Extended Uncertainty Principle Research Articles

Degeneracy pressure in the presence of maximum length for non-interacting electrons

Combining quantum theory with the fundamental principles of gravity results in the modification of the uncertainty principle. In this study, we employ the extended uncertainty principle (EUP) with the maximum length derived from the cosmological particle horizon. The impact of this specific kind of modification is examined in a non-interacting electron gas system. We analytically derive the generalized relations for the degeneracy pressure and the bulk modulus. An intriguing finding is that the degeneracy pressure is reduced, as confirmed by the observed size of white dwarfs, which is smaller than what is predicted by the standard theory. Nevertheless, it is still capable of providing support against gravitational collapse.

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose–Einstein condensate (BEC) described by the deformed one-dimensional Gross–Pitaevskii equation (GPE). Analytical solutions were derived for null potential while we used variational and numerical methods for a harmonic oscillator potential. The effects of EUP on stability, probability density, position, and momentum uncertainties of BEC are analyzed. The EUP is found to be applicable for the free dark soliton solution and in the presence of a harmonic potential within specific ranges of the deformation parameter α, while it is not valid for the free bright soliton solution.

Effects of the new type of extended uncertainty principle on Van der Waals black hole thermodynamics: A theoretical and deep learning approach

In this paper, we study the Van der Waals black holes (the case [Formula: see text]) in the anti-de Sitter space under the effect of the linear extended uncertainty principle (EUP). The analysis was undertaken using deep learning by employing physics-informed neural networks in addition to the semi-classical approach, we have calculated the thermal quantities, including mass, volume, temperature, entropy, and Gibbs free energy. Additionally, we visually depict the effects of the EUP-term on the thermodynamic properties of the studied black holes.

The vector DKP oscillator in the plane within the context of the extended uncertainty principle

The Extended Uncertainty Principle (EUP) is a gravitational correction to quantum mechanics that extends and modifies Heisenberg’s uncertainty principle. Particularly, it suggests the existence of a minimum measurable momentum scale, often referred to as the Minimal Momentum (MM), a quantity which is expected to influence the properties of all quantum mechanical systems. In this paper we investigate the effects of the EUP on the quantum features of the Two-Dimensional (2D) Duffin-Kemmer-Petiau Oscillator (DKPO) for spin-one particles subject to an external Homogeneous Magnetic Field (HMF). Using the position representation, we solve the corresponding problem and we obtain the exact wave functions and eigenenergies of the system, then we analyze how they are affected by the MM. We also examine the special case of a spin-one particle moving in a plane under a perpendicular HMF.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

Constraining a one-dimensional wave-type gravitational wave parameter through the shadow of M87* via Event Horizon Telescope

During the glorious success of the EHT in providing the first image of a black hole, numerous papers have been published about the effect of different astrophysical environments on black hole geometry. Motivated by the work on how gravitational wave affects the shadow of a Schwarzschild black hole [Eur. Phys. J. C 10.1140/epjc/s10052-021-09287-2], we extend it by considering a quantum correction on the black hole through the extended uncertainty principle (EUP). Along with this correction, we probe the gravitational wave’s effect on the null geodesics and photonsphere and find constraints to the gravitational wave parameter ϵ using the black hole shadow of M87* for some given test value for the gravitational wave frequency σ. Not only were some nodes found in the light trajectory, but the general behavior of paths changes periodically as the time t progresses. These patterns then confirm the chaotic formation of the shadow seen by some remote observer. Finally, the constraint that we find for ϵ is 10−10 orders of magnitude for the effect of the gravitational wave to be seen at a distance of D=16.8 Mpc. As a consequence of such a value for ϵ, another result reveals that while there is are gravitational wave effect on the shadow perceived at D, the deviations on the photonsphere are nearly non-existent. Apart from Earth-based detectors for gravitational waves, the study implies the possibility of an alternative detection method, especially if a gravitational wave source is near a lone black hole.

