Search Results (413)

Lindbladian formalism models open quantum systems using a ‘bottom-up’ approach, deriving linear dynamics from system–environment interactions. We present a ‘top-down’ approach starting with phenomenological constraints, focusing on a system’s structure, subsystems’ interactions, and environmental effects and often using a non-equilibrium variational principle designed to enforce strict thermodynamic consistency. However, incorporating the second law’s requirement—that Gibbs states are the sole stable equilibria—necessitates nonlinear dynamics, challenging no-signaling principles in composite systems. We reintroduce ‘local perception operators’ and show that they allow to model signaling-free non-local effects. Using the steepest-entropy-ascent variational principle as an example, we demonstrate the validity of the ‘top-down’ approach for integrating quantum mechanics and thermodynamics in phenomenological models, with potential applications in quantum computing and resource theories. Full article

We review and as well obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to the calculation of both the equilibrium and nonequilibrium Casimir and Casimir–Polder forces. After a brief summary of the properties of the polarization tensor of graphene obtained within the Dirac model in the framework of quantum field theory, we derive the expressions for the longitudinal and transverse dielectric functions. The behavior of these functions at different temperatures is investigated in the regions below and above the threshold. Special attention is paid to the double pole at zero frequency, which is present in the transverse response function of graphene. An application of the response functions of graphene to the calculation of the equilibrium Casimir force between two graphene sheets and the Casimir–Polder forces between an atom (nanoparticle) and a graphene sheet is considered with due attention to the role of a nonzero energy gap, chemical potential and a material substrate underlying the graphene sheet. The same subject is discussed for out-of-thermal-equilibrium Casimir and Casimir–Polder forces. The role of the obtained and presented results for fundamental science and nanotechnology is outlined. Full article

We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order models. Theoretically, we establish the uniqueness, linearity, and invariance of fuzzy statistical limits and prove a Cauchy characterization: fuzzy statistical convergence implies fuzzy statistical Cauchyness, while the converse holds in fuzzy-complete spaces (and in the completion, otherwise). We further develop an inclusion theory linking fuzzy strong Cesàro summability—including weighted means—to fuzzy statistical convergence. Via the discrete Q-operator, all statements transfer verbatim between nabla-left and delta-right GL forms, clarifying the binomial GL↔discrete Riemann–Liouville correspondence. Beyond structure, we propose density-based residual diagnostics for GL discretizations of fractional initial-value problems: when GL residuals are fuzzy statistically negligible, trajectories exhibit Ulam–Hyers-type robustness in the fuzzy topology. We also formulate a fuzzy Korovkin-type approximation principle under GL smoothing: Cesàro control on the test set $\{1,x,x^2\}$ propagates to arbitrary targets, yielding fuzzy statistical convergence for positive-operator sequences. Worked examples and an engineering-style case study (thermal balance with memory and bursty disturbances) illustrate how the diagnostics certify robustness of GL numerical schemes under sparse spikes and imprecise data. Full article

This study presents an exact analytical investigation into the static response of helical single-walled carbon nanotube (SWCNT) beams based on Eringen’s differential nonlocal elasticity theory, which captures nanoscale effects arising from interatomic interactions. A key contribution of this work is the derivation of the governing equations for helical SWCNT beams, based on the nonlocal Euler–Bernoulli theory, followed by their exact analytical solution using the initial value method. To the best of the authors’ knowledge, this represents the first closed-form formulation for such complex nanostructures using this theoretical framework of nonlocal elasticity theory. The analysis considers both cantilevered and clamped–clamped boundary conditions, under various concentrated force and moment loadings applied at the ends and midpoint of the helical beam. Displacements and rotational components are expressed in the Frenet frame, enabling direction-specific evaluation of the deformation behaviour. Parametric studies are conducted to investigate the influence of geometric parameters—such as the winding angle ($\alpha$) and aspect ratio ($R/d$) and the nonlocal parameter ($R/\gamma$). Results show that nonlocal elasticity theory consistently predicts higher displacements and rotations than the classical local theory, revealing its importance for accurate modelling of nanoscale structures. The proposed analytical framework serves as a benchmark reference for the modelling and design of nanoscale helical structures such as nano-springs, actuators, and flexible nanodevices. Full article

