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Keywords = semi-quantum approach

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15 pages, 3818 KB  
Article
Application of Physical and Quantum-Chemical Characteristics of Epoxy-Containing Diluents for Wear-Resistant Epoxy Compositions
by Andrii Kulikov, Kostyantyn Sukhyy, Oleksandr Yeromin, Marcel Fedak, Olena Prokopenko, Iryna Sukha, Oleksii Poloz, Oleh Mikats, Tomas Hrebik, Olha Kulikova and Martin Lopusniak
Materials 2025, 18(24), 5643; https://doi.org/10.3390/ma18245643 - 16 Dec 2025
Viewed by 469
Abstract
Low-viscosity epoxy-containing diluents are used to reduce the initial viscosity of highly filled, wear-resistant epoxy systems and to improve filler wetting and dispersion. This study determined physical parameters by an atomic-increment approach and electronic descriptors using the Parametric Method 3 (PM3) semi-empirical method. [...] Read more.
Low-viscosity epoxy-containing diluents are used to reduce the initial viscosity of highly filled, wear-resistant epoxy systems and to improve filler wetting and dispersion. This study determined physical parameters by an atomic-increment approach and electronic descriptors using the Parametric Method 3 (PM3) semi-empirical method. Clear relationships were established between the effective molar cohesion energy and the solubility parameter with van der Waals volume. Linear dependencies were also obtained between the diluent surface tension and spreading coefficients on model high-hardness fillers, including silicon carbide, boron carbide, and normal corundum. The activity of epoxy diluents depends on the lowest unoccupied molecular orbital energy. These diluents influence processing and the final physical and mechanical properties of composites, making their selection critical for strength, hardness, and wear resistance. Computational analysis enables prediction of diluent behavior, reducing experimental time and cost. Integrating physical and quantum-chemical data into epoxy diluent design accelerates the search for optimal components and improves production of durable, high-performance epoxy composites. Full article
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15 pages, 1044 KB  
Article
Quantum Private Array Content Comparison Based on Multi-Qubit Swap Test
by Min Hou, Yue Wu and Shibin Zhang
Mathematics 2025, 13(23), 3827; https://doi.org/10.3390/math13233827 - 28 Nov 2025
Viewed by 405
Abstract
Current private comparison schemes primarily focus on comparing single secret integers using quantum technologies, while the area of private array content comparison remains relatively unexplored. To bridge this gap, we introduce a quantum private array content comparison (QPACC) scheme based on multi-qubit swap [...] Read more.
Current private comparison schemes primarily focus on comparing single secret integers using quantum technologies, while the area of private array content comparison remains relatively unexplored. To bridge this gap, we introduce a quantum private array content comparison (QPACC) scheme based on multi-qubit swap test. This scheme integrates rotation operation, quantum homomorphic encryption (QHE), and multi-qubit swap test to facilitate the equality comparison of array contents while ensuring their confidentiality. In our approach, participants encode their array elements into the phases of quantum states using rotation operations, which are then encrypted via QHE. These encrypted quantum states are sent to a semi-honest third party (TP) who decrypts the encoded quantum states and computes the modulus squared sum of the inner products of these decoded quantum states using the multi-qubit swap test, thereby determining the equality relationship of the array contents. To verify the feasibility of the proposed scheme, we conduct a case simulation using IBM Qiskit. Security analysis indicates that the proposed scheme is resistant to quantum attacks (including intercept-resend, entangle-measure, and quantum Trojan horse attacks) from outsider eavesdroppers and attempts by curious participants. Full article
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16 pages, 334 KB  
Article
An Efficient and Secure Semi-Quantum Secret Sharing Scheme Based on W State Sharing of Specific Bits
by Kai Xing, Rongbo Lu, Sihai Liu and Lu Lan
Entropy 2025, 27(11), 1107; https://doi.org/10.3390/e27111107 - 26 Oct 2025
Viewed by 1062
Abstract
This paper presents a semi-quantum secret sharing (SQSS) protocol based on three-particle W states, designed for efficient and secure secret sharing in quantum-resource-constrained scenarios. In the protocol, a fully quantum-capable sender encodes binary secrets using W, while receivers with limited quantum capabilities [...] Read more.
