Search Results (762)

In this work, a theoretical study on the combined effects of an external electric field and a nonresonant intense laser field on the electronic properties of a quantum dot with a truncated cone shape is presented. This quantum dot was made from a type-II CdTe/CdSe heterostructure (core/shell). Using the effective mass approximation with parabolic bands and the finite element method, the Schrödinger equation was solved to analyze the confined states of electron, hole, and exciton. This study demonstrates the potential of combining nonresonant intense laser and electric fields to control confinement properties in semiconductor nanodevices, with potential applications in optoelectronics and quantum mechanics-related technologies. Full article

Traditional brain emulation approaches often rely on classical computational models that inadequately capture the stochastic, nonlinear, and potentially coherent features of biological neural systems. In this position paper, we introduce NeuroQ a quantum-inspired framework grounded in stochastic mechanics, particularly Nelson’s formulation. By reformulating the FitzHugh–Nagumo neuron model with structured noise, we derive a Schrödinger-like equation that encodes membrane dynamics in a quantum-like formalism. This formulation enables the use of quantum simulation strategies—including Hamiltonian encoding, variational eigensolvers, and continuous-variable models—for neural emulation. We outline a conceptual roadmap for implementing NeuroQ on near-term quantum platforms and discuss its broader implications for neuromorphic quantum hardware, artificial consciousness, and time-symmetric cognitive architectures. Rather than demonstrating a working prototype, this work aims to establish a coherent theoretical foundation for future research in quantum brain emulation. Full article

Optical solitons have emerged as a highly active research domain in nonlinear fiber optics, driving significant advancements and enabling a wide range of practical applications. This study investigates the dynamics of dark solitons in systems governed by the resonant nonlinear Schrödinger equation (RNLSE). For the RNLSE with third-order (3OD) and fourth-order (4OD) dispersions, the dark soliton solution of the equation in the (1+1)-dimensional case is derived using the F-expansion method, and the analytical study is extended to the (2+1)-dimensional case via the self-similar method. Subsequently, the nonlinear equation incorporating perturbation terms is further studied, with particular attention given to the dark soliton solutions in both one and two dimensions. The soliton dynamics are illustrated through graphical representations to elucidate their propagation characteristics. Finally, modulation instability analysis is conducted to evaluate the stability of the nonlinear system. These theoretical findings provide a solid foundation for experimental investigations of dark solitons within the systems governed by the RNLSE model. Full article

In this paper, we investigate the memory effects introduced by the time-fractional Schrödinger equation proposed by Naber on quantum entanglement and quantum dense coding under amplitude damping noise. Two formulations are analyzed: one with fractional operations applied to the imaginary unit and one without. Numerical results show that the formulation without fractional operations on the imaginary unit may be more suitable for describing non-Markovian (power-law) behavior in dissipative environments. This finding provides a more physically meaningful interpretation of the memory effects in time-fractional quantum dynamics and indirectly addresses fundamental concerns regarding the violation of unitarity and probability conservation in such frameworks. Our work offers a new perspective for the application of fractional quantum mechanics to realistic open quantum systems and shows promise in supporting the theoretical modeling of decoherence and information degradation. Full article

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

This article reviews several numerical methods for the time-dependent Schrödinger Equation (TDSE). We consider both the most commonly used approach—short-time propagation, which solves the TDSE by assuming that the Hamiltonian is time-independent over sufficiently small (time) intervals—as well as a number of higher-order alternatives. Our goal is to dispel the notion that the latter are too computationally demanding for practical use. To that end, we cover methods whose numerical building blocks are shared by short-time propagators or can be handled by standard libraries. Moreover, we make the case that these methods are best positioned to take advantage of parallel computing environments. One of the alternatives considered is a “double DVR” solver, which applies an expansion in a product basis of functions in space and time to obtain a solution (over all space and at multiple time points simultaneously) with a single linear system solve. To our knowledge, and despite its simplicity, this approach has not previously been applied to the TDSE. Full article

The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse problems of 1D and 2D CNLSEs. Specifically, a hybrid optimization strategy incorporating exponential learning rate decay is proposed to reconstruct data-driven solutions, including bright soliton for the 1D case and bright, dark soliton as well as periodic solutions for the 2D case. Moreover, we conduct a comprehensive discussion on varying parameter configurations derived from the equations and their corresponding solutions to evaluate the adaptability of the PINNs framework. The effects of residual points, network architectures, and weight settings are additionally examined. For the inverse problems, the coefficients of 1D and 2D CNLSEs are successfully identified using soliton solution data, and several factors that can impact the robustness of the proposed model, such as noise interference, time range, and observation moment are explored as well. Numerical experiments highlight the remarkable efficacy of PINNs in solution reconstruction and coefficient identification while revealing that observational noise exerts a more pronounced influence on accuracy compared to boundary perturbations. Our research offers new insights into simulating dynamics and discovering parameters of nonlinear chiral systems with deep learning. Full article

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the Mönch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results. Full article

This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Pohozaev identities, and prove the existence of radial, decreasing ground states, while showing nonexistence in the $L^2$-critical case. For $L^2$-supercritical exponents, we identify parameter regimes where ground states exist, characterized by a negative Lagrange multiplier. The analysis combines variational methods, scaling techniques, and the careful study of fibering maps to address challenges posed by competing nonlinearities and nonlocal interactions. Full article

