Article
Physics, Multidisciplinary
M. Samar, V. M. Tkachuk
Summary: In this paper, we define the delta '(x) potential as a linear kernel of the potential energy operator in momentum representation in the general case of deformed Heisenberg algebra leading to the minimal length. We find the exact energy level and corresponding eigenfunction for the delta '(x) and delta(x) - delta '(x) potentials in the deformed space with an arbitrary deformation function. The energy spectrum for different partial cases of deformation function is analyzed.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Particles & Fields
Fabian Wagner
Summary: The minimal and maximal uncertainties of position measurements are considered to be important characteristics of low-energy quantum and classical gravity. This study shows that the Generalized Extended Uncertainty Principle can be described in terms of quantum dynamics on a general curved cotangent manifold, with the curvature tensors being related to the noncommutativity of coordinates and momenta. The covariance of the approach leads to interesting subclasses of noncommutative geometries and enables the derivation of anisotropically deformed uncertainty relations from general background geometries.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Physics, Multidisciplinary
F. A. Dossa, J. T. Koumagnon, J. V. Hounguevou, G. Y. H. Avossevou
Summary: The dynamics of the Dirac oscillator in a magnetic field is studied, with the Heisenberg algebra constructed in detail in the noncommutative phase space. By using the Nikiforov-Uvarov method, exact energy eigenvalues are obtained and the corresponding wave functions are expressed in terms of hypergeometric functions in momentum space.
THEORETICAL AND MATHEMATICAL PHYSICS
(2022)
Article
Physics, Nuclear
Xiaobo Guo, Kangkai Liang, Benrong Mu, Peng Wang, Mingtao Yang
Summary: The study shows that the minimal measurable length has effects on the motion of particles near black holes, leading to stronger chaotic behavior. In the presence of minimal length effects, the scrambling time of black holes may be shorter and some Lyapunov characteristic exponents could exceed the surface gravity of the horizon.
Article
Astronomy & Astrophysics
N. Dimakis
Summary: Studying particle dynamics under the DISIMb(2) group in a space-time invariant setting reveals that breaking of Lorentz symmetry leads to the creation of higher order symmetries, connected to those broken at the space-time level. The Lorentz violation is linked to specific noncommutative relations in phase space through the perspective of conserved quantities in special relativity.
Article
Physics, Multidisciplinary
Geng Li, Jin-Fu Chen, C. P. Sun, Hui Dong
Summary: Shortcuts to isothermality are a strategy for driving a system to its equilibrium states and evaluating the impact of control. Finding the optimal scheme to minimize energy cost is crucial, and it has been proven to be equivalent to finding the geodesic path in the space of control parameters. This equivalence provides a systematic and universal approach to finding optimal control for reducing energy cost.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Salaheddine Bensalem, Djamil Bouaziz
Summary: The method for calculating the canonical partition function with deformed Heisenberg algebra, adapted to modified commutation relations including a maximal length, is applied to investigate the thermostatistics of an ideal gas and a system of harmonic oscillators. The effects of the maximal length on different systems vary, showing similarities to previously studied minimal length effects. Analysis of experimental data suggests that the maximal length can be viewed as a characteristic scale associated with the system under study.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Astronomy & Astrophysics
A. Alonso-Serrano, M. Liska
Summary: By heuristically deriving the Hawking temperature and Bekenstein entropy from the existence of a minimal resolvable area, we found quantum gravity corrections that are qualitatively consistent with results obtained by other methods. The size of the minimal area is constrained by semiclassical black hole physics, particularly by the entropy content of Hawking radiation. The derivation method is also applied to finding the Unruh temperature associated with causal diamonds and establishing a new relation between this temperature and the entropy of the causal diamond's horizon.
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
Mathematics
Vadim Bereznyuk
Summary: Given a free product of groups G = *j is an element of JAj and a natural number n, what is the minimal possible commutator length of an element gn is an element of G not conjugate to elements of the free factors? We provide a comprehensive answer to this question.