This paper presents a semi-quantum secret sharing (SQSS) protocol based on three-particle W states, designed for efficient and secure secret sharing in quantum-resource-constrained scenarios. In the protocol, a fully quantum-capable sender encodes binary secrets using W, while receivers with limited quantum capabilities reconstruct the secret through collaborative Z basis measurements and classical communication, ensuring no single participant can obtain the complete information independently. The protocol employs a four-state decoy photon technique ({|0,|1,|+,|}) and position randomization, combined with photon number splitting (PNS) and wavelength filtering (WF) technologies, to resist intercept–resend, entanglement–measurement, and double controlled-NOT(CNOT) attacks. Theoretical analysis shows that the detection probability of intercept–resend attacks increases exponentially with the number of decoy photons (approaching 1). For entanglement–measurement attacks, any illegal operation by an attacker introduces detectable quantum state disturbances. Double CNOT attacks are rendered ineffective by the untraceability of particle positions and mixed-basis strategies. Leveraging the robust entanglement of W states, the protocol proves that the mutual information between secret bits and single-participant measurement results is strictly zero, ensuring lossless reconstruction only through authorized collaboration. Full article
(This article belongs to the Special Issue Quantum Information Security)
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24 pages, 424 KB  
Article
Canonical Quantization of Metric Tensor for General Relativity in Pseudo-Riemannian Geometry
by Abdel Nasser Tawfik, Salah G. Elgendi, Sameh Shenawy and Mahmoud Hanafy
Physics 2025, 7(4), 52; https://doi.org/10.3390/physics7040052 - 20 Oct 2025
Viewed by 2373
Abstract
By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a [...] Read more.
By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a quantized Hamilton structure through the kinematics of a free-falling quantum particle with a positive mass, along with the introduction of the relativistic generalized uncertainty principle (RGUP) that generalizes quantum mechanics by integrating gravity. This transformation ensures the preservation of the positive one-homogeneity of both Finsler and Hamilton structures, while the RGUP dictates modifications in the noncommutative relations due to integrating consequences of relativistic gravitational fields in quantum mechanics. The anisotropic conformal transformation of the resulting metric tensor and its inverse in higher-dimensional spaces has been determined, particularly highlighting their translations to the four-dimensional fundamental metric tensor and its inverse. It is essential to recognize the complexity involved in computing the fundamental inverse metric tensor during a conformal transformation, as it is influenced by variables like spatial coordinates and directional orientation, making it a challenging task, especially in tensorial terms. We conclude that the derivations in this study are not limited to the structure in tangent and cotangent bundles, which might include both spacetime and momentum space, but are also applicable to higher-dimensional contexts. The theoretical framework of quantization of general relativity based on quantizing its metric tensor is primarily grounded in the four-dimensional metric tensor and its inverse in pseudo-Riemannian geometry. Full article
(This article belongs to the Special Issue Beyond the Standard Models of Physics and Cosmology: 2nd Edition)
14 pages, 1127 KB  
Article
A Quantitative Structure–Activity Relationship Study of the Anabolic Activity of Ecdysteroids
by Durbek Usmanov, Ugiloy Yusupova, Vladimir Syrov, Gerardo M. Casanola-Martin and Bakhtiyor Rasulev
Computation 2025, 13(8), 195; https://doi.org/10.3390/computation13080195 - 10 Aug 2025
Cited by 1 | Viewed by 2010
Abstract
Phytoecdysteroids represent a class of naturally occurring substances known for their diverse biological functions, particularly their strong ability to stimulate protein anabolism. In this study, a computational machine learning-driven quantitative structure–activity relationship (QSAR) approach was applied to analyze the anabolic potential of 23 [...] Read more.
