Search Results (71)

Solving Bayesian inverse problems efficiently stands as a major bottleneck in scientific computing. Although Bayesian Physics-Informed Neural Networks (B-PINNs) have introduced a robust way to quantify uncertainty, the high-dimensional parameter spaces inherent in deep learning often lead to prohibitive sampling costs. Addressing this, our work introduces Quantum-Encodable Bayesian PINNs trained via Classical Ensemble Kalman Inversion (QEKI), a framework that pairs Quantum Neural Networks (QNNs) with Ensemble Kalman Inversion (EKI). The core advantage lies in the QNN’s ability to act as a compact surrogate for PDE solutions, capturing complex physics with significantly fewer parameters than classical networks. By adopting the gradient-free EKI for training, we mitigate the barren plateau issue that plagues quantum optimization. Through several benchmarks on 1D and 2D nonlinear PDEs, we show that QEKI yields precise inversions and substantial parameter compression, even in the presence of noise. While large-scale applications are constrained by current quantum hardware, this research outlines a viable hybrid framework for including quantum features within Bayesian uncertainty quantification. Full article

Two-dimensional materials and their van der Waals heterostructures have shown great potential in quantum physics, flexible electronics, and optoelectronic devices. However, interfacial bubbles originated from trapped air, solvent residues, adsorbed molecules and reaction byproducts remain a key limitation to performance. This review provides a comprehensive overview of the formation mechanisms, characteristics, impacts, and optimization strategies related to bubbles in 2D heterostructures. We first summarize common fabrication approaches for constructing 2D heterostructures and discuss the mechanisms of bubble formation together with their physicochemical features. Then, we introduce characterization techniques ranging from macroscopic morphological observation to atomic-scale interfacial analysis, including optical microscopy, atomic force microscopy, transmission electron microscopy, and spectroscopic methods systematically. The effects of bubbles on the mechanical, electrical, thermal, and optical properties of 2D materials are subsequently examined. Finally, we compare key interface optimization strategies—such as thermal annealing, chemical treatments, AFM-based cleaning, electric field-driven approaches, clean assembly and AI-assisted methods. We demonstrate that, although substantial advances have been made in understanding interfacial bubbles, key fundamental challenges persist. Future breakthroughs will require the combined advancement of mechanistic insight, in situ characterization, and process engineering. Moreover, with the rapid adoption of AI and autonomous experimental platforms in materials fabrication and data analysis, AI-enabled process optimization and real-time characterization are emerging as key enablers for achieving high-cleanliness and scalable van der Waals heterostructures. Full article

We survey the recent developments on quantum invariants of 3-manifolds and links: $\widehat{Z}$ and $F_L$. They are q-series invariants originated from mathematical physics, inspired by the categorification of a numerical quantum invariant—the Witten–Reshetikhin–Turaev (WRT) invariant—of 3-manifolds. They exhibit rich features, for example, quantum modularity, infinite-dimensional Verma module structures, and knot–quiver correspondence. Furthermore, they have connections to the 3d-3d correspondence and other topological invariants. We also provide a review of an extension of the above series invariants to Lie superalgebras. Full article

This manuscript examines the rotational dynamics of rigid bodies in five-dimensional Euclidean space. This results in ten coupled nonlinear differential equations for angular velocities. Restricting rotations along certain axes reduces the 5D equations to sets of 4D Euler equations, which collapse to the classical 3D Euler equations. This demonstrates consistency with established mechanics. For bodies with equal principal moments of inertia (e.g., hyperspheres and Platonic solids), the rotation velocities remain constant over time. In cases with six equal and four distinct inertia moments, the solutions exhibit harmonic oscillations with frequencies determined by the initial conditions. Rotations are stable when the body spins around an axis with the largest or smallest principal moment of inertia, thus extending classical stability criteria into higher dimensions. This study defines a 5D angular momentum operator and derives commutation relations, thereby generalizing the familiar 3D and 4D cases. Additionally, it discusses the role of Pauli matrices in 5D and the implications for spin as an intrinsic property. While mathematically consistent, the hypothesis of a fifth spatial dimension is ultimately rejected since it contradicts experimental evidence. This work is valuable mainly as a theoretical framework for understanding spin and symmetry. This paper extends Euler’s equations to five dimensions (5D), demonstrates their reduction to four dimensions (4D) and three dimensions (3D), provides closed-form and oscillatory solutions under specific inertia conditions, analyzes stability, and explores quantum mechanical implications. Ultimately, it concludes that 5D space is not physically viable. Full article

