Article
Astronomy & Astrophysics
H. Garcia-Compean, D. Mata-Pacheco
Summary: In this study, the vacuum transition probabilities between two minima of a scalar field potential in the presence of gravity were investigated. A method to compute these probabilities was proposed by solving the Wheeler-DeWitt equation, and it was applied to specific metrics. The results showed that considering the Generalized Uncertainty Principle enhances the probability initially but leads to faster decay, resulting in a reduction of probability as the corresponding scale factor increases.
CLASSICAL AND QUANTUM GRAVITY
(2022)
Article
Astronomy & Astrophysics
Pasquale Bosso, Luciano Petruzziello, Fabian Wagner
Summary: This paper clarifies a foundational issue in the phenomenological approach to quantum gravity regarding the generalization of Heisenberg's uncertainty principle. The confusion between perturbative and non-perturbative methods in recent works has resulted in a blurred distinction between changes in the deformed algebra and changes in the representation of operators. This reasoning implies that the existence of a minimal length is representation-dependent and therefore unphysical.
Article
Quantum Science & Technology
S. Aghababaei, H. Moradpour
Summary: The emergence of the generalized uncertainty principle is closely related to the existence of a non-zero minimal length. The Heisenberg uncertainty principle is central to the EPR paradox. In this study, the implications of adopting the generalized uncertainty principle (or equivalently, the minimal length) instead of the Heisenberg uncertainty principle on quantum non-locality are examined through the Franson experiment, which relies on energy-time entanglement to understand and explain the results. The survey also demonstrates the power of this experiment in testing the generalized uncertainty principle.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Physics, Multidisciplinary
Jaume Gine
Summary: Using the generalized uncertainty principle, we calculated the first correction to the Hawking temperature associated with the Hawking effect. This allowed us to derive a new evaporation time and entropy for any Schwarzschild black hole by analyzing their expressions and consequences.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Andre Herkenhoff Gomes
Summary: The existence of a fundamental length scale in nature is predicted by various quantum gravity models. If discovered, it would have significant implications for our understanding of quantum phenomena and may lead to modifications of the Heisenberg uncertainty principle. Despite previous attention, there has not been a common framework for the systematic investigation of generalized uncertainty principles (GUP). In this study, we provide such a framework within the context of nonrelativistic quantum mechanics, based on a few assumptions and simple dimensional analysis.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Multidisciplinary
Prathamesh Yeole, Vipul Kumar, Kaushik Bhattacharya
Summary: This paper generalizes the concept of the Wigner function in quantum mechanics with a minimum length scale introduced by applying a generalized uncertainty principle. It presents the phase space formulation and properties of such theories, demonstrating that the Weyl transform and the Wigner function maintain most of their known properties in standard quantum mechanics. The generalized Wigner function is utilized to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying a deformed Heisenberg algebra, and it is shown that certain quantum mechanical operator averages may constrain the value of the deformation parameter in these theories.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Astronomy & Astrophysics
Pasquale Bosso, Giuseppe Gaetano Luciano, Luciano Petruzziello, Fabian Wagner
Summary: This study examines various arguments in quantum gravity, both model-dependent and model-independent, which suggest a modification of Heisenberg's uncertainty principle near the Planck scale. This modification is attributed to the existence of a minimal length. The study critically reviews the conceptual shortcomings of the underlying framework and recent developments in the field. It addresses issues such as relativity, field theory generalizations, the classical limit, and the application to composite systems. Additionally, the study comments on the use of heuristic arguments and presents a comprehensive list of constraints on the model parameter ss, considering their derivation rigor and potential problems with composites.
CLASSICAL AND QUANTUM GRAVITY
(2023)
Article
Physics, Multidisciplinary
B. Hamil, B. C. Lutfuoglu
Summary: One of the main features of Nouicer's GUP formalism is its consideration of deformation contributions to all orders of the Planck length. This manuscript applies the formalism to examine various interesting applications such as ideal gas thermodynamics, Unruh-Davies-DeWitt-Fulling effect, cosmological constant, and blackbody radiation spectrum. GUP corrected results are derived and compared with conventional ones in all cases.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2022)
Article
Quantum Science & Technology
Yuan Yuan, Yunlong Xiao, Zhibo Hou, Shao-Ming Fei, Gilad Gour, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo
Summary: Despite advancements in quantum uncertainty relations, the implementation of majorization uncertainty relations (MURs), the most current and widely applicable formalism, in experiments has been lacking. Previous studies have focused on the mathematical expressions of MURs, neglecting their physical interpretation. To address this, we use a guessing game approach to reveal physical differences between various forms of MURs. Additionally, we enhance the bounds of MURs through flatness processes and experimentally verify strong MURs in a photonic system to validate our theoretical results.
NPJ QUANTUM INFORMATION
(2023)
Article
Astronomy & Astrophysics
Michael Bishop, Joey Contreras, Douglas Singleton
Summary: In this study, an important feature of the generalized uncertainty principle (GUP) approach to quantizing gravity is highlighted: different pairs of modified operators can have different physical consequences, depending on the modifications to the position and/or momentum operators rather than just the resulting modified commutator.
Article
Astronomy & Astrophysics
Nana Cabo Bizet, Octavio Obregon, Wilfredo Yupanqui
Summary: The Heisenberg uncertainty principle is connected to the entropic uncertainty principle, and this correspondence is obtained using a Gaussian probability distribution for wave functions associated with the Shannon entropy. Additionally, the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP) due to quantum gravity effects. In this study, it is shown that GUP has been derived from considering non-extensive entropies proposed by one of the authors. The findings suggest that non-extensive statistics is a signature of quantum gravity.
Article
Astronomy & Astrophysics
Raghvendra Singh, Dawood Kothawala
Summary: We present a formulation of the generalized uncertainty principle based on a commutator between position and momentum operators defined in a covariant manner using normal coordinates. We show that any such commutator can acquire corrections if the momentum space is curved, resulting in noncommutativity of normal position coordinates. We also provide a construction for the momentum space geometry as a suitable extension of a geometry conformal to the three dimensional relativistic velocity space.
Article
Multidisciplinary Sciences
Hooman Moradpour, Sarah Aghababaei, Amir Hadi Ziaie
Summary: The implications of GUP and EUP on a system following the Juttner distribution are investigated in this study, with a focus on deriving the distribution function from the partition function and its relation to thermal energy to ultimately determine the corresponding energy density states.
Article
Quantum Science & Technology
Cong Xu, Zhaoqi Wu, Shao-Ming Fei
Summary: The uncertainty relation is a crucial issue in quantum mechanics and quantum information theory. In this study, the total and quantum uncertainty of quantum channels are identified using modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information. The elegant properties of the total uncertainty of quantum channels are explored, and trade-off relations with entanglement fidelity and entropy exchange/coherent information are established.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Astronomy & Astrophysics
Ana Alonso-Serrano, Mariusz P. Dabrowski, Hussain Gohar
Summary: In this study, we examine the impact of the generalized uncertainty principle (GUP) on nonextensive black hole thermodynamics using Renyi entropy. Our findings indicate that both Renyi entropy and temperature related to black holes have finite values at the end of the evaporation process when GUP effects are introduced. Furthermore, we explore the sparsity of radiation associated with Renyi temperature and compare it with Hawking radiation's sparsity, as well as investigate GUP modifications to the sparsity of radiation when applied to Renyi temperature.