Phytoecdysteroids represent a class of naturally occurring substances known for their diverse biological functions, particularly their strong ability to stimulate protein anabolism. In this study, a computational machine learning-driven quantitative structure–activity relationship (QSAR) approach was applied to analyze the anabolic potential of 23 ecdysteroid compounds. The ML-based QSAR modeling was conducted using a combined approach that integrates Genetic Algorithm-based feature selection with Multiple Linear Regression Analysis (GA-MLRA). Additionally, structure optimization by semi-empirical quantum-chemical method was employed to determine the most stable molecular conformations and to calculate an additional set of structural and electronic descriptors. The most effective QSAR models for describing the anabolic activity of the investigated ecdysteroids were developed and validated. The proposed best model demonstrates both strong statistical relevance and high predictive performance. The predictive performance of the resulting models was confirmed by an external test set based on R2test values, which were within the range of 0.89 to 0.97. Full article
(This article belongs to the Special Issue Feature Papers in Computational Chemistry)
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18 pages, 1199 KB  
Article
Adaptive, Privacy-Enhanced Real-Time Fraud Detection in Banking Networks Through Federated Learning and VAE-QLSTM Fusion
by Hanae Abbassi, Saida El Mendili and Youssef Gahi
Big Data Cogn. Comput. 2025, 9(7), 185; https://doi.org/10.3390/bdcc9070185 - 9 Jul 2025
Cited by 5 | Viewed by 3858
Abstract
Increased digital banking operations have brought about a surge in suspicious activities, necessitating heightened real-time fraud detection systems. Conversely, traditional static approaches encounter challenges in maintaining privacy while adapting to new fraudulent trends. In this paper, we provide a unique approach to tackling [...] Read more.
Increased digital banking operations have brought about a surge in suspicious activities, necessitating heightened real-time fraud detection systems. Conversely, traditional static approaches encounter challenges in maintaining privacy while adapting to new fraudulent trends. In this paper, we provide a unique approach to tackling those challenges by integrating VAE-QLSTM with Federated Learning (FL) in a semi-decentralized architecture, maintaining privacy alongside adapting to emerging malicious behaviors. The suggested architecture builds on the adeptness of VAE-QLSTM to capture meaningful representations of transactions, serving in abnormality detection. On the other hand, QLSTM combines quantum computational capability with temporal sequence modeling, seeking to give a rapid and scalable method for real-time malignancy detection. The designed approach was set up through TensorFlow Federated on two real-world datasets—notably IEEE-CIS and European cardholders—outperforming current strategies in terms of accuracy and sensitivity, achieving 94.5% and 91.3%, respectively. This proves the potential of merging VAE-QLSTM with FL to address fraud detection difficulties, ensuring privacy and scalability in advanced banking networks. Full article
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14 pages, 580 KB  
Article
Associative Hypercomplex Algebras Arise over a Basic Set of Subgeometric One-Dimensional Elements
by Alexander P. Yefremov
Mathematics 2025, 13(13), 2105; https://doi.org/10.3390/math13132105 - 26 Jun 2025
Cited by 1 | Viewed by 964
Abstract
An abstract set of one-dimensional (spinor-type) elements randomly oriented on a plane is introduced as a basic subgeometric object. Endowing the set with the binary operations of multiplication and invertible addition sequentially yields a specific semi-group (for which an original Cayley table is [...] Read more.
An abstract set of one-dimensional (spinor-type) elements randomly oriented on a plane is introduced as a basic subgeometric object. Endowing the set with the binary operations of multiplication and invertible addition sequentially yields a specific semi-group (for which an original Cayley table is given) and a generic algebraic system which is shown to generate, apart from algebras of real and complex numbers, the associative hypercomplex algebras of dual numbers, split-complex numbers, and quaternions. The units of all these algebras turn out to be composed of basic 1D elements, thus ensuring the automatic fulfillment of multiplication rules (once postulated). From the standpoint of a three-dimensional space defined by a vector quaternion triad, the condition of a standard (unit) length of 1D basis elements is considered; it is shown that fulfillment of this condition provides an equation mathematically equivalent to the main equation of quantum mechanics. The similarities and differences of the proposed logical scheme with other approaches that involve abstract subgeometric objects are discussed. Full article
(This article belongs to the Section E4: Mathematical Physics)
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14 pages, 254 KB  
Article
Multiparty Quantum Private Comparison Using Rotation Operations
by Min Hou and Yue Wu
Axioms 2025, 14(4), 274; https://doi.org/10.3390/axioms14040274 - 3 Apr 2025
Cited by 2 | Viewed by 724
Abstract
This paper presents a multiparty quantum private comparison (MQPC) protocol that facilitates multiple users to compare the equality of their private inputs while preserving the confidentiality of each input through the principles of quantum mechanics. In our approach, users initially convert their secret [...] Read more.
