Statistical properties of linear Majorana fermions

Abstract

A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation, where the spinor field is by definition equal to its charge-conjugate field. In this paper, we investigated Shannon's entropy of linear Majorana fermions to understand how this quantity is modified due to an external potential of the linear type linear. Subsequently, we turn our attention to the construction of an ensemble of these Majorana particles to study the thermodynamic properties of the model. Finally, we show how Shannon's entropy and thermodynamic properties are modified under the linear potential action.

Effects of Pöschl-Teller potential on approximate ℓ ≠ 0-states solution in topological defect geometry and Shannon entropy

“…Shannon's primary objective was to investigate the loss of information during transmission between a source and a receiver. Derived from probability density, Shannon entropy holds significance in the analysis of quantum systems, serving as a robust tool for assessing particle localization within these systems [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80].…”

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

“…This similarity of Shannon information and Boltzmann entropy allowed Shannon information to be called Shannon entropy [ 64 ]. Some conceptual applications of Shannon’s entropy help us understand the information and uncertainty measurement of quantum systems, e.g., Shannon entropy gives us the uncertainty of non-Hermitian particle systems [ 65 ]. Furthermore, Shannon formalism allowed the study of fermionic particles [ 66 ], problems with effective mass distribution [ 67 , 68 ], and mechanical-quantum models with double-well potential [ 69 ].…”

“…The entropic quantities of Equations ( 19 ) and ( 20 ) play a role analogous to the Heisenberg uncertainty measures [ 65 , 66 ]. An entropic uncertainty relation that relates to the entropic uncertainties was obtained by Beckner [ 71 ] and Bialynicki–Birula and Mycielski (BBM) [ 73 ].…”

Quantum information of the Aharanov-Bohm ring with Yukawa interaction in the presence of disclination

“…Some conceptual applications of Shannon's entropy help us understand the information and uncertainty measurement of quantum systems, e. g., the Shannon entropy gives us the uncertainty of non-Hermitian particle systems [55]. Furthermore, Shannon formalism allowed the study of fermionic particles [56], problems with effective mass distribution [57,58], and mechanical-quantum models with double-well potential [59].…”

“…The entropic quantities of Eqs. ( 20) and ( 21) play a role analogous to the Heisenberg uncertainty measures [55,56]. An entropic uncertainty relation that relates to the entropic uncertainties was obtained by Beckner [61], Bialynicki-Birula and Mycielski (BBM) [63].…”