics 28 (2016) 947-956.
[33] M. Gell-Mann, C. Tsallis, Nonextensive Entropy Interdisciplinary Application, Oxford University Press, New York, (2004).
[34] S. Abe, Y. Okamoto, Nonextensive Statistical Mechanics and its Application, Springer-Verlag, Berlin, Heidelberg, (2001).