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Modern Physics Letters A

Superstatistics of two electrons quantum dot

Sepideh Sargolzaeipor, HASSAN HASSANABADI, Won Sang Chung

Published Jan 16, 2019• 15 citations
Publisher

Abstract

In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.

DOI
10.1142/s0217732319500238

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Abstract We discuss the thermodynamic properties of a modified Rosen-Morse potential using the q -deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.
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The thermostatistic problems of a q -deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q -deformed Fermi–Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q -deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q -deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.
Quantum statistical aspects of the anharmonic crystal in equilibrium, the approach to equilibrinm, and the zero temperature properties of a conduction electron in a crystal lattice are treated. A description of the Bravais lattice without imperfections is given. The reduction of the harmonic part of H to normal modes is demonstrated. The quantum mechanical problem of the harmonic crystal is investigatad, including the effect of the anharmonic terms. Calculations of the free energy of a crystal, the lowtemperature limit, and other macroscopic quantities and microscopic averages were made. The development of a Hamiltonian for studying the equilibrium of a system composed of electrons in an insulating crysta is discussed. A rough calculation of B'. the interaction constant, is presented. The physical effects of the interaction of one electron with the photon gas are described. Diagram calculations for the partition function are presented and partial summation of diagrams is discussed. A mathematical description of the dissipation process is given, including derivation of the master equation which refers to states of the entire system. The Boltzmann equation for governing the momentum distribution of the electron as a function of time is derived. The effects of virtual emission in the electron- photon interactionsmore » were studied. (C.J.G.)« less
The spatial Fourier spectrum of the electron density distribution in a finite one-dimensional system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their behavior, which characterize the electron ordering and the deformation of Wigner crystal by boundaries. The distribution function has a $\ensuremath{\delta}$-like singularity at the Fermi momentum kF{k}_{F}kF​. The Fourier spectrum of the density has a steplike form at the wave vector 2kF2{k}_{F}2kF​, with the harmonics being absent or vanishing above this threshold. These features are found by calculations using exact diagonalization method. They are shown to be caused by Wigner ordering of electrons, affected by the boundaries. However, the common Luttinger liquid model with open boundaries fails to capture these features because it overestimates the deformation of the Wigner crystal. An improvement of the Luttinger liquid model is proposed, which allows one to describe the above features correctly. It is based on the corrected form of the density operator conserving the particle number.