We present a detailed derivation of the quantum and quantum–thermal effective action for non-relativistic systems, starting from the single-particle case and extending to the Gross–Pitaevskii (GP) field theory for weakly interacting bosons. In the single-particle framework, we introduce the one-particle-irreducible (1PI) effective action formalism, taking explicitly into account the choice of the initial quantum state, its saddle-point plus Gaussian-fluctuation approximation, and its finite-temperature extension via Matsubara summation, yielding a clear physical interpretation in terms of zero-point and thermal contributions to the Helmholtz free energy. The formalism is then applied to the GP action, producing the 1PI effective potential at zero and finite temperature, including beyond-mean-field Lee–Huang–Yang and thermal corrections. We discuss the gapless and gapped Bogoliubov spectra, their relevance to equilibrium and non-equilibrium regimes, and the role of regularization. Applications include the inclusion of an external potential within the local density approximation, the derivation of finite-temperature Josephson equations, and the extension to D-dimensional systems, with particular attention to the zero-dimensional limit. This unified approach provides a transparent connection between microscopic quantum fluctuations and effective macroscopic equations of motion for Bose–Einstein condensates. Full article

This study presents a tripartite analytical framework for the (1+1)-dimensional nonlinear Klein–Fock–Gordon equation, a key model for spinless particles in relativistic quantum mechanics. The investigation begins with a Painlevé analysis showing that the equation is completely integrable via the Painlevé test by using Maple. Subsequently, classical Lie symmetry analysis is employed to derive the infinitesimal generators of the equation. A Lagrangian formulation is constructed for these generators, from which similarity variables are systematically obtained. This framework enables a complete similarity reduction, transforming the complex nonlinear partial differential equation into a more tractable ordinary differential equation. To solve this reduced ordinary differential equation and to obtain a spectrum of soliton solutions, we implement the new generalized exponential differential rational function method. This advanced technique utilizes a rational trial function based on the $ith$ derivatives of exponentials, generating a diverse spectrum of closed-form soliton solutions through strategic choices of arbitrary constants. The novelty of this approach provides a unified framework for handling higher-order nonlinearities, yielding solutions such as multi-peakons and lump solitons, which are vividly characterized using Mathematica-generated 3D, 2D, and contour plots. These findings provide significant insights into nonlinear wave dynamics with potential applications in quantum field theory, nonlinear optics, plasma physics, etc. Full article

The design of multi-link vehicle suspension systems, such as the 3D double-wishbone, presents a critical challenge in automotive engineering. The process constitutes a high-dimensional, nonlinearly constrained optimization problem where traditional gradient-based methods often fail by converging to suboptimal local minima. This paper introduces a novel two-stage hybrid optimization framework designed to overcome this limitation by intelligently integrating quantum-inspired and classical techniques. The methodology explicitly defines a QUBO (Quadratic Unconstrained Binary Optimization) stage and an SQP (Sequential Quadratic Programming) stage. Stage 1 addresses the complex kinematic constraint problem by formulating it as a QUBO, which is then solved using Simulated Annealing to perform a global search, guaranteeing a physically feasible starting point. Subsequently, Stage 2 takes this feasible solution and employs an SQP algorithm to perform a high-precision local refinement, tuning the geometry to meet specific performance targets for camber and caster curves. The framework successfully converged to a design with a near-zero performance objective of 7.08 × 10⁻¹⁴. The efficacy of this hybrid approach is highlighted by the dramatic improvement from the high-error initial solution found by Simulated Annealing to the final, high-precision result from the SQP refinement. We conclude that this QUBO-SQP framework is a powerful and validated methodology for solving complex, real-world engineering design problems, effectively bridging the gap between global exploration and local precision. Full article

