Bells inequality is a strong criterion to distinguish classic and quantum mechanical aspects of reality. Its violation is the net effect of the non-locality stored in the Heisenberg uncertainty principle (HUP) generalized by quantum gravity scenarios
, called generalized uncertainty principle (GUP). Here, the effects of GUP on Bell-like operators of two, and three outcomes, as well as continuous cases, are studied. The achievements claim that the violation quality of Bells and Bell-like inequalities may be a proper tool to get better understanding of the quantum features of gravity and its effects on reality. Indeed, it is obtained that the current accuracy of Stern-Gerlach experiments implies $beta_0ll10^{23}$.
Hartree-Fock approximation suffers from two inabilities including i) the divergence of electron Fermi velocity , and ii) existence of bandwidth not con?rfimed 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 (?$beta$) lies within the range of 2 to 10, depending on the used metal. Indeed, the latter addresses an upper bound on ?$beta$? which is comparable with previous works meaning that these types of systems may be employed in testing quantum gravity scenarios. To overcome the in?nite Fermi velocity in Hartree-Fock method, the screening potential is used based on the Lindhard theory. We also ?nd that considering the generalized Heisenberg uncertainly leads to some additional oscillating terms in the Friedel oscillations.
The effect of Generalized Uncertainty Principle (GUP) on Berry phase is studied using the perturbation approach and up to the first order of approximation. Thereinafter, the obtained results are extended to a quantum ring in which two types of spin-o
rbit interactions, including Rashba and Dresselhaus interactions, can be felt by electrons. Comparing the final results with the accuracy of Berry phase detectors, one can find an upper bound on GUP parameter as $beta_{0}<10^{46}$ and $beta_{0}<10^{51}$ from Rashba and Dresselhaus interactions, respectively, in agreement with previous results.
It is argued that Planck mass may be considered as a candidate for the mass content of degrees 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 study some cosmological features of Tsallis holographic dark energy (THDE) in Cyclic, DGP and RS II braneworlds. In our setup, a flat FRW universe is considered filled by a pressureless source and THDE with the Hubble radius as the IR cutoff, whil
e there is no interaction between them. Our result shows that although suitable behavior can be obtained for the system parameters such as the deceleration parameter, the models are not always stable during the cosmic evolution at the classical level.
Accepting the Komar mass definition of a source with energy-momentum tensor $T_{mu u}$, and using the thermodynamic pressure definition, we find a relaxed energy-momentum conservation law. Thereinafter, we study some cosmological consequences of the
obtained energy-momentum conservation law. It has been found out that the dark sectors of cosmos are unifiable into one cosmic fluid in our setup. While this cosmic fluid impels the universe to enter an accelerated expansion phase, it may even show a baryonic behavior by itself during the cosmos evolution. Indeed, in this manner, while $T_{mu u}$ behaves baryonically, some parts of it, namely $T_{mu u}(e)$ which is satisfying the ordinary energy-momentum conservation law, are responsible for the current accelerated expansion.
Using the Tsallis generalized entropy, holographic hypothesis and also considering the Hubble horizon as the IR cutoff, we build a holographic model for dark energy and study its cosmological consequences in the Brans-Dicke framework. At first, we fo
cus on a non-interacting universe, and thereinafter, we study the results of considering a sign-changeable interaction between the dark sectors of the cosmos. Our investigations show that, compared with the flat case, the power and freedom of the model in describing the cosmic evolution is significantly increased in the presence of the curvature. The stability analysis also indicates that, independent of the universe curvature, both the interacting and non-interacting cases are classically unstable. In fact, both the classical stability criterion and an acceptable behavior for the cosmos quantities, including the deceleration and density parameters as well as the equation of state, are not simultaneously obtainable.