Thermodynamics under the extended uncertainty principle background: [formula omitted] criticality analysis

The study of thermodynamics in the background of the “extended uncertainty principle (EUP)” comes into interest in recent eras. In this article, we consider a charged black hole (BH) in higher dimensional space–time and present the thermodynamic parameters, based on a semiclassical framework, initially. Then we extend the same within the EUP background. We also analyze the Q−ϕ criticality and find the critical points (ϕc,Qc and Tc) when Q−ϕ criticality appears. We study the effects of EUP on phase transition for higher dimensions (d=5) by plotting the Q−ϕ diagrams. Further, we investigate the stability (thermal and global) of the BHs by employing the specific heat and the Gibbs free energy without and within EUP correction and compare the results with the Schwarzschild BHs in higher dimensions.

Bell nonlocality in maximal-length quantum mechanics

In this paper, we investigate the consequences of maximal length as well as minimal momentum scales on nonlocal correlations shared by two parties of a bipartite quantum system. To this aim, we rely on a general phenomenological scheme which is usually associated with the non-negligible spacetime curvature at cosmological scales, namely the extended uncertainty principle. In so doing, we find that quantum correlations are degraded if the deformed quantum mechanical model mimics a positive cosmological constant. This opens up the possibility to recover classicality at sufficiently large distances.

The gravitational baryogenesis and a new higher-order extended uncertainty principle with parameter adaptability for the minimum length

In this manuscript, we explore the baryon asymmetry of the universe by employing a novel higher-order extended uncertainty principle (EUP) that maintains a minimum length Δxmin=4|β0|ℓp for both positive and negative deformation parameters. Our results demonstrate that the influence of the EUP noticeably modifies the Friedmann equations, leading to a transformation in the characteristics of the pressure and density of the Universe, and subsequently disrupting its thermal equilibrium. Additionally, by amalgamating the adapted Friedmann equations with the conventional theory of gravitational baryogenesis, one can derive a non-zero factor of baryon asymmetry η, indicating that the quantity of matter in the universe surpasses that of antimatter. Finally, we also utilized astronomical observations to constrain the bounds for both the positive and negative deformation parameters.

Extended uncertainty principle and Van der Waals black holes

In this paper, we investigate the extended uncertainty principle (EUP) effects on the Van der Waals (VdW) black holes whose thermal quantities mimic the VdW liquid. We find that the considered formalism imposes an upper bound on the event horizon radius. Thus, the mass, Hawking temperature, and heat capacity become physically meaningful within a certain range of event horizon radii. At a large event horizon radius, the black hole has a remnant. We observe that for a given set of parameters, the VdW black hole can be completely unstable for all horizon radii, while for another set of parameters, it can be unstable or stable depending on the horizon radius.

Harmonic oscillator in the context of the extended uncertainty principle

At large-scale distances where the space-time is curved due to gravity, a nonzero minimal uncertainty in the momentum, [Formula: see text], is being estimated to emerge. The presence of minimal uncertainty in momentum allows a modification to the quantum uncertainty principle, which is known as the extended uncertainty principle (EUP). In this work, we handle the harmonic oscillator problem in the EUP scenario and obtain analytical exact solutions in classical and semi-classical domains. In the classical context, we establish the equations of motion of the oscillator and show that the EUP-corrected frequency is depending on the energy and deformation parameter. In the semi-classical domain, we derive the energy eigenvalue levels and demonstrate that the energy spectrum depends on [Formula: see text], as the feature of hard confinement. Finally, we investigate the impact of the EUP on the harmonic oscillator’s thermodynamic properties by using the EUP-corrected partition functions in the classical limit in the (A)dS backgrounds.

Entropy bound and EGUP correction of d-dimensional Reissner–Nordström black hole in rainbow gravity

Inspired by the pronounced effect of gravity’s Rainbow on black hole thermodynamics, entropy relations and bounds have been investigated for [Formula: see text]-dimensional Reissner–Nordström (RN) black hole in the framework of Rainbow gravity. Basic thermodynamic properties of the black hole have been derived for the event horizon and Cauchy horizon. Except for the horizon radius, they all crucially depend on the Rainbow functions. Bounds of the aforesaid thermodynamic quantities have been deduced for both horizons. Analyzing the specific heat capacity, stability conditions have been obtained. Also, the extremal phase of the black hole has been explored. Further, a comparative study has been carried out to distinguish between the effects of Rainbow gravity model parameters on the entropy bound by considering different Rainbow gravity functions. For massless scalar perturbation, quasinormal modes have been computed using modified WKB approach. We have investigated the quantum correction of the black hole in a Rainbow gravity background to obtain the effects of Extended Uncertainty Principle (EUP) and Generalized Uncertainty Principle (GUP) parameters. We have derived the Hawking temperature, specific heat, entropy and remnant masses of the black hole in the Extended General Uncertainty Principle (EGUP) framework, and with the help of graphical methods, we have compared our findings.