Integration in non-integer-dimensional spaces (NIDS) is actively used in quantum field theory, statistical physics, and fractal media physics. The integration over the entire momentum space with non-integer dimensions was first proposed by Wilson in 1973 for dimensional regularization in quantum field theory. However, self-consistent calculus of integrals and derivatives in NIDS and the vector calculus in NIDS, including the fundamental theorems of these calculi, have not yet been explicitly formulated. The construction of precisely such self-consistent calculus is the purpose of this article. The integral and differential operators in NIDS are defined by using the generalization of the Wilson approach, product measure, and metric approaches. To derive the self-consistent formulation of the NIDS calculus, we proposed some principles of correspondence and self-consistency of NIDS integration and differentiation. In this paper, the basic properties of these operators are described and proved. It is proved that the proposed operators satisfy the NIDS generalizations of the first and second fundamental theorems of standard calculus; therefore, these NIDS operators form a calculus. The NIDS derivative satisfies the standard Leibniz rule; therefore, these derivatives are integer-order operators. The calculation of the NIDS integral over the ball region in NIDS gives the well-known equation of the volume of a non-integer dimension ball with arbitrary positive dimension. The volume, surface, and line integrals in D-dimensional spaces are defined, and basic properties are described. The NIDS generalization of the standard vector differential operators (gradient, divergence, and curl) and integral operators (the line and surface integrals of vector fields) are proposed. The NIDS generalizations of the standard gradient theorem, the divergence theorem (the Gauss–Ostrogradsky theorem), and the Stokes theorem are proved. Some basic elements of the calculus of differential forms in NIDS are also proposed. The proposed NIDS calculus can be used, for example, to describe fractal media and the fractal distribution of matter in the framework of continuum models by using the concept of the density of states. Full article

We investigate the spatial structure of quantum entanglement in one- and two-dimensional lattice systems containing structural defects, using the Time-Dependent Quantum Monte Carlo (TDQMC) method. By constructing reduced density matrices from ensembles of guide waves, we resolve spatial variations in both Coulomb-mediated entanglement and coherence without requiring full many-body wavefunctions. This approach reveals localized regions, entanglement islands, where quantum correlations are enhanced or suppressed due to the presence of vacancies or interaction inhomogeneities. In 1D systems, entanglement tends to concentrate near defects, while in 2D systems, we observe bridge-like and radially symmetric domains. Our results demonstrate that TDQMC offers a scalable and physically transparent framework for real-space quantum information analysis, with implications for information transfer in atomic-size structures, quantum materials, entanglement-based sensing, and coherent state engineering. Full article

Motivated by the seminal discoveries in graphene, the exploration of novel physical phenomena in alternative two-dimensional (2D) materials has attracted tremendous attention. In this work, through theoretical investigation using first-principles calculations, we reveal that Mo-intercalated ${\mathrm{CrI}}_3$ bilayer exhibits ferromagnetic semiconductor behavior with a small easy-plane magnetocrystalline anisotropy energy (MAE) of 0.618 meV/Cr(Mo) between (100) and (001) magnetizations. The spin–orbit coupling (SOC) opens a narrow band gap at the Fermi level for both magnetization orientations with nonzero Chern number for realizing the quantum anomalous Hall effect (QAHE) in the former and with trivial topology in the latter. The small MAE implies the efficient experimental manipulation of magnetization between distinct topologies through an external magnetic field. Our findings provide compelling evidence that the QAHE in this system originates from the quantum spin Hall effect (QSHE), driven by intrinsic magnetism under broken time-reversal symmetry. These unique properties position Mo-intercalated ${\mathrm{CrI}}_3$ as a promising candidate for tunable spintronic applications. Full article

Two-dimensional (2D) van der Waals (vdW) magnetic materials have emerged as a frontier in condensed matter physics and materials science, offering unprecedented opportunities for next-generation spintronic technologies. This review examines the synthesis, properties, and transport phenomena of 2D magnetic materials, with particular emphasis on their integration into spintronic devices. A comprehensive historical overview of magnetic materials is provided, tracing the evolution of intrinsic ferromagnetism in the 2D limit, highlighting key materials such as Cr₂Ge₂Te₆, Fe₃GeTe₂, and CrI₃. Special attention is devoted to the fundamental magnetic properties—including magnetic anisotropy, Curie temperature, and spin polarization—that underpin their functional performance. Major synthesis strategies are evaluated, including chemical vapor deposition, micromechanical exfoliation, and molecular beam epitaxy, focusing on scalability, interface control, and material purity. Furthermore, hallmark transport phenomena are discussed, such as giant magnetoresistance, the quantum anomalous Hall effect, spin–orbit torque, and the role of exchange bias and skyrmions in vdW heterostructures. Throughout the review, current limitations, unresolved questions, and emerging research directions are identified that will accelerate the deployment of 2D magnetic materials in flexible, reconfigurable, and quantum spintronic systems. This work aims to guide ongoing experimental and theoretical efforts and articulate a vision for advancing the field toward device-level implementation. Full article

