Article
Astronomy & Astrophysics
Paolo Aschieri, Andrzej Borowiec, Anna Pachol
Summary: The study focuses on noncommutative deformations of the wave equation in curved backgrounds, discussing how the modification of dispersion relations due to noncommutativity combined with spacetime curvature. Using a noncommutative differential geometry approach based on Drinfeld twist deformation, the authors demonstrate its applicability for any twist and curved background. The Jordanian twist is discussed in detail, showing its impact on the speed of light variation in the presence of a cosmological background.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2021)
Article
Physics, Multidisciplinary
Otto C. W. Kong, Wei-Yin Liu
Summary: We present an isomorphic representation of the observable algebra in quantum mechanics using functions on the projective Hilbert space and its analog, the Hilbert space, with a noncommutative product defined by explicit coordinates. This representation allows us to translate the differential symplectic geometry of infinite dimensional manifolds onto the observable algebra as a noncommutative geometry. By doing so, we obtain a noncommutative geometry directly from the physical theory itself. This work introduces an extended mathematical formalism of the Schrödinger versus Heisenberg picture, which can be seen as a coordinate map from the phase space to a noncommutative geometry coordinated by six position and momentum operators. The observable algebra is taken as an algebra of formal functions on these operators. The significance of this article lies in the formulation of the intuitive idea that noncommutative geometry can be viewed as an alternative, noncommutative coordinate picture of the familiar quantum phase space, especially in terms of symplectic geometry.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Astronomy & Astrophysics
Saumya Ghosh, Sunandan Gangopadhyay, Prasanta K. Panigrahi
Summary: In this paper, we investigate a noncommutative quantum description of the Kantowski-Sachs cosmological model with the presence of perfect fluid matter field, as well as analyze the effect of noncommutativity on the model. The results demonstrate that a multiverse universe model is possible even in the absence of noncommutativity. The presence of noncommutativity is revealed by a decrease in the highest value of the individual peaks. Additionally, we discuss the unitarity of the model and show that it can be restored through a proper definition of inner product, similar to other anisotropic quantum cosmologies.
MODERN PHYSICS LETTERS A
(2022)
Article
Astronomy & Astrophysics
Hugo Garcia-Compean, Octavio Obregon, Cupatitzio Ramirez
Summary: This article reviews the work done by the authors and collaborators in the fields of supersymmetric quantum cosmology, noncommutative quantum cosmology, and the application of generalized uncertainty principles to quantum cosmology and black holes. The review is presented in chronological order and reflects the authors' personal views on the subjects.
Article
Multidisciplinary Sciences
Shi-Dong Liang
Summary: In this paper, we study the noncommutative relations of the position and momentum operators in four-dimensional space. By using the Seiberg-Witten (SW) map, we obtain the Heisenberg representation of these noncommutative algebras and introduce the noncommutative parameters associated with the Planck constant, Planck length, and cosmological constant. We show that the noncommutative effect can be interpreted as an effective gauge field, analogous to the electromagnetic gauge potential, which depends on the Plank constant and cosmological constant. Based on these noncommutative relations, we explore the Klein-Gordon (KG) equation and its properties in the noncommutative phase space, including canonical and Hamiltonian forms. We also analyze the symmetries of the KG equations and study observables such as velocity and force of free particles in the noncommutative phase space. Additionally, we provide a perturbation solution to the KG equation.
Article
Biochemistry & Molecular Biology
Angel Ballesteros, Giulia Gubitosi, Ivan Gutierrez-Sagredo, Francisco J. Herranz
Summary: In this work, it is shown that the noncommutative spacetimes associated with x-Poincare relativistic symmetries and their non-relativistic and ultra-relativistic limits cannot be distinguished based on their coordinates. However, by examining the associated spaces of time-like worldlines, it is found that these three quantum kinematical models can be differentiated. Specifically, the noncommutative spaces of time-like geodesics with x-Galilei and x-Carroll symmetries are constructed as contractions of the corresponding x-Poincare space, and it is demonstrated that these three spaces are defined by different algebras. Furthermore, the map between quantum spaces of geodesics and the corresponding noncommutative spacetimes is identified, requiring the extension of the space of geodesics by adding the noncommutative time coordinate.
