Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (81)

Search Parameters:
Keywords = Hamiltonian perturbations

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
13 pages, 1560 KiB  
Article
Short-Time Behavior of a System Ruled by Non-Hermitian Time-Dependent Hamiltonians
by Benedetto Militello and Anna Napoli
Symmetry 2025, 17(8), 1336; https://doi.org/10.3390/sym17081336 - 15 Aug 2025
Viewed by 207
Abstract
The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second-order perturbative approach. The resulting expression allows for the analysis of some situations which could be of interest in the field of [...] Read more.
The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second-order perturbative approach. The resulting expression allows for the analysis of some situations which could be of interest in the field of quantum technology. For example, it becomes possible to predict a quantum Zeno effect even in the presence of decay processes. Full article
Show Figures

Figure 1

21 pages, 2229 KiB  
Article
Efficient Reversible Data Hiding in Encrypted Point Clouds via KD Tree-Based Path Planning and Dual-Model Design
by Yuan-Yu Tsai, Chia-Yuan Li, Cheng-Yu Ho and Ching-Ta Lu
Mathematics 2025, 13(16), 2593; https://doi.org/10.3390/math13162593 - 13 Aug 2025
Viewed by 267
Abstract
Reversible data hiding in encrypted point clouds presents unique challenges due to their unstructured geometry, absence of mesh connectivity, and high sensitivity to spatial perturbations. In this paper, we propose an efficient and secure reversible data hiding framework for encrypted point clouds, incorporating [...] Read more.
Reversible data hiding in encrypted point clouds presents unique challenges due to their unstructured geometry, absence of mesh connectivity, and high sensitivity to spatial perturbations. In this paper, we propose an efficient and secure reversible data hiding framework for encrypted point clouds, incorporating KD tree-based path planning, adaptive multi-MSB prediction, and a dual-model design. To establish a consistent spatial traversal order, a Hamiltonian path is constructed using a KD tree-accelerated nearest-neighbor algorithm. Guided by this path, a prediction-driven embedding strategy dynamically adjusts the number of most significant bits (MSBs) embedded per point, balancing capacity and reversibility while generating a label map that reflects local predictability. The label map is then compressed using Huffman coding to reduce the auxiliary overhead. For enhanced security and lossless recovery, the encrypted point cloud is divided into two complementary shares through a lightweight XOR-based (2, 2) secret sharing scheme. The Huffman tree and compressed label map are distributed across both encrypted shares, ensuring that neither share alone can reveal the original point cloud or the embedded message. Experimental evaluations on diverse 3D models demonstrate that the proposed method achieves near-optimal embedding rates, perfect reconstruction of the original model, and significant obfuscation of the geometric structure. These results confirm the practicality and robustness of the proposed framework for scenarios involving secure 3D point cloud transmission, storage, and sharing. Full article
(This article belongs to the Special Issue Information Security and Image Processing)
Show Figures

Figure 1

25 pages, 4865 KiB  
Article
Mathematical Modeling, Bifurcation Theory, and Chaos in a Dusty Plasma System with Generalized (r, q) Distributions
by Beenish, Maria Samreen and Fehaid Salem Alshammari
Axioms 2025, 14(8), 610; https://doi.org/10.3390/axioms14080610 - 5 Aug 2025
Viewed by 237
Abstract
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized (r,q) distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. [...] Read more.
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized (r,q) distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article
(This article belongs to the Special Issue Trends in Dynamical Systems and Applied Mathematics)
Show Figures

Figure 1

24 pages, 4106 KiB  
Article
Visualizing Three-Qubit Entanglement
by Alfred Benedito and Germán Sierra
Entropy 2025, 27(8), 800; https://doi.org/10.3390/e27080800 - 27 Jul 2025
Viewed by 207
Abstract
We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric perspective and the tangle, deriving bounds that depend on the [...] Read more.
We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric perspective and the tangle, deriving bounds that depend on the entanglement class. Based on these insights, we conjecture a purely geometric expression for both the tangle and Cayley’s hyperdeterminant for non-generic states. As an application, we analyze the energy eigenstates of physical Hamiltonians, identifying the sufficient conditions for genuine tripartite entanglement to be robust under symmetry-breaking perturbations and level repulsion effects. Full article
(This article belongs to the Special Issue Editorial Board Members' Collection Series on Quantum Entanglement)
Show Figures

Figure 1

17 pages, 18705 KiB  
Article
A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
by Meng Wang and Chenyang Li
Molecules 2025, 30(9), 2082; https://doi.org/10.3390/molecules30092082 - 7 May 2025
Cited by 1 | Viewed by 499
Abstract
We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian [...] Read more.
We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme. Full article
Show Figures