Reinterpreting deformed Heisenberg algebras

Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its quantum analogue may also extend to the realm of curved momentum space as suggested, e.g. in the context of Relative Locality in Deformed Special Relativity. Drawing on earlier work, we show in an entirely Born reciprocal, i.e. position and momentum space covariant, way that the quadratic Generalized Extended Uncertainty principle can alternatively be described in terms of quantum dynamics on a general curved cotangent manifold. In the case of the Extended Uncertainty Principle the curvature tensor in position space is proportional to the noncommutativity of the momenta, while an analogous relation applies to the curvature tensor in momentum space and the noncommutativity of the coordinates for the Generalized Uncertainty Principle. In the process of deriving this map, the covariance of the approach constrains the admissible models to an interesting subclass of noncommutative geometries which has not been studied before. Furthermore, we reverse the approach to derive general anisotropically deformed uncertainty relations from general background geometries. As an example, this formalism is applied to (anti)-de Sitter spacetime.

Generalised uncertainty relations from finite-accuracy measurements

In this short note we show how the Generalised Uncertainty Principle (GUP) and the Extended Uncertainty Principle (EUP), two of the most common generalised uncertainty relations proposed in the quantum gravity literature, can be derived within the context of canonical quantum theory, without the need for modified commutation relations. A generalised uncertainty principle-type relation naturally emerges when the standard position operator is replaced by an appropriate Positive Operator Valued Measure (POVM), representing a finite-accuracy measurement that localises the quantum wave packet to within a spatial regionσg> 0. This length scale is the standard deviation of the envelope function,g, that defines the positive operator valued measure elements. Similarly, an extended uncertainty principle-type relation emerges when the standard momentum operator is replaced by a positive operator valued measure that localises the wave packet to within a regionσ̃g>0in momentum space. The usual generalised uncertainty principle and extended uncertainty principle are recovered by settingσg≃ℏG/c3, the Planck length, andσ̃g≃ℏΛ/3, where Λ is the cosmological constant. Crucially, the canonical Hamiltonian and commutation relations, and, hence, the canonical Schrödinger and Heisenberg equations, remain unchanged. This demonstrates that generalised uncertainty principle and extended uncertainty principle phenomenology can be obtained without modified commutators, which are known to lead to various pathologies, including violation of the equivalence principle, violation of Lorentz invariance in the relativistic limit, the reference frame-dependence of the “minimum” length, and the so-called soccer ball problem for multi-particle states.

Tunneling and thermodynamics evolution of the magnetised Ernst-like black hole

We investigate the tunneling phenomenon of particles through the horizon of a magnetized Ernst-like black hole. We employ the modified Lagrangian equation with the extended uncertainty principle for this black hole. We determine a tunneling rate and the related Hawking temperature for this black hole by using the WKB approach in the field equation. In addition, we examine the graph behavior of the Hawking temperature in relation to the black hole event horizon. We explore the stability analysis of this black hole by taking into account the impact of quantum gravity on Hawking temperatures. The temperature for a magnetised Ernst-like black hole rises as the correction parameter is decreased. Moreover, we analyze the thermodynamics quantities such as Hawking temperature, heat capacity and Bekenstein entropy by using the different approach. We obtain the corrected entropy to study the impact of logarithmic corrections on the different thermodynamic quantities. It is shown that these correction terms makes the system stable under thermal fluctuations.

