Low temperature behavior of entropy and specific heat of a three dimensional quantum wire: Shannon and Tsallis entropies
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Low temperature behavior of entropy and specific heat of a three dimensional quantum wire: Shannon and Tsallis entropies Mojtaba Servatkhah 1 , Reza Khordad 2,a , Arezoo Firoozi 2 , Hamid Reza Rastegar Sedehi 3 , and Ahmad Mohammadi 4 1 2 3 4
Department Department Department Department
of of of of
Physics, Physics, Physics, Physics,
Marvdasht Branch, Islamic Azad University, Marvdasht, Iran College of Sciences, Yasouj University, Yasouj 75918-74934, Iran Jahrom University, 74137-66171 Jahrom, Iran Persian Gulf University, 75196 Bushehr, Iran
Received 13 January 2020 / Received in final form 29 April 2020 Published online 15 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. In this work, we first use the finite-differential time-domain (FDTD) to calculate the eigenenergies and eigenfunctions of a three dimensional (3D) cylindrical quantum wire. We assume that the inside of the wire is at zero potential. But, the outside of the wire has been chosen at different potentials as infinite and finite values. This is a true 3D procedure based on a direct implementation of the time-dependent Schr¨ odinger equation. Then, we apply the Shannon and Tsallis entropy to obtain entropy and specific of the system. The results show that (i) the specific heat obtained by Tsallis has a peak structure. (ii) The entropy behavior for the finite and infinite confining potential has the same behavior at low temperatures. (iii) The peak value of specific heat increases with enhancing the quantum wire radius.
1 Introduction In the past three decades, low dimensional structures like quantum wires and dots have attracted much attention. The concepts of quantum wires and quantum dots have been introduced for the first time in 1975 [1]. Wirelike semiconductor structures with nanometer sizes have attracted great interest among researchers [1–4]. Quantum wires play an important role in the field of quantum nanodevices. They have potential applications in quantum electronics, quantum computers and nonlinear optics [5,6]. Physical properties of quantum wires have been extensively studied in the past two decades. Examples of the properties are electronic, magnetic, optical and thermodynamic properties of quantum wires. To obtain information about the properties, the reader can refer to [7–12]. To determine the eigenenergies and eigenfunctions of quantum wires with considering a given confining potential, one should solve the Schr¨ odinger equation analytically or numerically. To solve numerically the Schr¨ odinger equation, there are several methods such as diagonalization procedure, finite differential method and finite-differential time-domain (FDTD) [13–15]. FDTD is a useful method which is used to describe to accurately model long, thin wires without using excessive computer resources. Burke et al [16] have used FDTD to find optimized potentials [17,18] as well as to analyze the character of a potential. FDTD is em
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