Figure 1

19 pages, 1772 KiB  
Article
Analysis of Near-Polar and Near-Circular Periodic Orbits Around the Moon with J2, C22 and Third-Body Perturbations
by Xingbo Xu
Symmetry 2025, 17(5), 630; https://doi.org/10.3390/sym17050630 - 22 Apr 2025
Viewed by 365
Abstract
In the Moon–Earth elliptic restricted three-body problem, near-polar and near-circular lunar-type periodic orbits are numerically continued from Keplerian circular orbits using Broyden’s method with line search. The Hamiltonian system, expressed in Cartesian coordinates, is treated via the symplectic scaling method. The radii of [...] Read more.
In the Moon–Earth elliptic restricted three-body problem, near-polar and near-circular lunar-type periodic orbits are numerically continued from Keplerian circular orbits using Broyden’s method with line search. The Hamiltonian system, expressed in Cartesian coordinates, is treated via the symplectic scaling method. The radii of the initial Keplerian circular orbits are then scaled and normalized. For cases in which the integer ratios {j/k} of the mean motions between the inner and outer orbits are within the range [9,150], some periodic orbits of the elliptic restricted three-body problem are investigated. For the middle-altitude cases with j/k[38,70], the perturbations due to J2 and C22 are incorporated, and some new near-polar periodic orbits are computed. The orbital dynamics of these near-polar, near-circular periodic orbits are well characterized by the first-order double-averaged system in the Poincaré–Delaunay elements. Linear stability is assessed through characteristic multipliers derived from the fundamental solution matrix of the linear varational system. Stability indices are computed for both the near-polar and planar near-circular periodic orbits across the range j/k[9,50]. Full article
(This article belongs to the Section Mathematics)
Show Figures

Figure 1

25 pages, 378 KiB  
Article
The Intrinsic Exceptional Point: A Challenge in Quantum Theory
by Miloslav Znojil
Foundations 2025, 5(1), 8; https://doi.org/10.3390/foundations5010008 - 1 Mar 2025
Cited by 1 | Viewed by 1020
Abstract
In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian H(IC)=p2+ix3 does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic [...] Read more.
In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian H(IC)=p2+ix3 does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic exceptional point” (IEP) features of H(IC) and, in particular, to the phenomenon of a high-energy asymptotic parallelization of its bound-state-mimicking eigenvectors. In this paper, it is argued that the operator H(IC) (and the like) can only be interpreted as a manifestly unphysical, singular IEP limit of a hypothetical one-parametric family of certain standard quantum Hamiltonians. For explanation, ample use is made of perturbation theory and of multiple analogies between IEPs and conventional Kato’s exceptional points. Full article
(This article belongs to the Section Physical Sciences)
62 pages, 523 KiB  
Article
Existence and Mass Gap in Quantum Yang–Mills Theory
by Logan Nye
Int. J. Topol. 2025, 2(1), 2; https://doi.org/10.3390/ijt2010002 - 25 Feb 2025
Viewed by 4510
Abstract
This paper presents a novel approach to solving the Yang–Mills existence and mass gap problem using quantum information theory. We develop a rigorous mathematical framework that reformulates the Yang–Mills theory in terms of quantum circuits and entanglement structures. Our method provides a concrete [...] Read more.
This paper presents a novel approach to solving the Yang–Mills existence and mass gap problem using quantum information theory. We develop a rigorous mathematical framework that reformulates the Yang–Mills theory in terms of quantum circuits and entanglement structures. Our method provides a concrete realization of the Yang–Mills theory that is manifestly gauge-invariant and satisfies the Wightman axioms. We demonstrate the existence of a mass gap by analyzing the entanglement spectrum of the vacuum state, establishing a direct connection between the mass gap and the minimum non-zero eigenvalue of the entanglement Hamiltonian. Our approach also offers new insights into non-perturbative phenomena such as confinement and asymptotic freedom. We introduce new mathematical tools, including entanglement renormalization for gauge theories and quantum circuit complexity measures for quantum fields. The implications of our work extend beyond the Yang–Mills theory, suggesting new approaches to quantum gravity, strongly coupled systems, and cosmological problems. This quantum information perspective on gauge theories opens up exciting new directions for research at the intersection of quantum field theory, quantum gravity, and quantum computation. Full article
18 pages, 1149 KiB  
Article
Applications of the Kosambi–Cartan–Chern Theory to Hamiltonian Systems on a Cotangent Bundle: Linking Geometric Quantities to the Self-Similar Motions of Three Point Vortices
by Yuma Hirakui and Takahiro Yajima
Mathematics 2025, 13(1), 126; https://doi.org/10.3390/math13010126 - 31 Dec 2024
Cited by 1 | Viewed by 741
Abstract
This study presents a differential geometric framework for Hamiltonian systems expressed in terms of first-order differential equations. For systems governed by second-order ordinary differential equations on tangent bundles, such as Euler–Lagrange systems, the stability of trajectories under perturbations is analyzed based on the [...] Read more.
This study presents a differential geometric framework for Hamiltonian systems expressed in terms of first-order differential equations. For systems governed by second-order ordinary differential equations on tangent bundles, such as Euler–Lagrange systems, the stability of trajectories under perturbations is analyzed based on the eigenvalue of the deviation curvature tensor. Building upon this Jacobi stability analysis approach, four geometric quantities for Hamiltonian systems are derived considering perturbations to trajectories on a cotangent bundle. As a specific Hamiltonian system, a hydrodynamic three-point vortex system is examined, and its four geometric quantities are computed using the Hamiltonian equation. The eigenvalues of these geometric quantities are then used to classify the divergent and collapsing trajectories of point vortices. Specifically, for the divergent trajectories of vortices, the eigenvalues of the geometric quantities converge to zero over time. Conversely, for their collapsing trajectories, the eigenvalues increase with time. This result implies that at the point of vortex collapse, the system becomes geometrically unstable, with diverging trajectory perturbations. Full article
Show Figures

