Superstatistics of two electrons quantum dot

Sargolzaeipor, S.; Hassanabadi, H.; Chung, Won Sang

doi:10.1142/s0217732319500238

Cited by 14 publications

(8 citation statements)

References 32 publications

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“…It is worth mentioning that several authors have used the standard definition of an expectation value for their calculations in order to explore the thermodynamic consequences of a superstatistical treatment in different scenarios: the thermodynamical properties of the anharmonic canonical ensemble within the cosmic-string framework [46], the impact of the non-commutativity of the space for systems with thermal fluctuations [49], the effective Quantum Chromodynamics phase diagram [67] and the anharmonic oscillator for non-relativistic and relativistic Klein-Gordon equations [101], among others [53,90]. We suggest the restoration of the Legendre invariance in Refs.…”

Section: Resultsmentioning

confidence: 99%

Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin–orbit interaction

Castaño-Yepes

Amor-Quiroz

2020

Physica A: Statistical Mechanics and its Applications

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We examine the effect of non-equilibrium processes modeled by the introduction of a generalized Boltzmann factor on the thermal and magnetic properties of an array of two-dimensional GaAs quantum dots in the presence of an external uniform and constant magnetic field. The model consists of a single-electron subject to a confining Gaussian potential with a spin-orbit interaction in the Rashba approach. We compute the specific heat and the magnetic susceptibility within the formalism of χ 2 -superstatistics from the exact solution of the Schrödinger equation. Furthermore, an analytic solution for the partition function allows a study of the impact of the number of subsystems on the superstatistical corrections and confirms that the ordinary thermo-magnetic properties are recovered whenever the thermal distribution can be approximated by a Dirac delta. Also, we found a progressive disappearance of the Schottky anomaly with decreasing number of subsystems, while the specific heat ceases to be a monotonically increasing function with respect to the average temperature when the χ 2 -distribution is spread over a large range of temperatures. Remarkably, the introduction of fluctuations in the temperature is found to suppress the paramagnetic phase transition that would otherwise appear at low temperatures. Finally, we emphasize that an appropriate construction of the definition of physical observables is crucial for obtaining a correct description of the physics derived from a non-extensive construction of the entropy.

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Section: Resultsmentioning

confidence: 99%

Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin–orbit interaction

Castaño-Yepes

Amor-Quiroz

2020

Physica A: Statistical Mechanics and its Applications

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“…is the probability density. Besides we state here the modified form of Dirac delta function used in this study as [75]:…”

Section: Superstatistics Mechanicsmentioning

confidence: 99%

“…(39) can be found in Appendix A of Ref. [75] and references therein. The partition function for the modified Dirac delta distribution has the following form [75]:…”

Section: Superstatistics Mechanicsmentioning

confidence: 99%

Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

et al. 2020

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Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

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“…Super-statistics (SS), developed by Beck and Cohen, is an effective way to study the non-equilibrium processes based on the idea that the thermodynamics of a system that passes through several equilibrium thermodynamic states or is divided into subsystems, each in local equilibrium, can be approximated by postulating an average Boltzmann factor weighted with the density probability function of fluctuations [1][2][3]. It has been applied to many topics: turbulence models [4,5], cosmic rays [6], quantum cromodynamics [7,8], quantum dots [9,10], out-of-equilibrium Ising models [11], quantum field theory [12,13], among others [14][15][16][17]. Then, SS is a subject that deserves attention.…”

Section: Introductionmentioning

confidence: 99%

Super-statistics and quantum entanglement in the isotropic spin-1/2 XX dimmer from a non-additive thermodynamics perspective

Castaño-Yepes,

Ramirez-Gutierrez

2021

Preprint

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Superstatistics of two electrons quantum dot

Cited by 14 publications

References 32 publications

Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin–orbit interaction

Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin–orbit interaction

Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

Super-statistics and quantum entanglement in the isotropic spin-1/2 XX dimmer from a non-additive thermodynamics perspective

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