Article
Astronomy & Astrophysics
Pasquale Bosso
Summary: Quantum mechanical models with a minimal length often involve modifying the relationship between position and momentum. While this is a minor complication in momentum space, the representation in (quasi-)position space poses many issues and leads to misunderstandings. This work reviews and clarifies some aspects of minimal length models, focusing on the representation of the position operator.
CLASSICAL AND QUANTUM GRAVITY
(2021)
Article
Astronomy & Astrophysics
Pasquale Bosso
Summary: Phenomenological studies of quantum gravity propose modifying the commutator between position and momentum in quantum mechanics to introduce minimal uncertainty in position. This study demonstrates the influence of space and time transformations on shaping quantities like momentum, energy, and their relationships with transformation generators. This influence determines the time evolution of quantum systems, with the Schrodinger equation identical to the ordinary case in the example of Galilean transformations.
CLASSICAL AND QUANTUM GRAVITY
(2023)
Article
Physics, Fluids & Plasmas
Jin-Fu Ma, Jin-Fu Chen, C. P. Sun, Hui Dong
Summary: Landauer's principle imposes a fundamental limit on the energy cost of perfectly initializing a classical bit, but in practical operations, the finite operation time leads to an increase in energy cost. Specifically, when initializing the bit, the smaller the error, the higher the energy cost. A finite-time isothermal process can be used for bit initialization, and an optimal protocol to minimize the energy cost is proposed.
Article
Astronomy & Astrophysics
Pasquale Bosso
Summary: Several approaches to quantum gravity suggest the existence of a minimal measurable length at high energies, contradicting the Heisenberg Uncertainty Principle. To address this issue, the Generalized Uncertainty Principle is introduced in phenomenological approaches to quantum gravity, affecting several features of quantum mechanics, such as the exclusion of position eigenstates in models with a minimal length.
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
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
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
Materials Science, Multidisciplinary
Bhaskar Mukherjee, Debasish Banerjee, K. Sengupta, Arnab Sen
Summary: The study reveals extensive fragmentation of the Hilbert space in this model, leading to a breakdown of thermalization despite the nonintegrable nature of the Hamiltonian. Different types of anomalous eigenstates are discussed, as well as the consequences of adding a magnetic field and a PXP term to the model.
Article
Physics, Multidisciplinary
Heru Sukamto, Lila Yuwana, Agus Purwanto
Summary: This paper discusses the influence of minimal length on relativistic physical systems, particularly the efficiency of a relativistic quantum heat engine. The chosen working substance is a Dirac particle trapped in a one-dimensional infinite potential well. The efficiency of the quantum heat engine is calculated analytically and numerically in three thermodynamic cycles: Carnot, Otto, and Brayton cycles. The research reveals that the minimal length acts as a correction factor for relativistic energy and can either increase or decrease the efficiency of the relativistic quantum heat engine depending on the particle mass, expansion parameter, and thermodynamic cycle.
Article
Astronomy & Astrophysics
Pasquale Bosso, Juan Manuel Lopez Vega
Summary: The generalized uncertainty principle (GUP) introduces the concept of a minimal length by modifying the uncertainty relation between momentum and position, as predicted by quantum gravity theories. By incorporating GUP, Planck's distribution can be derived and used to explain the thermodynamics of black body radiation, leading to modifications of Wien's law and the Stefan-Boltzmann law at the Planck scale.
CLASSICAL AND QUANTUM GRAVITY
(2022)
Article
Astronomy & Astrophysics
Li-Hua Wang, Meng-Sen Ma
Summary: This paper re-derives the black hole entropy of static spherically symmetric black holes based on the concept of fractal black hole horizon. The temperatures and heat capacities of Schwarzschild, Reissner-Nordstrom, and RN-AdS black holes are calculated, showing that these black holes are thermodynamically stable. The heat capacity of RN-AdS black hole exhibits Schottky anomaly-like behavior, indicating the existence of discrete energy levels and restricted microscopic degrees of freedom.
Article
History & Philosophy Of Science
John W. Keck
Summary: This paper demonstrates the connection between Aristotle's core concepts and quantum mechanics and relativity, and explores the relationship between matter, motion, mobility, and indeterminacy through the study of massless particles.
Article
Astronomy & Astrophysics
Andre Herkenhoff Gomes
Summary: Motivated by current searches for signals of Lorentz symmetry violation, this paper investigates generalized uncertainty principle (GUP) models in anisotropic space. The authors identify GUP models that satisfy two criteria: (i) invariance of commutators under canonical transformations, and (ii) physical independence of position and momentum on the ordering of auxiliary operators in their definitions. These criteria place important restrictions on how GUP models may be approached algebraically.
CLASSICAL AND QUANTUM GRAVITY
(2023)
Article
Physics, Particles & Fields
Ziemowit Domanski, Maciej Blaszak
Summary: This theory develops a complete non-formal deformation quantization theory, showing a nonzero minimal uncertainty in position. It introduces an appropriate integral formula for the star-product, a suitable space of functions on which the star-product is well defined, and proves basic properties of the star-product. It constructs a C*-algebra of observables and a space of states, and presents an operator representation in momentum space.
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS
(2021)
Article
Physics, Particles & Fields
Anna Pachol, Aneta Wojnar
Summary: We investigate the application of incorporating corrections from the Snyder model and the Generalized Uncertainty Principle into the equation of state to describe the behavior of matter in a low-mass star. The resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realism, we are able to effectively constrain the theory parameters beyond existing astrophysical bounds.
EUROPEAN PHYSICAL JOURNAL C
(2023)