Figure 1

19 pages, 1337 KiB  
Article
Two-Loop Corrections in Power Spectrum in Models of Inflation with Primordial Black Hole Formation
by Hassan Firouzjahi
Universe 2024, 10(12), 456; https://doi.org/10.3390/universe10120456 - 13 Dec 2024
Cited by 1 | Viewed by 1025
Abstract
We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving [...] Read more.
We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate herein the fractional two-loop correction in power spectrum scales, like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase. Full article
(This article belongs to the Special Issue Primordial Black Holes from Inflation)
Show Figures

Figure 1

24 pages, 6146 KiB  
Article
On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment
by Nicolae Herisanu, Bogdan Marinca and Vasile Marinca
Mathematics 2024, 12(23), 3836; https://doi.org/10.3390/math12233836 - 4 Dec 2024
Viewed by 750
Abstract
The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the [...] Read more.
The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the nonlinear differential equations were obtained for the pinned–pinned boundary conditions with the help of the Galerkin–Bubnov procedure and Hamiltonian approach. The nonlinear differential equations were studied using an original, explicit, and very efficient technique, namely the optimal auxiliary functions method (OAFM). It should be emphasized that our procedure assures a rapid convergence of the approximate analytical solutions after only one iteration, without the presence of a small parameter in the governing equations or boundary conditions. Detailed results are presented on the effects of some parameters, among them being analyzed were the damping, frequency, electromagnetic, and nonlinear elastic foundation coefficients. The local stability of the equilibrium points was performed by introducing two variable expansion method, the homotopy perturbation method, and then applying the Routh–Hurwitz criteria and eigenvalues of the Jacobian matrix. Full article
Show Figures

