98 Results Found

The original Bohr-Sommerfeld theory of quantization did not give operators of transitions between quantum quantum states. This paper derives these operators, using the first principles of geometric quantization.

Outliers significantly impact the accuracy of geometric model fitting. Previous approaches to handling outliers have involved threshold selection and scale estimation. However, many scale estimators assume that the inlier distribution follows a Gauss...

In this paper, quantized residual preference is proposed to represent the hypotheses and the points for model selection and inlier segmentation in multi-structure geometric model fitting. First, a quantized residual preference is proposed to represen...

The seminal paper by Niels Bohr followed by a paper by Arnold Sommerfeld led to a revolutionary Bohr–Sommerfeld theory of atomic spectra. We are interested in the information about the structure of quantum mechanics encoded in this theory. In particu...

Using Spatial Domain Correlation Pattern Recognition (CPR) in Internet-of-Things (IoT)-based applications often faces constraints, like inadequate computational resources and limited memory. To reduce the computation workload of inference due to larg...

Quantum mechanics postulates wave–particle duality and assigns amplitudes of the form $e^{iS/\hslash }$, yet no existing formulation explains why physical observables depend only on the phase of the action. Here we show that if the quantum of action...

We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of qua...

The industrial dismantling and recycling of end-of-life photovoltaic (PV) modules require robust visual inspection under dust contamination, inter-class similarity, and constrained edge-computing conditions. This study proposes an end-to-end framewor...

Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Ent...

We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider $C^{\ast }$-algebra quantization obtained through groupoid techniques, an...

Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of e...

This article discusses the quantization of linear Hamiltonian systems, a historically rich but under explored line of research. The key idea is that a classical linear Hamiltonian system induces on its phase space a compatible complex structure and s...

Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a st...

This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We first prese...

Any quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map...

We show that a discrete quantization law for cosmological entropy emerges naturally within a meta-geometric gauge theory of gravity, when the standard de Sitter entropy relation is combined with the topological structure of the theory. Our framework...

To address the challenges of copyright protection for marine environmental datasets in open sharing environments, this paper proposes ST-Mark, a robust watermarking framework that synergistically integrates established geometric invariants and Quanti...

The thermal Hall effect has emerged as a fundamental tool for probing exotic quasiparticles and topological order, particularly in magnetic insulators where electronic conduction is suppressed. Much like skyrmions, which are characterized by their to...

Near-lossless coding schemes traditionally rely on uniform quantization to control the maximum absolute error ($L_{\infty }$ norm) of residual signals, often assuming a parametric model for the source distribution. This paper introduces a novel design fra...

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 derive...

Deploying EEG classification networks on resource-constrained brain–computer interface (BCI) hardware motivates structured filter pruning, yet which importance criterion to trust in already-compact architectures is unclear. We present a leakage...

This paper undertakes an in-depth exploration into the issue of quantization errors that occur during color gamut conversion within LED full-color display systems. To commence, a CIE-xyY colorimetric framework, which is customized to the unique chara...

This paper summarises a new framework of Stochastic Geometric Mechanics that attributes a fundamental role to Hamilton–Jacobi–Bellman (HJB) equations. These are associated with geometric versions of probabilistic Lagrangian and Hamiltonia...

Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case without appea...

This paper develops a systematic and geometric theory of optimal quantization on the unit sphere ${\mathbb{S}}^2$, focusing on finite uniform probability distributions supported on the spherical surface—rather than on lower-dimensional geodesic subsets such...

Omnidirectional images have gained significant popularity and drawn great attention nowadays, which poses challenges to omnidirectional image processing in solving the bottleneck of storage and transmission. Projecting onto a two-dimensional image pl...

This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It i...

Most quantum gravity theories quantize space-time on the order of Planck length (${\ell }_p^{}$). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LI...

Existing watermarking methods for copyright protection of OpenDRIVE high-definition maps have difficulty balancing robustness and geometric accuracy. This study proposes a geometry-constrained robust watermarking algorithm that exploits the parametri...

This article presents a comprehensive and analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric. Focusing on highly symmetric configurations on the unit sphere ${\mathbb{S}}^2$, we investigate three...

Whether an algebraic or a geometric or a phenomenological prescription is applied, the first fundamental form is unambiguously related to the modeling of the curved spacetime. Accordingly, we assume that the possible quantization of the first fundame...

The purpose of image registration is to find the symmetry between the reference image and the image to be registered. In order to improve the registration effect of unmanned aerial vehicle (UAV) remote sensing imagery with a special texture backgroun...

We develop a useful model considering an atom-field system interaction in the framework of pseudoharmonic oscillators. We examine qualitatively the different physical quantities for a two-level atom (TLA) system interacting with a quantized coherent...

We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approache...

In the spirit of the thin-layer quantization scheme, we give the effective Shrödinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the attractive wells...

Wave propagation in periodic media is governed by energy–momentum relations and geometric phases characterizing band topology, such as Zak phase in one-dimensional lattices. We demonstrate that, in the off-diagonal trimer lattices, Zak phase ca...

Over the last decade, various deep neural network models have achieved great success in image recognition and classification tasks. The vast majority of high-performing deep neural network models have a huge number of parameters and often require sac...

We present a pre-geometric gauge theory in which spacetime geometry and gravity emerge from spontaneous symmetry breaking and a concurrent topological phase transition. The theory is formulated on a four-dimensional manifold without presupposed metri...

The Berry phase plays a central role in modern electronics and acts as a foundation for a wide range of phenomena, from the anomalous Hall effect to topological insulators and valleytronics. However, in conventional analytical treatments, its geometr...

Both geometric and wave optical models, as well as classical and quantum mechanics, realize linear transformations with matrices; for plane optics, these are $2\times 2$ and of unit determinant. Students and some researchers could assume that the structure o...

We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford’s geometric algebra. Consequently, we establish a connection between a three-dimension...

In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement $C\left(K\right)$...

Contemporary spectroscopic studies of astrophysical and laboratory plasmas frequently deal with extremely large values of principle quantum numbers of atomic systems. These atomic states are very sensitive to electric and magnetic fields of the surro...

This review paper comprehensively examines the influence of spatial torsion on quantum fluctuations from the perspectives of metric-affine gravity (MAG) and the stochastic variational method (SVM). We first outline the fundamental framework of MAG, a...

We present a canonical quantization framework for static spherically symmetric spacetimes described by the Einstein–Hilbert action with a cosmological constant. In addition to recovering the classical Schwarzschild–(Anti)-de Sitter soluti...

To protect the copyright of the color image, a color image watermarking scheme based on quaternion discrete Fourier transform (QDFT) and tensor decomposition (TD) is presented. Specifically, the cover image is partitioned into non-overlapping blocks,...

The mathematical representation of discrete signals is classically governed by linear basis transforms, such as the Discrete Fourier Transform (DFT), which treat spectral projection as a rigid, deterministic geometric operation. Under this paradigm,...

It is well known that Einstein’s equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that time evolution of the gravitatio...

It has been shown by explicit and exact calculation that the geometric product formula i.e., area (or entropy) product formula of outer horizon ( ${\mathcal{H}}^{+}$ ) and inner horizon ( ${\mathcal{H}}^{-}$ ) for charged accelerating black hole (BH) should ne...

Urban-forest monitoring increasingly requires intelligent sensor-driven systems capable of characterizing short-term tree responses while operating efficiently within Internet of Things (IoT) and edge-computing environments. This study proposes a fus...