This paper presents a multiparty quantum private comparison (MQPC) protocol that facilitates multiple users to compare the equality of their private inputs while preserving the confidentiality of each input through the principles of quantum mechanics. In our approach, users initially convert their secret integers into binary representations, which are then encoded into single photons that act as carriers of the information. These encoded single-photon states undergo encryption via rotational operations, effectively obscuring the original inputs before transmission to a semi-honest third party (TP). The TP decrypts the quantum states and conducts Z-basis measurements to derive the comparison results. To enhance security, the protocol incorporates decoy photons, enabling participants to detect potential eavesdropping on the quantum channel. Importantly, even if the TP or other participants attempt to glean insights into each other’s inputs, the encryption via rotational operations ensures that private information remains inaccessible. This protocol demonstrates significant advancements in practicality compared to existing MQPC frameworks that rely on complex quantum technologies, such as entanglement swapping and multi-particle entanglement. By leveraging the simplicity of single photons, rotation operations, and Z-basis measurements, our protocol is more accessible for implementation. Full article
(This article belongs to the Section Mathematical Physics)
38 pages, 9980 KB  
Review
Metasurfaces with Multipolar Resonances and Enhanced Light–Matter Interaction
by Evan Modak Arup, Li Liu, Haben Mekonnen, Dominic Bosomtwi and Viktoriia E. Babicheva
Nanomaterials 2025, 15(7), 477; https://doi.org/10.3390/nano15070477 - 21 Mar 2025
Cited by 8 | Viewed by 5612
Abstract
Metasurfaces, composed of engineered nanoantennas, enable unprecedented control over electromagnetic waves by leveraging multipolar resonances to tailor light–matter interactions. This review explores key physical mechanisms that govern their optical properties, including the role of multipolar resonances in shaping metasurface responses, the emergence of [...] Read more.
Metasurfaces, composed of engineered nanoantennas, enable unprecedented control over electromagnetic waves by leveraging multipolar resonances to tailor light–matter interactions. This review explores key physical mechanisms that govern their optical properties, including the role of multipolar resonances in shaping metasurface responses, the emergence of bound states in the continuum (BICs) that support high-quality factor modes, and the Purcell effect, which enhances spontaneous emission rates at the nanoscale. These effects collectively underpin the design of advanced photonic devices with tailored spectral, angular, and polarization-dependent properties. This review discusses recent advances in metasurfaces and applications based on them, highlighting research that employs full-wave numerical simulations, analytical and semi-analytic techniques, multipolar decomposition, nanofabrication, and experimental characterization to explore the interplay of multipolar resonances, bound and quasi-bound states, and enhanced light–matter interactions. A particular focus is given to metasurface-enhanced photodetectors, where structured nanoantennas improve light absorption, spectral selectivity, and quantum efficiency. By integrating metasurfaces with conventional photodetector architectures, it is possible to enhance responsivity, engineer photocarrier generation rates, and even enable functionalities such as polarization-sensitive detection. The interplay between multipolar resonances, BICs, and emission control mechanisms provides a unified framework for designing next-generation optoelectronic devices. This review consolidates recent progress in these areas, emphasizing the potential of metasurface-based approaches for high-performance sensing, imaging, and energy-harvesting applications. Full article
(This article belongs to the Section Nanophotonics Materials and Devices)
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13 pages, 1405 KB  
Article
Quantum Private Set Intersection Scheme Based on Bell States
by Min Hou, Yue Wu and Shibin Zhang
Axioms 2025, 14(2), 120; https://doi.org/10.3390/axioms14020120 - 7 Feb 2025
Cited by 5 | Viewed by 1293
Abstract
In this paper, we introduce a quantum private set intersection (QPSI) scheme that leverages Bell states as quantum information carriers. Our approach involves encoding private sets into Bell states using unitary operations, enabling the computation of the intersection between two private sets from [...] Read more.