This study introduces a novel numerical approach to analyze the axisymmetric bending behavior of functionally graded (FG) graphene platelet (GPL)-reinforced annular sandwich nanoplates featuring a porous core. The nanostructures are exposed to coupled magnetic and hygrothermal environments. The porosity distribution and GPL weight fraction are modeled as nonlinear functions through the thickness, capturing realistic gradation effects. The governing equations are derived using the virtual displacement principle, taking into account the Lorentz force and the interaction with an elastic foundation. To address the size-dependent behavior and thickness-stretching effects, the model employs the nonlocal strain gradient theory (NSGT) integrated with a modified version of Shimpi’s quasi-3D higher-order shear deformation theory (Q3HSDT). The differential quadrature method (DQM) is applied to obtain numerical solutions for the displacement and stress fields. A detailed parametric study is conducted to investigate the influence of various physical and geometric parameters, including the nonlocal parameter, strain gradient length scale, magnetic field strength, thermal effects, foundation stiffness, core thickness, and radius-to-thickness ratio. The findings support the development of smart, lightweight, and thermally adaptive nano-electromechanical systems (NEMS) and provide valuable insights into the mechanical performance of FG-GPL sandwich nanoplates. These findings have potential applications in transducers, nanosensors, and stealth technologies designed for ultrasound and radar detection. Full article

This paper undertakes a rigorous analytical exposition of the approximate controllability of a novel class of Sobolev-type stochastic impulsive differential inclusions, incorporating the Atangana–Baleanu fractional derivative in the Caputo configuration under the influence of Wiener process and Poissonian discontinuities. The system’s analytical landscape is further enriched by the incorporation of Clarke sub-differentials, facilitating the treatment of nonsmooth, nonconvex, and multivalued dynamics. The inherent complexity arising from the confluence of fractional memory, stochastic perturbations, and impulsive phenomena necessitates the deployment of a sophisticated apparatus from variational analysis, measurable selection theory, and multivalued fixed point frameworks within infinite-dimensional Banach spaces. This study delineates rigorous sufficient conditions, ensuring controllability under such hybrid influences, thereby generalizing classical paradigms to encompass nonlocal and discontinuous dynamical regimes. A precisely articulated exemplar is included to validate the theoretical constructs and demonstrate the operational efficacy of the proposed analytical methodology. Full article

In recent years, quantum network technology has been rapidly developing, with new theories, solutions, and protocols constantly emerging. The breakthrough experiments and achievements are impressive, such as the construction and operation of ultra-long-distance and multi-user quantum key distribution (QKD) networks, the proposal, verification, and experimental demonstration of new network nonlocality characteristics, etc. The results of recent research on QKD and network nonlocality are summarized and analyzed in this paper, including CV-MDI-QKD (continuous-variable measurement-device-independent QKD), TF-QKD (twin-field QKD), AMDI-QKD (asynchronous MDI-QKD), the generalization, sharing, and certification of network nonlocality, as well as the main achievements and related research tools of full network nonlocality and genuine network nonlocality, aiming to identify the current status and future development paths of the QKD and network nonlocality. Full article

This paper discusses the asymptotic controllability of fractional-order Sobolev-type perturbed stochastic control systems with Brownian motion and nonlocal fractional-order Sobolev stochastic conditions. A new set of sufficient conditions is established using the theory of semigroups together with iterative methods, with some advancements on the Brownian motion properties. Our main results are obtained assuming that the associated linear system is controllable. A most essential example is brought to illustrate the analysis obtained. Full article

In the nonlocal Almgren problem, the goal is to investigate the convexity of a minimizer under a mass constraint via a nonlocal free energy generated with a nonlocal perimeter and convex potential. In this paper, the main result is a quantitative stability theorem for the nonlocal free energy under a symmetry assumption on the potential. In addition, several results that involve uniqueness, non-existence, and moduli estimates from the theory of crystals are also proven in the nonlocal context. Full article

Elastic solutions of a differential system of vibrational responses of a bidirectional porous functionally graded plate (BPFG) are described by employing high-order normal and shear deformation theory, in the present study. Natural frequency values are computed for the plates with simply supported boundary conditions and taking into consideration the thickness stretching effect. Grading of the effective material property for the BPFG plate is defined according to a power-law distribution. Navier’s approach is applied to determine the governing differential equations solution of the studied model derived by Hamilton’s principle. To confirm the reliability of the solution and the model accuracy, a comparison study with various studies that are presented in the literature is carried out. Numerical illustrations are presented to discuss the influences of the plate geometry, the porosity, the volume fraction distribution, and the nonlocality on the vibration behaviors of the model. The dynamic responses of unidirectional and bidirectional porous functionally graded nanoplates are analyzed in detail, employing two parametric numerical examples. Numerical results show the sensitivity of frequencies to the studied parametric factors and their dependence on porosity and nonlocality coefficients. Frequencies of BPFG with uneven/even distribution porosity decrease when increasing the transverse and axial power-law indexes ($P\ne 0$), and the same effect appears when increasing the nonlocal parameter. Full article

