Quantum entanglement of fermions–antifermions pair creation modes in noncommutative Bianchi I space–time

Abstract

The non-commutative Bianchi I curved space-time vierbeins and spin connections are derived. Moreover, the corresponding non-commutative Dirac equation as well as its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann fermion-antifermion pair creation quantum entanglement entropy is studied. It is shown that its behaviour is strongly dependent on the value of the non-commutativity θ parameter, k ⊥ -modes frequencies and the structure of the curved space-time. Various discussions of the obtained features are presented.

Spin quantum entanglement in non-commutative curved space–time

“…On the other hand, as we mentioned in the introduction, NC parameter was considered as having antigravity properties (quintessence, dark energy, etc. ), so NC parameter can induce two terms with opposing signs and that was confirmed in [ 48 , 49 ]…”

“…1 , 2 , 3 , 4 , 5 and 6 ), the variation of the quantum entanglement as a function of , the NC parameter and the black hole charge y is discussed. We have noticed that the NC effect on becomes more important in a charged black hole, so the behavior of depends on the black hole’s characteristics and not only on the kind of particles (bosons or fermions) [ 48 ]. We found as NC parameter increases, decreases, as if NC parameter is playing the role of gravity.…”

Quantum Entanglement and Thermodynamics of Boson-Antiboson Pair Creation Modes in the Noncommutative Bianchi I Universe

“…It is worth mentioning, as pointed out in references [5,29,[33][34][35] that since the metric presents a space-like singularity at t = 0, it is difficult to define the particle state within the adiabatic approach. To do so, we first follow a quasiclassical approach of Ref.…”

“…During the last few years, The quantum entanglement (Q.E.) phenomenon has been of great interest for many people in the field of quantum information in both flat and curved spacetime [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Moreover, it turns out that the pair creation process is intimately related to the quantum entanglement and strongly depends on the nature of the particles as well as on the structure of the spacetime [5,9,11,15,16].…”

“…phenomenon has been of great interest for many people in the field of quantum information in both flat and curved spacetime [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Moreover, it turns out that the pair creation process is intimately related to the quantum entanglement and strongly depends on the nature of the particles as well as on the structure of the spacetime [5,9,11,15,16]. Furthermore, as a possible scenario to explain dark matter and dark energy as well as the anisotropies found in the cosmic microwave background (C.M.B.…”