Generalized Uncertainty Principle Research Articles

Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.

Thermodynamics of Schwarzschild black hole surrounded by quintessence with generalized uncertainty principle

In this manuscript, we consider a deformation on the Heisenberg algebra and investigate the effects on the thermodynamics of the Schwarzschild black hole that is surrounded by quintessence matter. To this end, we obtain the temperature, entropy and heat capacity functions of the black hole by using the standard laws of thermodynamic according to the considered deformation. We show that upper and lower bound values appear on these functions based on the quintessence and deformed algebra. Then, we derive the corrected density of quintessence matter and the black hole’s equation of state functions. We compare these results with the standard Schwarzschild black hole with and without quintessence with the graphical methods and interpret the quantum deformation effects.

Thermodynamics of the Schwarzschild and Reissner–Nordström black holes under higher-order generalized uncertainty principle

In this manuscript, the modification of thermodynamic properties of Schwarzschild and Reissner–Nordström black holes in the presence of higher-order generalized uncertainty principle (GUP) have been investigated. We considered heuristic analysis versus the behavior of a particle that is absorbed by the black hole, and then, we studied the thermodynamic properties of the black holes such as temperature-mass, temperature-charge-mass, entropy, and heat capacity functions up to the first- and second order of the GUP parameter. We compared the behaviors the GUP-corrected thermodynamic properties for both black holes with graphical methods.

Quantum cycle in relativistic non-commutative space with generalized uncertainty principle correction

Quantum heat cycles and quantum refrigerators are analyzed using various quantum systems as their working mediums. For example, to evaluate the efficiency and the work done of the Carnot cycle in the quantum regime, one can consider the harmonic oscillator as a working medium. For all these well-defined working substances (which are analyzed in commutative space structure), the efficiency of the engine is not up to the mark of the Carnot efficiency. So, one inevitable question arise, can one observe a catalytic effect on the efficiency of the engines and refrigerators when the space structure is changed? In this paper, two different working substances in non-commutative spacetime with relativistic and generalized uncertainty principle corrections have been considered for the analysis of the efficiency of the heat engine cycles. The efficiency of the quantum heat engine gets a boost for higher values of the non-commutative parameter with a harmonic oscillator as the working substance. In the case of the second working medium (one-dimensional infinite potential well), the efficiency shows a constant result in the non-commutative space structure.

Polarization-spatial Gaussian entanglement in partially coherent light fields.

The problem of bipartite entanglement in partially coherent paraxial vector light fields is addressed. A generalized uncertainty principle suited for the polarization-spatial degrees of freedom is introduced. Partial transpose is implemented through the obtained generalized uncertainty principle. Partial transpose is shown to be necessary and sufficient in detecting entanglement for a class of partially coherent vector light fields which have a spatial part to be Gaussian. An experimental realization of the studied entangled states using classical optical interferometry is outlined.

Higher-order generalized uncertainty principle corrections to the Jeans mass

The Jeans instability is regarded as an important tool for analyzing the dynamics of a self-gravitating system. However, this theory is challenging since astronomical observation data show some Bok globules, whose masses are less than the Jeans mass and still have stars or at least undergo the star formation process. To explain this problem, we investigate the effects of the higher-order generalized uncertainty principle on the Jeans mass of the collapsing molecular cloud. The results in this paper show that the higher order generalized uncertainty principle has a very significant effect on the canonical energy and gravitational potential of idea gas, and finally leads to a modified Jeans mass lower than the original case, which is conducive to the generation of stars in small mass Bok globules. Furthermore, we estimate the new generalized uncertainty principle parameter gamma _0 by applying various data of Bok globules, and find that the range of magnitude of gamma _0 is {10^{11}} {-} {10^{12}}.

Constraining the generalized uncertainty principle with neutron interferometry

The non-zero minimal length arises in various theories of gravity, leading to the so-called generalized uncertainty principle (GUP). In this short paper we analyze the GUP effects on neutron interferometry, showing that the obtained phase shifts depend on the mass and velocity of the particle. New upper bounds on the dimensionless GUP parameter have been found that are in agreement with the literature.