The aim of our work is to theoretically model the conversion of C6 and C5 carbohydrates derived from lignocellulosic biomass waste into C1–C5 carboxylic acids such as levulinic, oxalic, lactic, and formic acids. Understanding the mechanism of these processes will provide the necessary knowledge to better plan the structure of zeolite. In this article, we focus on the theoretical modeling of two carbohydrates, representing C5 and C6, namely xylose and fructose, into levulinic acid (LE) and formic acid (FA). The modeling was carried out with the participation of Na-BEA zeolite in a hierarchical form, due to the large size of the carbohydrates. The density functional theory (DFT) method (StoBe program) was used, employing non-local generalized gradient-corrected functions according to Perdew, Burke, and Ernzerhof (RPBE) to account for electron exchange and correlation and using the nudged elastic band (NEB) method to determine the structure and energy of the transition state. The modeling was performed using cluster representations of hierarchical Na-Al₂Si₁₂O₃₉H₂₃ and ideal Al₂Si₂₂O₆₄H₃₄ beta zeolite. However, to accommodate the size of the carbohydrate molecules in reaction paths, only hierarchical Na-Al₂Si₁₂O₃₉H₂₃ was used. Sodium ions were positioned above the aluminum centers within the zeolite framework. Full article

In this paper, we investigate the existence of multiple solutions for a Kirchhoff-type equation with Dirichlet boundary conditions defined on locally finite graphs. Our study extends some previous results on nonlinear Laplacian equations to the more complex Kirchhoff equation which incorporates a nonlocal term. By employing an abstract three critical points theorem that is based on Morse theory, we provide sufficient conditions that guarantee the existence of at least three distinct solutions, including two strictly positive solutions. We also present an example to verify our results. Full article

This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing a more accurate description of thermal and mechanical responses in semiconductor materials. The effects of rotation, ramp-type heating, and semiconductor properties on elastic wave propagation are analyzed theoretically. Governing equations are formulated and solved analytically, with numerical simulations illustrating the variations in thermal and elastic wave behavior. The key findings highlight the significant impact of rotation, nonlocal parameters $e_{0}a$, and time derivative fractional order (FO) $\alpha$ on physical quantities, offering insights into the thermoelastic performance of semiconductor nanostructures under dynamic thermal loads. A comparison is made with the previous results to show the impact of the external parameters on the propagation phenomenon. The numerical results show that increasing the rotation rate $\mathsf{\Omega }=5$ causes a phase lag of approximately 22% in thermal and elastic wave peaks. When the thermoelectric coupling parameter ${\mathsf{\epsilon }}_3$ is increased from $-0.8\times {10}^{-42}$ to $1.2\times {10}^{-42}$. The temperature amplitude rises by 17%, while the carrier density peak increases by over 25%. For nonlocal parameter values $\mathsf{\epsilon }=0.3\to 0.6$, high-frequency stress oscillations are damped by more than 35%. The results contribute to the understanding of wave propagation in advanced semiconductor materials, with potential applications in microelectronics, optoelectronics, and nanoscale thermal management. Full article

In device-independent (DI) quantum protocols, security statements are agnostic to the internal workings of the quantum devices—they rely solely on classical interactions with the devices and specific assumptions. Traditionally, such protocols are set in a non-local scenario, where two non-communicating devices exhibit Bell inequality violations. Recently, a new class of DI protocols has emerged that requires only a single device. In this setting, the assumption of no communication is replaced by a computational one: the device cannot solve certain post-quantum cryptographic problems. Protocols developed in this single-device computational setting—such as for randomness certification—have relied on ad hoc techniques, making their guarantees difficult to compare and generalize. In this work, we introduce a modular proof framework inspired by techniques from the non-local DI literature. Our approach combines tools from quantum information theory, including entropic uncertainty relations and the entropy accumulation theorem, to yield both conceptual clarity and quantitative security guarantees. This framework provides a foundation for systematically analyzing DI protocols in the single-device setting under computational assumptions. It enables the design and security proof of future protocols for DI randomness generation, expansion, amplification, and key distribution, grounded in post-quantum cryptographic hardness. Full article

This study focuses on the numerical solution and dynamics analysis of fractional governing equations related to double-layer nanoplates based on the shifted Legendre polynomials algorithm. Firstly, the fractional governing equations of the complicated mechanical behavior for bilayer nanoplates are constructed by combining the Fractional Kelvin–Voigt (FKV) model with the Caputo fractional derivative and the theory of nonlocal elasticity. Then, the shifted Legendre polynomial is used to approximate the displacement function, and the governing equations are transformed into algebraic equations to facilitate the numerical solution in the time domain. Moreover, the systematic convergence analysis is carried out to verify the convergence of the ternary displacement function and its fractional derivatives in the equation, ensuring the rigor of the mathematical model. Finally, a dimensionless numerical example is given to verify the feasibility of the proposed algorithm, and the effects of material parameters on plate displacement are analyzed for double-layer plates with different materials. Full article