JOURNAL OF ALGEBRA
(2023)
Article
Physics, Multidisciplinary
Zi-Long Zhao, Qi-Kang Ran, Hassan Hassanabadi, Yi Yang, Hao Chen, Zheng-Wen Long
Summary: This paper proposes a new high-order generalized uncertainty principle to provide a phenomenological explanation for the existence of the minimum observable length, deduce the allowable maximum observable momentum, and discuss the functional analysis of position operator and maximum localization states.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics, Applied
Ranadip Gangopadhyay, Ashok Kumar, Hemangi Madhusudan Shah, Bankteshwar Tiwari
Summary: This paper investigates three-dimensional upper half space H-3 equipped with various Kropina metrics obtained by deforming the hyperbolic metric of H-3 through 1-forms. A partial differential equation characterizing minimal surfaces immersed in it is obtained. It is proved that such minimal surfaces can only be obtained when the hyperbolic metric is deformed along the x(3) direction. The classification of such minimal surfaces is provided, and it is shown that the flag curvature of these surfaces is always non-positive. The geodesics of this surface are also obtained, indicating that these surfaces do not have forward conjugate points and are not forward complete.
RESULTS IN MATHEMATICS
(2022)
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
Michele Arzano, Andrea Bevilacqua, Jerzy Kowalski-Glikman, Giacomo Rosati, Josua Unger
Summary: In this work, a construction of kappa-deformed complex scalar field theory is presented to investigate the impact of deformation on discrete symmetries and CPT invariance. The study reveals that particles and antiparticles are characterized by different mass-shell constraints, leading to a subtle departure from CPT invariance. The remaining part of the work focuses on the detailed description of the action of deformed Poincare and discrete symmetries on the complex field.
Article
Mathematics
Matus Dirbak, L'ubomir Snoha, Vladimir Spitalsky
Summary: This article introduces the concept of minimal spaces and their product-minimality, as well as the definition of homeo-product-minimal spaces. It proves that many classical examples of minimal spaces are homeo-product-minimal, and provides examples where the product of two minimal spaces is not minimal.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Physics, Multidisciplinary
A. R. Kuzmak, V. M. Tkachuk
Article
Physics, Mathematical
M. I. Samar, V. M. Tkachuk
JOURNAL OF MATHEMATICAL PHYSICS
(2020)
Article
Astronomy & Astrophysics
H. P. Laba, V. M. Tkachuk
MODERN PHYSICS LETTERS A
(2020)
Article
Physics, Condensed Matter
A. R. Kuzmak, V. M. Tkachuk
CONDENSED MATTER PHYSICS
(2020)
Article
Physics, Multidisciplinary
H. P. Laba, V. M. Tkachuk
Summary: The paper discusses the continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra, leading to the minimal length. The flow probability density is calculated explicitly for plane wave and superposition of two plane waves, and applied to tunneling problem through potential barrier in a space with deformed algebra.
Article
Physics, Multidisciplinary
Kh P. Gnatenko, V. M. Tkachuk
Summary: Graph states generated by Ising Hamiltonian operators were studied to analyze the geometric measure of entanglement between a spin and other spins in the graph state. Using IBM Q Valencia, the quantum computations were in good agreement with theoretical results, indicating a relationship between the geometric measure of entanglement and the degree of the corresponding spin vertex in the graph.
Article
Physics, Multidisciplinary
Kh P. Gnatenko, H. P. Laba, V. M. Tkachuk
Summary: The study reveals that the time dependence of the mean value of a physical quantity is related to the transition energies of a quantum system. A method for detecting energy levels of physical systems on a quantum computer by evolution of a physical quantity is proposed and verified on IBM's quantum computers.