Figure 1

14 pages, 285 KiB  
Article
Evolution of Quantum Systems with a Discrete Energy Spectrum in an Adiabatically Varying External Field
by Yury Belousov
Symmetry 2024, 16(11), 1466; https://doi.org/10.3390/sym16111466 - 4 Nov 2024
Viewed by 1394
Abstract
We introduce a new approach for describing nonstationary quantum systems with a discrete energy spectrum. The essence of this approach is that we describe the evolution of a quantum system in a time-dependent basis. In a sense, this approach is similar to the [...] Read more.
We introduce a new approach for describing nonstationary quantum systems with a discrete energy spectrum. The essence of this approach is that we describe the evolution of a quantum system in a time-dependent basis. In a sense, this approach is similar to the description of the system in the interaction representation. However, the time dependence of the basic states of the representation is determined not by the evolution operator with a time-independent Hamiltonian but by the eigenstates of the time-dependent Hamiltonian defined at the current time. The time dependence of the basic states of the representation leads to the appearance of an additional term in the Schrödinger equation, which in the case of slowly changing parameters of the Hamiltonian can be considered as a small perturbation. The adiabatic representation is suitable in cases where it is impossible to apply the standard interaction representation. The application of the adiabatic representation is illustrated by the example of two spins connected by a magnetic dipole–dipole interaction in a slowly varying external magnetic field. Full article
(This article belongs to the Section Physics)
19 pages, 2533 KiB  
Article
Fisher Information-Based Optimization of Mapped Fourier Grid Methods
by Sotiris Danakas and Samuel Cohen
Atoms 2024, 12(10), 50; https://doi.org/10.3390/atoms12100050 - 8 Oct 2024
Viewed by 1180
Abstract
The mapped Fourier grid method (mapped-FGM) is a simple and efficient discrete variable representation (DVR) numerical technique for solving atomic radial Schrödinger differential equations. It is set up on equidistant grid points, and the mapping, a suitable coordinate transformation to the radial variable, [...] Read more.
The mapped Fourier grid method (mapped-FGM) is a simple and efficient discrete variable representation (DVR) numerical technique for solving atomic radial Schrödinger differential equations. It is set up on equidistant grid points, and the mapping, a suitable coordinate transformation to the radial variable, deals with the potential energy peculiarities that are incompatible with constant step grids. For a given constrained number of grid points, classical phase space and semiclassical arguments help in selecting the mapping function and the maximum radial extension, while the energy does not generally exhibit a variational extremization trend. In this work, optimal computational parameters and mapping quality are alternatively assessed using the extremization of (coordinate and momentum) Fisher information. A benchmark system (hydrogen atom) is employed, where energy eigenvalues and Fisher information are traced in a standard convergence procedure. High-precision energy eigenvalues exhibit a correlation with the extrema of Fisher information measures. Highly efficient mapping schemes (sometimes classically counterintuitive) also stand out with these measures. Same trends are evidenced in the solution of Dalgarno–Lewis equations, i.e., inhomogeneous counterparts of the radial Schrödinger equation occurring in perturbation theory. A detailed analysis of the results, implications on more complex single valence electron Hamiltonians, and future extensions are also included. Full article
Show Figures

Figure 1

29 pages, 3713 KiB  
Article
New Coupled Optical Solitons to Birefringent Fibers for Complex Ginzburg–Landau Equations with Hamiltonian Perturbations and Kerr Law Nonlinearity
by Emmanuel Yomba and Poonam Ramchandra Nair
Mathematics 2024, 12(19), 3073; https://doi.org/10.3390/math12193073 - 30 Sep 2024
Cited by 1 | Viewed by 791
Abstract
In this study, we use an analytical method tailored for the in-depth exploration of coupled nonlinear partial differential equations (NLPDEs), with a primary focus on the dynamics of solitons. Traditional methods are quite effective for solving individual nonlinear partial differential equations (NLPDEs). However, [...] Read more.
In this study, we use an analytical method tailored for the in-depth exploration of coupled nonlinear partial differential equations (NLPDEs), with a primary focus on the dynamics of solitons. Traditional methods are quite effective for solving individual nonlinear partial differential equations (NLPDEs). However, their performance diminishes notably when addressing systems of coupled NLPDEs. This decline in effectiveness is mainly due to the complex interaction terms that arise in these coupled systems. Commonly, researchers have attempted to simplify coupled NLPDEs into single equations by imposing proportional relationships between various solutions. Unfortunately, this simplification often leads to a significant deviation from the true physical phenomena that these equations aim to describe. Our approach is distinctively advantageous in its straightforwardness and precision, offering a clearer and more insightful analytical perspective for examining coupled NLPDEs. It is capable of concurrently facilitating the propagation of different soliton types in two distinct systems through a single process. It also supports the spontaneous emergence of similar solitons in both systems with minimal restrictions. It has been extensively used to investigate a wide array of new coupled progressive solitons in birefringent fibers, specifically for complex Ginzburg–Landau Equations (CGLEs) involving Hamiltonian perturbations and Kerr law nonlinearity. The resulting solitons, with comprehensive 2D and 3D visualizations, showcase a variety of coupled soliton configurations, including several that are unprecedented in the field. This innovative approach not only addresses a significant gap in existing methodologies but also broadens the horizons for future research in optical communications and related disciplines. Full article
(This article belongs to the Section E4: Mathematical Physics)
Show Figures

Figure 1

113 pages, 1053 KiB  
Article
Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework
by Thomas Thiemann
Universe 2024, 10(9), 372; https://doi.org/10.3390/universe10090372 - 18 Sep 2024
Cited by 7 | Viewed by 1661
Abstract
In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, [...] Read more.
In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers. Full article
Show Figures

Figure A1

Back to TopTop