PESTICIDE BIOCHEMISTRY AND PHYSIOLOGY
(2023)
Article
Physics, Multidisciplinary
Muhittin Cenk Eser, Mustafa Riza
Summary: In this study, the effects of noncommutative Quantum Mechanics on the energy-levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction were investigated. The first-order corrections to the energy levels were obtained in closed form in the low energy limit of weak noncommutativity, showing that all energy corrections due to noncommutativity are negative and increase in magnitude with increasing Quantum numbers and magnetic field.
Article
Astronomy & Astrophysics
J. A. Astorga-Moreno, Miguel A. Garcia-Aspeitia, E. A. Mena-Barboza
Summary: This article explores the quantum cosmology (QC) of a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe within the framework of classical Unimodular Gravity (UG), considering inflationary scenario and introducing a deformation on the commutation relations for the minisuperspace variables (NCC).
MODERN PHYSICS LETTERS A
(2022)
Article
Physics, Multidisciplinary
Liu-Biao Ma, Qing Wang, Ling-Bao Kong, Jian Jing
Summary: The Spavieri effect in noncommutative space is investigated using two different methods, the Bopp shift and the Seiberg-Witten map. It is shown that both methods reach the same conclusion, up to the first order of the noncommutative parameter, that the spatial noncommutativity does not lead to corrections to the Spavieri effect, despite the distinct mechanisms of the two methods. The studies also demonstrate the persistence of the equivalence between the Spavieri and Aharonov-Bohm effects in noncommutative space.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Manjari Dutta, Shreemoyee Ganguly, Sunandan Gangopadhyay
Summary: This paper investigates the existence of Berry phase in time-dependent harmonic oscillators in noncommutative space, considering two systems. By calculating the eigenstates and the Berry phase with appropriate forms, it is revealed that a scale invariant time reversal symmetry breaking term may not always lead to a non-trivial Berry phase.
Article
Physics, Particles & Fields
Partha Nandi, Sankarshan Sahu, Sayan Kumar Pal
Summary: This study presents a captivating analysis of Ward-Takahashi identities in a generalized quantum Hall system with broken dilatation or scale symmetry, revealing the noncommutativity between spatial coordinates at a large magnetic field limit. The derivation of a path-integral action for the noncommutative quantum system and the discussion of the equivalence between the considered noncommutative system and the generalized Landau problem lead to an effective commutative description. Further investigation into the unintegrated scale or dilatation anomaly for the generalized Landau system using Fujikawa's method reveals an anomalous nature induced by the noncommutative structure between spatial coordinates.
Article
Astronomy & Astrophysics
J. A. Astorga-Moreno, U. I. Castellanos-Cervantes, E. Diaz-Gutierrez, E. A. Mena-Barboza
Summary: In this work, the asymptotic behavior of a commutative and noncommutative Mixmaster model in a Quantum Cosmology (QC) and semiclassical scenario is investigated. The calculations are explicitly shown, and asymptotically equivalent functions are applied to analyze the equivalence between Bianchi IX and Bianchi II models.
MODERN PHYSICS LETTERS A
(2022)
Article
Physics, Multidisciplinary
Masoud Khalkhali, Nathan Pagliaroli
Summary: This study presents an analytic proof of phase transition in certain random noncommutative geometries in the large N limit, showing both single and double cut regions for specific values of the order parameter and determining the exact value of the transition.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Astronomy & Astrophysics
Fedele Lizzi, Flavio Mercati
Summary: In this study, we explore the challenges in constructing a multiparticle field theory on a kappa-Minkowski noncommutative spacetime, particularly focusing on the existence of multilocal functions respecting deformed symmetries. It is found that a braided tensor product is necessary for the invariance of the tensor product algebra under the coaction of the kappa-Poincare group. Additionally, it is demonstrated that kappa-Poincare-invariant N-point functions belong to an Abelian subalgebra, making them commutative.