Quantum gravity effect on the entropy of a novel four-dimensional Gauss-Bonnet black hole

Taking the generalized uncertainty principle into account, we apply the corrected state density and brick-wall method to calculate the entropy of a novel four-dimensional Gauss-Bonnet black hole surrounded by an arbitrary field with spin . It is shown that the leading and logarithmic terms of the entropy are respectively modified by the quantum gravity effect and spin of the field. Meanwhile, the correction coming from gravitational interaction has the same form as the leading term, that is, they all are proportional to the horizon area and inversely proportional to the gravity correction factor. The ratio of the correction term to the leading one is respectively −5/7 and −1395/1764 for Bose and Fermi cases, where negative sign means that the effect of quantum gravity decreases the entropy. It is very interesting that these proportion values are independent of the black hole characteristics.

Zitterbewegung particles tunneling from Reissner-Nordström AdS black hole surrounded by quintessence

We study quantum gravity corrections to the thermodynamic quantities of Reissner-Nordström anti-de Sitter black hole surrounded by quintessence by evaluating the Hawking radiation of zitterbewegung particles under the Generalized Uncertainty Principle (GUP) effect. By using the modified Hawking temperature of the black hole, we derive the thermodynamic equation of state and the Helmholtz free energy. We discuss global stability conditions and phase transitions by plotting the and planes. We also assume that the black hole is a heat engine where the Carnot cycle is performed. We observe that the efficiency under the GUP effect is higher than the standard one when attractive Coulomb interaction is considered with the influence of zitterbewegung particles.

Collective states of even–even nuclei in γ-rigid quadrupole Hamiltonian with minimal length under the sextic potential

In the present paper, we study the collective states of even–even nuclei in γ-rigid mode within the sextic potential and the minimal length (ML) formalism in Bohr–Mottelson model. The eigenvalues problem for the latter is solved by combined means of quasi-exact solvability and a quantum perturbation method. Numerical calculations are performed for 35 nuclei: 98−108Ru, 100−102Mo, 116−130Xe, 180−196Pt, 172Os, 146−150Nd, 132−134Ce, 154Gd, 156Dy and 150−152Sm. Through this study, it appears that our elaborated model leads to an improved agreement of the theoretical results with the corresponding experimental data by reducing the rms with a rate going up to 63% for some nuclei. This comes from the fact that we have combined the sextic potential, which is a very useful phenomenological potential, with the formalism of the ML, which is based on the generalized uncertainty principle and which is in turn a quantum concept widely used in quantum physics. In addition, we investigate the effect of ML on energy ratios, transition rates, moments of inertia and a shape phase transition for the most numerous isotopic chains, namely Ru, Xe, Nd and Pt.

Discussion on Exact Solution of Dirac Equation with Generalized Exponential Potential in the Presence of Generalized Uncertainty Principle

Discussion on Exact Solution of Dirac Equation with Generalized Exponential Potential in the Presence of Generalized Uncertainty Principle

Path-integral action in the generalized uncertainty principle framework

Various gedanken experiments of quantum gravity phenomenology in search of a complete theory of gravity near the Planck scale indicate a modification of the Heisenberg uncertainty principle to the generalized uncertainty principle (GUP). This modification leads to nontrivial contributions on the Hamiltonian of a nonrelativistic particle moving in an arbitrary potential. In this paper we study the path integral representation of a particle moving in an arbitrary potential using the most general form of the GUP containing both the linear and quadratic contributions in momentum. First we work out the action of the particle in an arbitrary potential and hence find an upper bound to the velocity of a free particle. This upper bound interestingly imposes restrictions on the relation between the GUP parameters $\alpha$ and $\beta$. Analysis shows that $ \beta > 4 \alpha^2$. We then deduce the mathematical expressions of classical action and the quantum fluctuations for both free particle and the harmonic oscillator systems.

Tsallis statistics and generalized uncertainty principle

It has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter beta , which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.

Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices

Dirac fermions in graphene may experiment dispersive pseudo-Landau levels due to a homogeneous pseudomagnetic field and a position-dependent Fermi velocity induced by strain. In this paper, we study the (semi-classical) dynamics of these particles under such a physical context from an approach of coherent states. For this purpose we use a Landau-like gauge to built Perelomov coherent states by the action of a non-unitary displacement operator $D(\alpha)$ on the fundamental state of the system. We analyze the time evolution of the probability density and the generalized uncertainty principle as well as the Wigner function for the coherent states. Our results show how $x$-momentum dependency affects the motion periodicity and the Wigner function shape in phase space.

