It is argued that Planck mass may be considered as a candidate for the mass content of each degree of freedom of holographic screen. In addition, employing the Verlinde hypothesis on emergent gravity and considering holographic screen degrees of freedom as a q-deformed fermionic system, it is obtained that the heat capacity per degree of freedom inspires the MOND interpolating function. Moreover, the MOND acceleration is achieved as a function of Planck acceleration. Both ultra-relativistic and non-relativistic statistics are studied. We, therefore, believe that our results can at least mathematically be employed to write the MOND theory corresponding to various samples.
Since the conformal transformations of metric do not change its causal structure, we use these transformations to embed the Lemaitre metrics into the FRW background. In our approach, conformal transformation is in agreement with the universe expansion regimes. Indeed, we use the Lemaitre metrics because the horizon singularity is eliminated in these metrics. For our solutions, there is an event horizon while its physical radii is increasing as a function of the universe expansion provided suitable metrics for investigating the effects of the universe expansion on the Black Holes. In addition, the physical and mathematical properties of the introduced metrics have welldefined behavior on the event horizon. Moreover, some physical and mathematical properties of the introduced metrics have been addressed.
Hartree-Fock approximation suffers from two inabilities including i) the divergence of electron Fermi velocity , and ii) existence of bandwidth not confirmed experimentally. Here, we study the effects of minimal length on the ground state energy of the electron gas in the Hartree-Fock approximation. Our results indicate that considering some mathematical terms, similar to those of used for the minimal length correction to the Hamiltonian of system, can eliminate the weaknesses of Hartree-Fock approximation. These corrections, on the other hand, can be considered as relativistic corrections of electron in solids. Physically, it is obtained that electrons in metals can be employed to test the quantum gravity scenario, if the value of its parameter (β) lies within the range of 2 to 10, depending on the used metal. Indeed, the latter addresses an upper bound on β which is comparable with previous works meaning that these types of systems may be employed in testing quantum gravity scenarios. To overcome the infinite Fermi velocity in Hartree-Fock method, the screening potential is used based on the Lindhard theory. We also find that considering the generalized Heisenberg uncertainly leads to some additional oscillating terms in the Friedel oscillations.
Instead of solving Dirac (or Klein-Gordon) equation for a many body system, in this paper a variational method has been used to investigate the properties of two dimensional (2D) strongly interacting fermions and the results have been applied to 2D liquid 3 He as the only real fermion system. Our results show that this variational method, known as lowest order constrained variational method, can be used to relativistic 2D fermion systems with a good accuracy. In the case of 2D liquid 3 He, Our calculations showed that at higher temperatures relativistic effects are more significant and quantum mechanical effects play a minor role. Also, we have found that in this system, as expected, relativistic effects are not considerable at low temperatures.
In the presence of magnetic field, we have employed a spin-dependent correlation function to investigate the properties of liquid 3 He using the variational method based on the cluster expansion of the energy. It has been indicated that at all relevant magnetic fields and densities, the inclusion of spin-dependency for the correlation function leads to the lower magnitudes for the kinetic, magnetic and potential energies, and therefore the total energy of this system. We have seen that the spin–spin correlation affects the system to be less magnetized compared to the case in which we consider the spin-independent correlation, especially at low densities. In the case of spin–spin correlation function, our results show a maximum in the magnetic susceptibility, and therefore a meta-magnetic instability for the system for the magnetic fields in the range 50 T ≤ B ≤ 60 T . This behavior has not been observed in the case of spin-independent correlation.
Using the spin-dependent (SD) and spin-independent (SI) correlation functions, we have investigated the properties of liquid [Formula: see text] in the presence of magnetic field at finite temperature. Our calculations have been done using the variational method based on cluster expansion of the energy functional. Our results show that the low field magnetic susceptibility obeys Curie law at high temperatures. This behavior is in a good agreement with the experimental data as well as the molecular field theory results in which the spin dependency has been introduced in correlation function. Reduced susceptibility as a function of temperature as well as reduced temperature has been also investigated, and again we have seen that the spin-dependent correlation function leads to a good agreement with the experimental data. The Landau parameter, [Formula: see text], has been calculated, and for this parameter, a value about [Formula: see text] has been found in the case of spin–spin correlation. In the case of spin-independent correlation function, this value is about [Formula: see text]. Therefore, inclusion of spin dependency in the correlation function leads to a more compatible value of [Formula: see text] with experimental data. The magnetization and susceptibility of liquid [Formula: see text] have also been investigated as a function of magnetic field. Our results show a downward curvature in magnetization of system with spin-dependent correlation for all densities and relevant temperatures. A metamagnetic behavior has been observed as a maximum in susceptibility versus magnetic field, when the spin–spin correlation has been considered. This maximum occurs at [Formula: see text] for all densities and temperatures. This behavior has not been observed in the case of spin-independent correlation function.
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