Article
Mechanics
Yasushi Yoneta, Akira Shimizu
Summary: A phase coexistence state cannot be uniquely determined by intensive parameters, so an appropriate set of additive observables is needed. Existing statistical ensembles may fail when additive observables do not commute, but we propose a generalized ensemble that can handle phase coexistence states specified by noncommutative additive observables. We prove that this ensemble correctly gives the density matrix and thermodynamic functions for general quantum systems. Our formulation is convenient for practical calculations and directly provides values of temperature and other intensive parameters from the expectation values of additive observables. We demonstrate its application to a two-dimensional system with a noncommuting order parameter.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2023)
Article
Astronomy & Astrophysics
C. Gomes, O. Bertolami
Summary: In this study, we restrict the viable models of Horndeski gravity, formulated as the equivalent Generalised Galileon version, using the Witten positive energy theorem. The analysis reveals that the free function G(3)(phi, X) in the Lagrangian is solely dependent on the scalar field, G(3)(phi), and establishes relationships among the free functions. Additionally, stability criteria such as gravity attractiveness and Dolgov-Kawasacki instability are examined, and cosmological applications are discussed.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2022)
Article
Astronomy & Astrophysics
Orfeu Bertolami, Maria Margarida Lima, Filipe C. Mena
Summary: The existence of magnetic fields in the universe is observed at all scales, but their origin remains unknown. In the context of non-minimal coupling gravity theory, it is found that under certain conditions, the generated magnetic fields during inflation can be compatible with large-scale observations.
GENERAL RELATIVITY AND GRAVITATION
(2022)
Article
Astronomy & Astrophysics
Orfeu Bertolami, Frederico Francisco
Summary: A classification scheme for rocky planets is proposed based on the Landau-Ginzburg Theory, and the impact of Earth's transition from Holocene to Anthropocene on other planets is discussed. The similarities between Earth and Venus are highlighted, suggesting the possibility of a hot-house Earth scenario resulting from the Anthropocene transition.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2022)
Article
Mathematics
Nuno C. Dias, Franz Luef, Joao N. Prata
Summary: In this paper, we translate the uncertainty principles of Cowling-Price-Heisenberg-type into a variational principle on modulation spaces. We investigate compact localization operators with symbols in modulation spaces, where the optimal constant in these uncertainty principles is determined by the smallest eigenvalue of the inverse of a compact localization operator. The Euler-Lagrange equations associated with the functional provide equations for the eigenfunctions of the smallest eigenvalue of these compact localization operators. As a result, we also generalize an inequality for Wigner and Ambiguity functions in mixed-norm spaces, originally proposed by Lieb.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Physics, Multidisciplinary
Nuno Costa Dias, Joao Nuno Prata
Summary: This article addresses a recent conjecture proposed by Z. Van Herstraeten and N. J. Cerf, which claims that the Shannon entropy of positive Wigner functions is bounded below by a positive constant only attainable by Gaussian pure states. A new definition of entropy for all absolutely integrable Wigner functions is introduced, which is the Shannon entropy of positive Wigner functions. Moreover, it is proven, in arbitrary dimension, that this entropy is indeed bounded below by a positive constant that is relatively close to the constant suggested by Van Herstraeten and Cerf. An analogous result is also proven for another conjecture concerning the Renyi entropy of positive Wigner functions. As a result, a new inequality for the radar-ambiguity function (and for the Wigner distribution) is derived, which resembles Lieb's inequalities.
ANNALES HENRI POINCARE
(2023)
Article
Physics, Multidisciplinary
A. E. Bernardini, O. Bertolami
Summary: Quantum mechanics plays a crucial role in modeling competitive ecological systems and self-organizing structures. The dynamics of prey-predator competition in phase space can be described within the framework of Weyl-Wigner quantum mechanics, with quantum states convoluted by statistical gaussian ensembles. Quantum modifications on the equilibrium and stability of the prey-predator dynamics can be identified through the Wigner current fluxes obtained from an onset Hamiltonian background. Additionally, emergent topological quantum domains affect the stability properties of gaussian ensembles localized around the equilibrium point, leading to extinction and revival scenarios or perpetual coexistence of prey and predator agents.