Extended Uncertainty Principle for Inventory Control: An Updated Review of Environments and Applications

This paper provides a comprehensive evaluation and categorization of the various uncertain environment employed by researchers and scientists to model and analyze inventory management systems in diverse sectors, including healthcare, supply chain, and routing issues. Additionally, it examines the challenges associated with the classical inventory model and introduces the concepts of fuzzy theory and the extended fuzzy principle in inventory management. The article presents important definitions related to fuzzy theory, including the fuzzy inventory model and its challenges. It also explores the applications of the extended fuzzy principle in real-life problems. The study focuses on inventory management under the extended fuzzy principle (Intuitionistic, Neutrosophic, Pythagorean, and so on), considering uncertain demand and imprecise data. The research contributes to the field by providing insights into the potential of fuzzy theory in overcoming the challenges of classical models and improving decision-making in inventory management.

Generalized Extended Uncertainty Principle Black Holes: Shadow and Lensing in the Macro- and Microscopic Realms

Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and quantum black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale, L*, up to two standard deviations level were also found using the Event Horizont Telescope (EHT) data: for black hole Sgr. A*, L*=5.716×1010 m, while for M87* black hole, L*=3.264×1013 m. Under the GEUP effect, the value of the shadow radius behaves the same way as in the Schwarzschild case due to a static observer, and the effect only emerges if the mass, M, of the black hole is around the order of magnitude of L* (or the Planck length, lPl). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for quantum black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of L* and M are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world.

Fractal properties of particle paths due to generalised uncertainty relations

We determine the Hausdorff dimension of a particle path, D_textrm{H}, in the recently proposed ‘smeared space’ model of quantum geometry. The model introduces additional degrees of freedom to describe the quantum state of the background and gives rise to both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP) without introducing modified commutation relations. We compare our results to previous studies of the Hausdorff dimension in GUP models based on modified commutators and show that the minimum length enters the relevant formulae in a different way. We then determine the Hausdorff dimension of the particle path in smeared momentum space, {tilde{D}}_textrm{H}, and show that the minimum momentum is dual to the minimum length. For sufficiently coarse grained paths, D_textrm{H} = {tilde{D}}_textrm{H} = 2, as in canonical quantum mechanics. However, as the resolutions approach the minimum scales, the dimensions of the paths in each representation differ, in contrast to their counterparts in the canonical theory. The GUP-induced corrections increase D_textrm{H} whereas the EUP-induced corrections decrease {tilde{D}}_textrm{H}, relative to their canonical values, and the extremal case corresponds to D_textrm{H} = 3, {tilde{D}}_textrm{H} = 1. These results show that the GUP and the EUP affect the fractal properties of the particle path in fundamentally different, yet complimentary, ways.

Hawking temperature for 4D-Einstein-Gauss-Bonnet black holes from uncertainty principle

Inspired by string theory, Heisenberg's uncertainty principle can be generalized to include the photon-electron gravitational interaction, which leads to the Generalized Uncertainty Principle (GUP). Although GUP considers gravitational uncertainty at the minimum fundamental length scale in physics, it does not consider the effects of spacetime curvature on quantum mechanical uncertainty relations. The Extended Uncertainty Principle (EUP) is a generalization of Heisenberg's Uncertainty Principle that, unlike the GUP, applies to large length scales. GEUP is also a linear combination of EUP and GUP that creates minimal uncertainty on large length scales. The Einstein-Gauss-Bonnet theory (EGB) can be considered as one of the most promising candidates for modified gravity. In this paper, by using GUP, EUP, and GEUP, we intend to obtain the Hawking temperature of a four-dimensional EGB black hole in the asymptotically flat and (Anti)-de Sitter spacetime. We show that coupling constant, cosmological constant, mass, and radius significantly affect Hawking temperature and decrease or increase Hawking temperature depending on the chosen horizons.

EUP-corrected thermodynamics of BTZ black hole

In this paper, we investigate the influence of the extended uncertainty principle (EUP) on the thermodynamics of a charged rotating Bañados, Teitelboim and Zanelli (BTZ) black hole in ([Formula: see text])-dimensional anti-de Sitter (AdS) space–time. To this end, we derive EUP-corrected Hawking temperature, pressure, entropy, Gibbs free energy and heat capacity functions. We observe that EUP-based quantum corrections decrease pressure and entropy functions in AdS space–time. Such decreases show up itself only in physically meaningful region for Gibbs free energy and specific heat functions.