scholarly journals On the reformulation of the Thomas–Fermi model to make it compatible with the Planck-scale

2021 ◽  
pp. 2150130
Author(s):  
Himangshu Barman ◽  
Anisur Rahaman ◽  
Sohan Kumar Jha
Keyword(s):  
Scale Effect ◽  
Relativistic Effect ◽  
Uncertainty Relation ◽  
Planck Scale ◽  
Relativistic Case ◽  
Fermi Model ◽  
Thomas Fermi

Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.

On the Thomas–Fermi model at the Planck scale

2019 ◽  
Vol 383 (11) ◽  
pp. 1105-1109 ◽  
Author(s):  
Homa Shababi ◽  
Kamel Ourabah
Keyword(s):  
Planck Scale ◽  
Fermi Model ◽  
Thomas Fermi

Comparison of Variational Solutions of the Thomas-Fermi Model in Terms of the Corrected Ionization Energy

1987 ◽  
Vol 42 (9) ◽  
pp. 943-947
Author(s):  
I. Agil ◽  
A. Alharkan ◽  
H . Alhendi ◽  
A. Alnaghmoosh
Keyword(s):  
Ionization Energy ◽  
Trial Function ◽  
Binding Energies ◽  
Initial Slope ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Variational Solutions ◽  
Comparison Of The Results

It is shown that leading corrections, to the ionization energy, of many-electrons atom, can be expressed as leading corrections of initial slope of trial variational solutions of the Thomas-Fermi equation. Some variational solutions with different initial slopes are compared. A comparison of the results shows, that as far as the binding energies are concerned a trial function with its slope not close to the (negative) Baker’s constant may not be suited.

On sodium clusters in C60 fullerides

1997 ◽  
Vol 75 (1) ◽  
pp. 77-82 ◽  
Author(s):  
M. Apostol ◽  
F. Rachdi ◽  
C. Goze ◽  
L. Hajji
Keyword(s):  
Electric Charge ◽  
The Body ◽  
Electron Charge ◽  
Body Centered Cubic ◽  
Fermi Theory ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Sodium Clusters ◽  
Alkali Fullerides

Sodium (Na) clusters in octahedral cages of Na-intercalated fullerides Na6C60 and Na11C60 are studied within a Thomas–Fermi model. It is shown that the tetrahedral Na4 cluster in Na6C60 has an electric charge ~ +2.7 (in electron charge units), while the body-centered cubic Na9 cluster in Na11C60 is almost electrically neutral. Keywords: sodium clusters, alkali fullerides, Thomas–Fermi theory, ionization charge.

scholarly journals Relativistic quantum heat engine from uncertainty relation standpoint

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Pritam Chattopadhyay ◽  
Goutam Paul
Keyword(s):  
Uncertainty Relation ◽  
Relativistic Quantum ◽  
Heat Engine ◽  
Potential Well ◽  
Relativistic Case ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Thermodynamic Variables ◽  
The One ◽  
Work Done

AbstractEstablished heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

The Thomas-Fermi model: momentum expectation values

1983 ◽  
Vol 44 (3) ◽  
pp. 333-342 ◽  
Author(s):  
I.K. Dmitrieva ◽  
G.I. Plindov
Keyword(s):  
Expectation Values ◽  
Fermi Model ◽  
Thomas Fermi
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