Interacting quintessence in light of generalized uncertainty principle: cosmological perturbations and dynamics

We consider a cosmological scenario endowed with an interaction between the universe’s dark components – dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty Principle. The latter modification introduces new higher-order terms of fourth-derivative due to quantum corrections in the scalar field’s equation of motion. Then, we investigate asymptotic dynamics and general behaviour of solutions of the field equations for some interacting models of special interests in the literature. At the background level, the present interacting model exhibits the matter-dominated and de Sitter solutions which are absent in the corresponding quintessence model. Furthermore, to boost the background analysis, we study cosmological linear perturbations in the Newtonian gauge where we show how perturbations are modified by quantum corrected terms from the quadratic Generalized Uncertainty Principle. Depending on the coupling parameters, scalar perturbations show a wide range of behavior.

Research and Development of Uncertainty Relations, and Reconsider and Description of Duality

First, based on the uncertainty principle in quantum theory and new generalized uncertainty principle, we research uncertain relations of entropy, information and thermodynamics, and propose the speed of light and some fundamental constants should be uncertain. Next, in the quantum entangled states, velocities of different phases may be superluminal, and obey possibly general Lorentz transformation (GLT). Third, we search its possible development in superstring, and the extensive quantum theory, various matters and different phases, etc. Fourth, the duality exists probably only under interactions. Some nonlinear quantum equations and wave equations have soliton solutions, which correspond to particles. This is mathematical description of wave-particle duality. Fifth, based on the soliton-chaos double solutions of nonlinear equations, we propose the field-particle duality, and field (wave)-quantum-chaos ternary. Sixth, the irreversibility and statistics are discussed, and we derive operators of entropy, etc. New measuring technology and some developed theories already challenge the uncertainty principle and duality, which may not be held under certain conditions, and must be modified and developed.

Minimal length, maximal momentum and stochastic gravitational waves spectrum generated from cosmological QCD phase transition

We investigate thoroughly the temporal evolution of the universe temperature as a function of the Hubble parameter associated with the Stochastic Gravitational Wave (SGW), that formed at the cosmological QCD phase transition epoch to the current epoch, within the Generalized Uncertainty Principle (GUP) framework. Here we use GUP version which provide constraints on the minimum measurable length and the maximum observable momentum, that characterized by a free parameter α. We study the effect of this parameter on the SGW background. We show that the effect can slightly enhance the SGW frequency in the lower frequency regime which might be important in the detection of SGW in the future GW detection facilities.

New Higher-Order Generalized Uncertainty Principle: Applications

Recently Chung and Hassanabadi proposed a higher order general uncertainty principle (GUP∗) that predicts a minimal length as well as possesses a upper bound momentum limit. In this article, we have discussed an ideal gas system and its thermal properties using that deformed canonical algebra introduced by them. Moreover, we examined blackbody radiation spectrum and the cosmological constant in the presence of the GUP∗. After a comparison with the existing literature, we concluded that the given formalism of Chung and Hassanabadi yields more accurate results.

Thermodynamic quantities in the high-temperature limit in the GUP framework

We study the values of thermodynamic quantities of physical systems at high temperatures in the framework of the generalized uncertainty principle (GUP). First, we obtain the semi-classical partition function, internal energy, and heat capacity for physical systems in a general case of deformed algebra. We show that at the high-temperature limit the heat capacity vanishes and the internal energy is maximized. We calculate this temperature for the ultra-relativistic system in approximate form. Finally, the maximum temperature and maximum energy for the ultra-relativistic system are obtained in the framework of two different GUPs.

Extended GUP corrected thermodynamics, shadow radius and quasinormal modes of charged AdS black holes in Gauss–Bonnet gravity

This paper explores the influence of special type of higher order generalized uncertainty principle on the thermodynamics of five-dimensional black hole in Einstein–Gauss–Bonnet gravity coupled to nonlinear electrodynamics. We examine the corrected thermodynamical properties of the black hole with some interesting limiting cases [Formula: see text] and [Formula: see text] and compared our results with usual thermodynamical relations. We observe that the influence of GUP correction stabilizes the BH and BH solution remains physical throughout the region of horizon radius. In this framework, we also uncover the relationship of shadow radius and quasinormal modes of the mentioned black hole. We conclude that shadow radius of our considered black hole is a perfect circle and it decreases with increasing values of charge and Gauss–Bonnet parameter. We also verify the inverse relation between the quasinormal modes frequencies and shadow radius, i.e. quasinormal modes should increase with increasing values of Gauss–Bonnet parameter and electric charge.