FOUNDATIONS OF PHYSICS
(2023)
Article
Astronomy & Astrophysics
Orfeu Bertolami
Summary: The vacuum can have two different phases, one dominated by non-relativistic matter and the other being a de Sitter phase, according to the Chaplygin equation or its generalised version. Particle production during the matter-like phase can generate entanglement entropy and the interactions provide the environment for gravitational quantum features to become classical. In the de Sitter phase, the cosmological constant can be suppressed by inflation.
CLASSICAL AND QUANTUM GRAVITY
(2023)
Article
Physics, Fluids & Plasmas
A. E. Bernardini, O. Bertolami
Summary: This paper investigates the nonequilibrium and instability features of prey-predator-like systems associated with topological quantum domains emerging from a quantum phase-space description. By reporting the generalized Wigner flow for one-dimensional Hamiltonian systems, the prey-predator dynamics driven by Lotka-Volterra equations is mapped onto the Heisenberg-Weyl noncommutative algebra. The result shows that the equilibrium and stability parameters for the prey-predator-like dynamics are affected by quantum distortions, quantified in terms of Wigner currents and Gaussian ensemble parameters.
Article
Astronomy & Astrophysics
Orfeu Bertolami, Claudio Gomes, Paulo M. Sa
Summary: In this paper, we investigate whether inflationary solutions driven by a single scalar field can be consistent with the swampland conjectures in string theory, in the context of alternative theories of gravity with nonminimal coupling between matter and curvature. Our findings suggest that the slow-roll conditions are not compatible with the swampland conjectures for a vast range of inflationary solutions in these alternative theories of gravity.
Article
Physics, Fluids & Plasmas
A. E. Bernardini, O. Bertolami
Summary: The study investigates the Lotka-Volterra dynamics within the framework of Weyl-Wigner quantum mechanics. The research finds that the variables in LV dynamics can be interpreted as canonical variables in quantum mechanics, allowing for the understanding of the changes in the number of individuals in a prey-predator system. The results provide insights into how classical and quantum evolution coexist and offer a quantification of quantum analog effects.
Article
Optics
A. E. Bernardini, O. Bertolami
Summary: Phase-space features of one-dimensional systems with a constrained Hamiltonian are obtained analytically using Wigner functions and currents. Profiles for thermodynamic and Gaussian ensembles are identified, and the results are specialized to the Harper Hamiltonian system. This generalized Wigner approach serves as a probe for quantumness and classicality of Harper-like systems, and it can be extended to any quantum system described by specific Hamiltonians.
Article
Astronomy & Astrophysics
Riccardo March, Orfeu Bertolami, Marco Muccino, Claudio Gomes, Simone Dell'Agnello
Summary: We investigate a nonminimally coupled curvature-matter gravity theory that involves a Yukawa-type fifth force and a non-Newtonian extra force arising from the nonminimal coupling in the solar interior and atmosphere. The extra force depends on the spatial gradient of space-time curvature R. We examine the conditions under which these forces can be screened by the chameleon mechanism and be consistent with the Cassini measurement of the parametrized post-Newtonian parameter gamma. Constraints from spectroscopic observations of the solar atmosphere are also considered.
Article
Engineering, Aerospace
Andre G. C. Guerra, Orfeu Bertolami, Paulo J. S. Gil
Summary: By evaluating four different propulsion methods, we found that combining ion engine technology with a classical chemical engine can achieve the shortest mission time with the lowest mass. The Pure Electro-Magnetic Thrust (PEMT) technology may be more suitable for destinations beyond Mars.
JOURNAL OF THE ASTRONAUTICAL SCIENCES
(2022)
Article
Hematology
Miguel Coelho, Catarina Bastos, Jose Figueiredo
Summary: Intra-articular administration of tranexamic acid is superior to other techniques in reducing perioperative blood loss and hemoglobin variation in total knee arthroplasty. It also has lower blood loss, hematocrit variation, need for blood transfusion, and shorter in-hospital stay compared to other techniques.
JOURNAL OF BLOOD MEDICINE
(2022)
