Exploring a Graph Complement in Quadratic Congruence

In this work, we investigate essential definitions, defining G as a simple graph with vertices in Zn and subgraphs Γu and Γq as unit residue and quadratic residue graphs modulo n, respectively. The investigation extends to the degree of G, Γu, and Γq, illuminating the properties of these subgraphs in the context of quadratic congruences

Quantum correlations beyond entanglement between two moving atoms interacting with a coherent cavity

Studying the ability of atom-photon interactions, especially in two two-level atomic systems, to generate quantum information resources has recently become an important research topic in quantum information science. Therefore, this paper explores the ability of two moving atoms coupling with a coherent field through a two-photon transition to generate atomic quantum correlations by using local quantum uncertainty (LQU), local quantum Fisher information (LQFI) as well as logarithmic negativity (LN). Schrödinger equation is used to obtain the time evolution of the atom-cavity-atom interactions with an initial coherent cavity state and an initial atomic uncorrelated pure state. The generation of atomic LQU, LQFI, and LN correlations are exactly examined under the unitary interaction parameter effects, including the atom-cavity coupling strengths, the cavity field half-wave number, and the initial coherent state intensity. The atom-cavity-atom interaction parameters lead to notable changes in the amplitudes, speed, and regularity of the LQU, LQFI, and LN dynamics, which can be enhanced by increasing the initial coherent intensity. The cavity field half-wave number leads to generating atomic quantum correlations with regular oscillatory behavior. The sudden death-birth phenomenon of the logarithmic negativity depends on the atom-cavity-atom interaction and the atomic location parameter

Local quantum Fisher information and Jensen-Shannon coherence dynamics of two-spin-qubits XYZ-Heisenberg state

In this study, we investigate the impact of the XYZ-DM-Heisenberg model on quantum resources, including local quantum Fisher information, concurrence, and Jensen-Shannon coherence, in the presence of intrinsic decoherence. By exploring various spin-exchange interactions, with a focus on the role of the y-DM interaction, we reveal how these interactions affect quantum correlations and coherence dynamics. We find that the system transitions from separability to the generation of quantum properties when spin interactions are introduced. The specific parameter choices significantly influence the dynamic map of quantum functions. Notably, strong y-DM interaction, in combination with equal spin interaction, leads to pronounced fluctuations, while weak DM interaction results in sudden death and rebirth in the x direction. Additionally, ferro- and anti-ferromagnetic regimes impact the quantum functions differently. In the presence of intrinsic decoherence, fluctuations decrease, and coherence remains robust compared to the local quantum Fisher information and entanglement, reducing loss

A Novel Framework of <i>q</i>-Rung Orthopair Fuzzy Sets in Field

In this manuscript, we proposed a novel framework of the q-rung orthopair fuzzy subfield (q-ROFSF) and illustrate that every Pythagorean fuzzy subfield is a q-rung orthopair fuzzy subfield of a certain field. We extend this theory and discuss its diverse basic algebraic characteristics in detail. Furthermore, we prove some fundamental results and establish helpful examples related to them. Moreover, we present the homomorphic images and pre-images of the q-rung orthopair fuzzy subfield (q-ROFSF) under field homomorphism. We provide a novel ideology of a non-standard fuzzy subfield in the extension of the q-rung orthopair fuzzy subfield (q-ROFSF)

Erratum:Molecular-scale thermoelectricity: as simple as 'ABC' (Nanoscale Adv. (2020) 2 (5329–5334) DOI: 10.1039/D0NA00772B)

The authors regret that the name of one of the authors (Troy L. R. Bennett) was shown incorrectly in the original article. The corrected author list is as shown above. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers

Multi-component self-assembled molecular-electronic films:towards new high-performance thermoelectric systems

The thermoelectric properties of parallel arrays of organic molecules on a surface offer the potential for large-area, flexible, solution processed, energy harvesting thin-films, whose room-temperature transport properties are controlled by quantum interference (QI). Recently, it has been demonstrated that constructive QI (CQI) can be translated from single molecules to self-assembled monolayers (SAMs), boosting both electrical conductivities and Seebeck coefficients. However, these CQI-enhanced systems are limited by rigid coupling of the component molecules to metallic electrodes, preventing the introduction of additional layers which would be advantageous for their further development. These rigid couplings also limit our ability to suppress the transport of phonons through these systems, which could act to boost their thermoelectric output, without comprising on their impressive electronic features. Here, through a combined experimental and theoretical study, we show that cross-plane thermoelectricity in SAMs can be enhanced by incorporating extra molecular layers. We utilize a bottom-up approach to assemble multi-component thin-films that combine a rigid, highly conductive ‘sticky’-linker, formed from alkynyl-functionalised anthracenes, and a ‘slippery’-linker consisting of a functionalized metalloporphyrin. Starting from an anthracene-based SAM, we demonstrate that subsequent addition of either a porphyrin layer or a graphene layer increases the Seebeck coefficient, and addition of both porphyrin and graphene leads to a further boost in their Seebeck coefficients. This demonstration of Seebeck-enhanced multi-component SAMs is the first of its kind and presents a new strategy towards the design of thin-film thermoelectric materials