scholarly journals Tsallis statistics and generalized uncertainty principle

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Giuseppe Gaetano Luciano
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Unruh Effect ◽  
Heisenberg Uncertainty ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Effective Description ◽  
Monotonic Relation

AbstractIt 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 $$\beta $$ β , 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.

scholarly journals Phenomenology of the Pauli exclusion principle violations due to the non-perturbative generalized uncertainty principle

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Andrea Addazi ◽  
Pierluigi Belli ◽  
Rita Bernabei ◽  
Antonino Marcianò ◽  
Homa Shababi
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Pauli Exclusion Principle ◽  
Momentum Conservation ◽  
Exclusion Principle ◽  
Precision Data ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Energy Dependent

Abstract New phenomenological implications of the Generalized Uncertainty Principle (GUP), a modification of the Heisenberg Uncertainty Principle (HUP) are explored in light of constraints arising from underground experiments. An intimate link intertwines the symplectic structure of a theory, which is at the very base of the formulation of the HUP and thus a pillar of quantum mechanics, with the symmetries of space-time and the spin-statistics. Within this wide framework, a large class of non-perturbative GUPs inevitably lead to energy-dependent violations of the total angular momentum conservation rules, and imply hence tiny Pauli Exclusion Principle (PEP) violating transitions. Exotic PEP violating nuclear transitions can be tested, for example, through extremely high precision data provided by the DAMA/LIBRA experiment. We show that several GUP violations are already ruled out up to the quantum gravity Planck scale.

scholarly journals Phenomenological implications of the generalized uncertainty principleThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 233-240 ◽  
Author(s):  
Saurya Das ◽  
Elias C. Vagenas
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Landau Levels ◽  
Quantum Mechanical ◽  
Reflection And Transmission ◽  
Heisenberg Uncertainty Principle ◽  
Transmission Coefficients ◽  
Heisenberg Uncertainty ◽  
Planck Energy

Various theories of quantum gravity argue that near the Planck scale, the Heisenberg uncertainty principle should be replaced by the so called generalized uncertainty principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp4 and β2p6, respectively, where β ∼ 1/(MPlc)2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a scanning tunnel microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.

scholarly journals Mathematical Uncertainty Relations and their Generalization for Multiple Incompatible Observables

2017 ◽  
Vol 33 (1) ◽  
Author(s):  
Hung Quang Nguyen ◽  
Tu Quang Bui
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Schwarz Inequality ◽  
Uncertainty Relations ◽  
Heisenberg Uncertainty Relation ◽  
Generalized Uncertainty Relation ◽  
Heisenberg Uncertainty ◽  
Incompatible Observables

We show that the famous Heisenberg uncertainty relation for two incompatible observables can be generalized elegantly to the determinant form for N arbitrary observables. To achieve this purpose, we propose a generalization of the Cauchy-Schwarz inequality for two sets of vectors. Simple consequences of the N-ary uncertainty relation are also discussed. Keywords: Generalized uncertainty relation, Generalized uncertainty principle, Generalized Cauchy-Schwarz inequality.

scholarly journals Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Pasquale Bosso ◽  
Giuseppe Gaetano Luciano
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Exact Form ◽  
Ladder Operators ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

AbstractSeveral models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

scholarly journals Entropic uncertainty relation based on generalized uncertainty principle

2017 ◽  
Vol 32 (28) ◽  
pp. 1750145 ◽  
Author(s):  
Li-Yi Hsu ◽  
Shoichi Kawamoto ◽  
Wen-Yu Wen
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Thought Experiments ◽  
Small Deformation ◽  
Entropic Uncertainty Relation ◽  
Deformation Parameters ◽  
Gaussian Wave Function

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

scholarly journals Towards Thermodynamics with Generalized Uncertainty Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Farag Ali ◽  
Mohamed Moussa
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Considerable Change ◽  
Heisenberg Uncertainty Principle ◽  
Ideal Gases ◽  
Quantum Gravity Effect ◽  
Photon Gas ◽  
Heisenberg Uncertainty

Various frameworks of quantum gravity predict a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. In this paper we investigate the modification in thermodynamic properties of ideal gases and photon gas. The partition function is calculated and using it we calculated a considerable growth in the thermodynamical functions for these considered systems. The growth may happen due to an additional repulsive force between constitutes of gases which may be due to the existence of GUP, hence predicting a considerable increase in the entropy of the system. Besides, by applying GUP on an ideal gas in a trapped potential, it is found that GUP assumes a minimum measurable value of thermal wavelength of particles which agrees with discrete nature of the space that has been derived in previous studies from the GUP.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

scholarly journals Bounds on large extra dimensions from the Generalized Uncertainty Principle

2017 ◽  
Vol 32 (15) ◽  
pp. 1750082
Author(s):  
Marco Cavaglià ◽  
Benjamin Harms ◽  
Shaoqi Hou
Keyword(s):  
Black Hole ◽  
Lower Bounds ◽  
Uncertainty Principle ◽  
Extra Dimensions ◽  
Large Extra Dimensions ◽  
Production Cross ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Minimum Length ◽  
Minimum Length Scale

The Generalized Uncertainty Principle (GUP) implies the existence of a physical minimum length scale [Formula: see text]. In this scenario, black holes must have a radius larger than [Formula: see text]. They are hotter and evaporate faster than in standard Hawking thermodynamics. We study the effects of the GUP on black hole production and decay at the LHC in models with large extra dimensions. Lower bounds on the fundamental Planck scale and the minimum black hole mass at formation are determined from black hole production cross-section limits by the CMS Collaboration. The existence of a minimum length generally decreases the lower bounds on the fundamental Planck scale obtained in the absence of a minimum length.

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