In this study, the extended (3 + 1)-dimensional Jimbo–Miwa equation, which has not been previously studied using Lie symmetry techniques, is the focus. We derive new symmetry reductions and exact invariant solutions, including lump and rogue wave structures. Additionally, precise solitary wave solutions of the extended (3 + 1)-dimensional Jimbo–Miwa equation using the multivariate generalized exponential rational integral function technique (MGERIF) are studied. The extended (3 + 1)-dimensional Jimbo–Miwa equation is crucial for studying nonlinear processes in optical communication, fluid dynamics, materials science, geophysics, and quantum mechanics. The multivariate generalized exponential rational integral function approach offers advantages in addressing challenges involving exponential, hyperbolic, and trigonometric functions formulated based on the generalized exponential rational function method. The solutions provided by MGERIF have numerous applications in various fields, including mathematical physics, condensed matter physics, nonlinear optics, plasma physics, and other nonlinear physical equations. The graphical features of the generated solutions are examined using 3D surface graphs and contour plots, with theoretical derivations. This visual technique enhances our understanding of the identified answers and facilitates a more profound discussion of their practical applications in real-world scenarios. We employ the MGERIF approach to develop a technique for addressing integrable systems, providing a valuable framework for examining nonlinear phenomena across various physical contexts. This study’s outcomes enhance both nonlinear dynamical processes and solitary wave theory. Full article

We present an analytic continuation of the central charge c in two-dimensional conformal field theory (2D CFT), modeled as a Nevanlinna function—an analytic map from the upper half-plane to itself. Motivated by the structure of vacuum energies arising from the quantization of spin-j conformal fields on the circle, we derive a discrete spectrum of central charges $c\left(j\right)=1+6j(j+1)$ and extend it continuously via $c\left(z\right)=1+6z$. The Möbius-inverted form $f\left(z\right)=1-6/z$ satisfies the conditions of a Nevanlinna function, providing a physically consistent analytic structure that captures both the unitarity of minimal models ($c<1$) and the continuous spectrum for $c\ge 1$. This unified framework highlights the connection between spectral theory, analyticity, and conformal symmetry in quantum field theory. Full article

Recent work has demonstrated a correspondence that bridges quantum information processing and high-energy physics: discrete quantum cellular automata (QCA) can, in the continuum limit, reproduce quantum field theories (QFTs). This QCA/QFT correspondence raises fundamental questions about how matter/energy, information, and the nature of spacetime are related. Here, we show that free QED is equivalent to the continuous-space-and-time limit of Fermi and Bose QCA theories on the cubic lattice derived from quantum random walks satisfying simple symmetry and unitarity conditions. In doing so, we define the Fermi and Bose theories in a unified manner using the usual fermion internal space and a boson internal space that is six-dimensional. We show that the reduction to a two-dimensional boson internal space (two helicity states arising from spin-1 plus the photon transversality condition) comes from restricting the QCA theory to positive energies. We briefly examine common symmetries of QCAs and how time-reversal symmetry demands the existence of negative-energy solutions. These solutions produce a tension in coupling the Fermi and Bose theories, in which the strong locality of QCAs seems to require a non-zero amplitude to produce negative-energy states, leading to an unphysical cascade of negative-energy particles. However, we show in a 1D model that, by extending interactions over a larger (but finite) range, it is possible to exponentially suppress the production of negative-energy particles to the point where they can be neglected. Full article

Cracking in hydraulic buried engineering can cause localized damage or complete structural failure, potentially resulting in catastrophic project outcomes. Traditional methods for detecting cracks in hydraulic concrete buried engineering are often insufficient in terms of reliability and accuracy. With the development and application of particle-based technology, it has been widely used in the field of crack detection. This research investigates the support pier of the Yingxiuwan Hydropower Plant and the lock pier of the Yuzixi Hydropower Plant. Employing principles from quantum physics, quantum particle non-destructive detection technology is introduced to identify crack locations. A three-dimensional simulation model is constructed and verified accurately through integration with CT scanning techniques. The results demonstrate that particle detection technology effectively detects cracks in hydraulic concrete buried engineering, exhibiting minimal susceptibility to external interference. The particle detection data enable 3D visualization of cracks, accurately reflecting the conditions within embedded concrete components. This method provides a reliable and advanced technical solution for precise crack detection in concrete-embedded engineering and offers critical data for exploring crack propagation mechanisms. Full article