Article
Physics, Multidisciplinary
Kh P. Gnatenko, H. P. Laba, V. M. Tkachuk
Summary: This paper proposes a method for detecting energy levels of arbitrary spin systems on a quantum computer and successfully applies it to different spin systems. The method is efficient, reliable, and shows potential for achieving quantum supremacy.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Physics, Multidisciplinary
M. Samar, V. M. Tkachuk
Summary: In this paper, we define the delta '(x) potential as a linear kernel of the potential energy operator in momentum representation in the general case of deformed Heisenberg algebra leading to the minimal length. We find the exact energy level and corresponding eigenfunction for the delta '(x) and delta(x) - delta '(x) potentials in the deformed space with an arbitrary deformation function. The energy spectrum for different partial cases of deformation function is analyzed.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Kh P. Gnatenko, H. P. Laba, V. M. Tkachuk
Summary: The geometric properties of evolutionary graph states of spin systems generated by the Ising Hamiltonian operator were examined, showing their relationship with energy fluctuations. It was found that the geometric characteristics of the graph states depend on properties of the corresponding graphs, specifically relating to the total number of edges, triangles, and squares in the graphs.
Article
Astronomy & Astrophysics
Kh. P. Gnatenko, V. M. Tkachuk
Summary: This paper examines the implementation of the weak equivalence principle in quantized spaces described by different types of deformed algebras. It is found that the deformation of commutation relations leads to mass-dependent particle motion and violation of the weak equivalence principle. The conclusion is that by considering the parameters of the deformed algebras to be determined by particle masses, this principle can be recovered in quantized spaces.
FRONTIERS IN ASTRONOMY AND SPACE SCIENCES
(2022)
Article
Physics, Multidisciplinary
Kh. P. Gnatenko, V. M. Tkachuk
Summary: Spin-1 tunneling and energy level splitting are explicitly observed on IBM's quantum computer, ibmq-bogota. The spin-1 is realized using two spins-1/2. By studying the time dependence of the mean value of z-component of spin-1 on the quantum device, oscillations of spin-1 between opposite directions in the result of tunneling are detected. The energy level splitting is quantified by observing the eigenvalues of the Hamiltonian describing the spin tunneling on IBM's quantum computer.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
Kh. P. Gnatenko, V. M. Tkachuk
Summary: This paper reviews the results of recovering the weak equivalence principle in a space with deformed commutation relations for operators of coordinates and momenta. Different types of deformed algebras leading to space quantization are considered, including noncommutative algebra of a canonical type, algebra of the Lie type, the Snyder algebra, the Kempf algebra, and nonlinear deformed algebra with an arbitrary function of deformation depending on momenta. The motion of particles and composite systems in a gravitational field is examined, and the implementation of the weak equivalence principle is studied. It is concluded that the Eotvos parameter is not equal to zero even when the gravitational mass is equal to the inertial mass. The principle can be preserved in a quantized space by considering parameters of deformed algebras to be dependent on mass. It is also shown that the dependencies of parameters of deformed algebras on mass lead to preserving the properties of kinetic energy in quantized spaces and solving the problem of the significant effect of space quantization on the motion of macroscopic bodies (the soccer-ball problem).
JOURNAL OF PHYSICAL STUDIES
(2023)
Proceedings Paper
Quantum Science & Technology
Kh P. Gnatenko, H. P. Laba, V. M. Tkachuk
Summary: By studying the evolution of the mean value of a physical quantity, the energy levels and degeneracy of quantum systems can be determined, even in complex spin systems. This approach has been successfully tested on IBM's quantum computers, offering a potential path to achieving quantum supremacy in solving challenging quantum problems.
2021 IEEE INTERNATIONAL CONFERENCE ON QUANTUM COMPUTING AND ENGINEERING (QCE 2021) / QUANTUM WEEK 2021
(2021)
Article
Physics, Multidisciplinary
A. R. Kuzmak, V. M. Tkachuk
Summary: In this study, we investigate the entanglement between a certain qubit and the remaining system in rank-2 mixed states prepared on a quantum computer. The proposed protocol is based on the relation between geometric measure of entanglement and qubit correlations, with special consideration given to a two-qubit rank-2 mixed state. We measure the geometric measure of entanglement in 2- and 4-qubit mixed quantum states on the ibmq-melbourne quantum computer, particularly focusing on Schrodinger cat states, and study the dependence of entanglement value on the parameter defining the weight of pure states. Finally, we determine the concurrence of a 2-qubit mixed state.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)