Darboux transformations are relations between the eigenfunctions and coefficients of a pair of linear differential operators, while Painlevé equations are nonlinear ordinary differential equations whose solutions arise in diverse areas of applied mathematics and mathematical physics. Here, we describe the use of confluent Darboux transformations for Schrödinger operators, and how they give rise to explicit Wronskian formulae for certain algebraic solutions of Painlevé equations. As a preliminary illustration, we briefly describe how the Yablonskii–Vorob’ev polynomials arise in this way, thus providing well-known expressions for the tau functions of the rational solutions of the Painlevé II equation. We then proceed to apply the method to obtain the main result, namely, a new Wronskian representation for the Ohyama polynomials, which correspond to the algebraic solutions of the Painlevé III equation of type $D_7$. Full article

This article examines a hybrid generation of cryptographic keys, whose novelty lies in the fusion of a multiscale subkey generation with prime sieve and subkeys inspired by quantum mechanics. It combines number theory with techniques emulated and inspired by quantum mechanics, also based on two demons capable of dynamically modifying the cryptographic model. The integration is structured through the JDL. In fact, a specific information fusion model is used to improve security. As a result, the resulting key depends not only on the individual components, but also on the fusion path itself, allowing for dynamic and cryptographically agile configurations that remain consistent with quantum mechanics-inspired logic. The proposed approach, called quantum and prime information fusion (QPIF), couples a simulated quantum entropy source, derived from the numerical solution of the Schrödinger equation, with a multiscale prime number sieve to construct multilevel cryptographic keys. The multiscale sieve, based on recent advances, is currently among the fastest available. Designed to be compatible with classical computing environments, the method aims to contribute to cryptography from a different perspective, particularly during the coexistence of classical and quantum computers. Among the five key generation algorithms implemented here, the ultra-optimised QRNG offers the most effective trade-off between performance and randomness. The results are validated using standard NIST statistical tests. This hybrid framework can also provide a conceptual and practical basis for future work on PQC aimed at addressing the challenges posed by the quantum computing paradigm. Full article

In this article, we describe an approach to teaching introductory quantum mechanics and machine learning techniques. This approach combines several key concepts from both fields. Specifically, it demonstrates solving the Schrödinger equation using the discrete-variable representation (DVR) technique, as well as the architecture and training of neural network models. To illustrate this approach, a Python-based Jupyter notebook is developed. This notebook can be used for self-learning or for learning with an instructor. Furthermore, it can serve as a toolbox for demonstrating individual concepts in quantum mechanics and machine learning and for conducting small research projects in these areas. Full article

The primary objective of this paper is to derive a non-relativistic system of equations for a spin-2 particle in the presence of an external Coulomb field, solve these equations, and determine the corresponding energy spectra. We begin with the known radial system of 39 equations formulated for a free spin-2 particle and modify it to incorporate the effects of the Coulomb field. By eliminating the 28 components associated with vector and rank-3 tensor fields, we reduce the system to a set of 11 second-order equations related to scalar and symmetric tensor components. In accordance with parity constraints, this system naturally groups into two subsystems consisting of three and eight equations, respectively. To perform the non-relativistic approximation, we employ the method of projective operators constructed from the matrix ${\Gamma }^0$ of the original matrix equation. This approach allows us to derive two non-relativistic subsystems corresponding to the parity restrictions, comprising two and three coupled differential equations. Through a linear similarity transformation, we further decouple these into five independent equations with a Schrödinger-type non-relativistic structure, leading to explicit energy spectra. Special attention is given to the case of the minimal quantum number of total angular momentum, $j=0$, which requires separate consideration. Full article

We investigate a generalized quantum Schrödinger equation in a comb-like structure that imposes geometric constraints on spatial variables. The model is extended by the introduction of nonlocal and fractional potentials to capture memory effects in both space and time. We consider four distinct scenarios: (i) a time-dependent nonlocal potential, (ii) a spatially nonlocal potential, (iii) a combined space–time nonlocal interaction with memory kernels, and (iv) a fractional spatial derivative, which is related to distributions asymptotically governed by power laws and to a position-dependent effective mass. For each scenario, we propose solutions based on the Green’s function for arbitrary initial conditions and analyze the resulting quantum dynamics. Our results reveal distinct spreading regimes, depending on the type of non-locality and the fractional operator applied to the spatial variable. These findings contribute to the broader generalization of comb models and open new questions for exploring quantum dynamics in backbone-like structures. Full article

This is a numerical investigation of optical and electronic characteristics of GaAs spherical quantum dots based on single and double quartic potentials and presenting a hydrogenic impurity at their center. The radial Schrödinger equation was solved using the finite difference method (FDM) to obtain the energy levels and the wavefunctions. These physical quantities were then used to compute the dipole matrix elements, the total optical absorption coefficient (TOAC), and the binding energies. The impact of the structural parameters in the confining potentials on the red and blue shifts of the TOAC is discussed in the presence and absence of hydrogenic impurity. Our results indicate that the structural parameter $k$ in both potentials plays a crucial role in tuning the TOAC. In the case of single quartic potential, increasing $k$ produces a blue shift; however, its augmentation in the case of double quartic potential displays a blue shift at first, and then a red shift. Furthermore, the augmentation of the parameter $k$ can control the binding energies of the two lowest states, ($1s$) and ($1p$). In fact, enlarging this parameter reduces the binding energies and converges them to constant values. In general, the modification of the potential’s parameters, which can engender two shapes of confining potentials (single quartic and double quartic), enables the experimenters to control the desired energy levels and consequently to adjust and select the suitable TOAC between the two lowest energy states (ground ($1s$) and first excited ($1p$)). Full article