In this paper, we introduce a quantum private set intersection (QPSI) scheme that leverages Bell states as quantum information carriers. Our approach involves encoding private sets into Bell states using unitary operations, enabling the computation of the intersection between two private sets from different users while keeping their individual sets undisclosed to anyone except for the intersection result. In our scheme, a semi-honest third party (TP) distributes the first and second qubits of the Bell states to the two users. Each user encodes their private sets by applying unitary operations on the received qubits according to predefined encoding rules. The modified sequence is encrypted and then sent back to TP, who can compute the set intersection without learning any information about the users’ private inputs. The simulation outcomes on the IBM quantum platform substantiate the viability of our scheme. We analyze the security and privacy aspects of the sets, showing that both external attacks and internal threats do not compromise the security of the private inputs. Furthermore, our scheme exhibits better practicality by utilizing easily implementable Bell states and unitary operations, rather than relying on multiple encoded states for set intersection calculations. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Mechanics and Mathematical Physics)
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17 pages, 1341 KB  
Article
Two-Party Quantum Private Comparison Protocol for Direct Secret Comparison
by Min Hou and Yue Wu
Mathematics 2025, 13(2), 326; https://doi.org/10.3390/math13020326 - 20 Jan 2025
Cited by 4 | Viewed by 1550
Abstract
In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their [...] Read more.
In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their private information, other than the final comparison results. Our protocol encodes participants’ secret integers directly into the amplitudes of single-photon states and introduces a novel method for secret-to-secret comparison rather than the traditional bit-to-bit comparison, resulting in improved scalability. To ensure security, the encoded single-photon states are concealed using rotation operations. The comparison results are derived through the implementation of the swap test. A simulation on the IBM Quantum Platform demonstrates the protocol’s feasibility, and a security analysis confirms its robustness against potential eavesdropping and participant attacks. Compared with existing QPC protocols that employ bit-to-bit comparison methods, our approach offers improved practicality and scalability. Specifically, it integrates single-photon states, rotation operations, and the swap test as key components for direct secret comparison, facilitating easier implementation with quantum technology. Full article
(This article belongs to the Section E4: Mathematical Physics)
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21 pages, 501 KB  
Article
Towards Ginzburg–Landau Bogomolny Approach and a Perturbative Description of Superconducting Structures
by Łukasz T. Stȩpień and Krzysztof Pomorski
Quantum Rep. 2025, 7(1), 4; https://doi.org/10.3390/quantum7010004 - 19 Jan 2025
Viewed by 1591
Abstract
The Bogomolny approach to the Ginzburg–Landau equations in the context of strong and semi-strong necessary conditions is formulated for various superconducting structures in a quasi-one-dimensional description, considering both flat and curved geometries. This formulation is justified by a perturbative approach to the Ginzburg–Landau [...] Read more.
The Bogomolny approach to the Ginzburg–Landau equations in the context of strong and semi-strong necessary conditions is formulated for various superconducting structures in a quasi-one-dimensional description, considering both flat and curved geometries. This formulation is justified by a perturbative approach to the Ginzburg–Landau theory applied to a superconducting structure that is polarized by an electric charge moving across two neighboring quantum dots. The situation considered involves an interface between a Josephson junction and a semiconductor quantum dot system in a one-dimensional setting. Full article
(This article belongs to the Special Issue Semiconductor and Superconductor Quantum Devices)
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19 pages, 3781 KB  
Article
Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots
by James R. Hamilton, Raphael D. Levine and Francoise Remacle
Nanomaterials 2024, 14(24), 2056; https://doi.org/10.3390/nano14242056 - 23 Dec 2024
Cited by 3 | Viewed by 1291
Abstract
Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent [...] Read more.
Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients. There are possible applications to the dynamics of systems of coupled coherent two-state systems, such as qubits, pumped by optical excitation and other addressing inputs. Thereby, the interaction of the system with the excitation is bilinear in the coherence between the two states and in the strength of the time-dependent excitation. The total Hamiltonian is a sum of such bilinear terms and of terms linear in the populations. The terms in the Hamiltonian form a basis for Lie algebra, which can be represented as coupled individual two-state systems, each using the population and the coherence between two states. Using the factorization approach of Wei and Norman, we construct a unitary quantum mechanical evolution operator that is a factored contribution of individual two-state systems. By that one can accurately propagate both the wave function and the density matrix with special relevance to quantum computing based on qubit architecture. Explicit examples are derived for the electronic dynamics in coupled semi-conducting nanoparticles that can be used as hardware for quantum technologies. Full article
(This article belongs to the Special Issue Quantum Computing and Nanomaterial Simulations)
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12 pages, 276 KB  
Article
Quantum Private Comparison Based on Four-Particle Cluster State
by Min Hou and Yue Wu
Appl. Sci. 2024, 14(22), 10759; https://doi.org/10.3390/app142210759 - 20 Nov 2024
Cited by 2 | Viewed by 1376
Abstract
A quantum private comparison (QPC) protocol enables two parties to securely compare their private data without disclosing the actual values to one another, utilizing quantum mechanics to maintain confidentiality. Many current QPC protocols mainly concentrate on comparing the equality of private information between [...] Read more.
A quantum private comparison (QPC) protocol enables two parties to securely compare their private data without disclosing the actual values to one another, utilizing quantum mechanics to maintain confidentiality. Many current QPC protocols mainly concentrate on comparing the equality of private information between two users during a single execution, which restricts their scalability. To overcome this limitation, we present an efficient QPC protocol aimed at evaluating the equality of private information between two groups of users in one execution. This is achieved by leveraging the entanglement correlations present in each particle of a four-particle cluster state. In our approach, users encode their private data using bit flip or phase shift operators on the quantum sequence they receive, which is then sent back to a semi-trusted party which then determines whether the secrets of the two groups are equal and communicates the results to the users. By employing this method and facilitating the distributed transmission of the quantum sequence, our protocol achieves a qubit efficiency of 50%. Security analyses reveal that neither external attacks nor insider threats can successfully compromise the confidentiality of private data. Full article
(This article belongs to the Special Issue Quantum Communication and Applications)
13 pages, 812 KB  
Article
Model and Energy Bounds for a Two-Dimensional System of Electrons Localized in Concentric Rings
by Orion Ciftja, Josep Batle, Mahmoud Abdel-Aty, Mohammad Ahmed Hafez and Shawkat Alkhazaleh
Nanomaterials 2024, 14(20), 1615; https://doi.org/10.3390/nano14201615 - 10 Oct 2024
Cited by 4 | Viewed by 1488
Abstract
We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means [...] Read more.
We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means of a standard Coulomb interaction potential. The classical version of this two-dimensional quantum model can be viewed as representing a system of electrons orbiting planar equidistant concentric rings where the kinetic energy may be discarded when one is searching for the lowest possible energy. Within this framework, the lowest possible energy of the system is the one that minimizes the total Coulomb interaction energy. This is the equilibrium energy that is numerically determined with high accuracy by using the simulated annealing method. This process allows us to obtain both the equilibrium energy and position configuration for different system sizes. The adopted semi-classical approach allows us to provide reliable approximations for the quantum ground state energy of the corresponding quantum system. The model considered in this work represents an interesting problem for studies of low-dimensional systems, with echoes that resonate with developments in nanoscience and nanomaterials. Full article
(This article belongs to the Special Issue Fundamental and Applied Aspects of Physics in Low-Dimensional Systems)
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