Search Results (139)

The unique properties of graphene have allowed for the development of graphene-based field-effect transistors (GFETs) for applications in biosensors and chemical devices. However, the modeling and optimization of GFET performance exhibit great challenges. Herein, we propose a quantum transport simulation model for graphene-based field-effect transistors (GFETs) implemented in the open-source Octave programming language. The proposed simulation model (named SimQ) combines the Landauer–Büttiker formalism with self-consistent Schrödinger–Poisson solutions, enabling reliable simulations of transport phenomena. Our approach agrees well with established models, achieving Landauer–Büttiker transmission and tunneling transmission of 0.28 and 0.92, respectively, which are validated against experimental data. The model can predict key GFET characteristics, including carrier mobilities (500–4000 cm²/V·s), quantum capacitance effects, and high-frequency operation (80–100 GHz). SimQ offers detailed insights into charge distribution and wave function evolution, achieving an enhanced computational efficiency through optimized algorithms. Our work contributes to the modeling of graphene-based field-effect transistors, providing a flexible and accessible simulation platform for designing and optimizing GFETs with potential applications in the next generation of electronic devices. 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

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

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

From an arbitrary definition of operators inspired by oscillators of Virasoro, an algebra is derived. It fits the structure of Virasoro algebra with null central charge or Witt algebra. The resulting formalism has yielded commutators with a dependence on integer numbers, and it follows the Witt-like algebra. Also, the quantum mechanics evolution operator for the case of the quantum harmonic oscillator was identified. Furthermore, the Schrödinger equation was systematically derived under the present framework. When operators are expressed in the framework of Hilbert space states, the resulting Witt algebra seems to be proportional to the well-known canonical commutation relation. This has demanded the development of a formalism based on arbitrary and physical operators as well as well-defined rules of commutation. The Witt-like was also redefined through the direct usage of the uncertainty principle. The results of the paper might suggest that Witt algebra encloses not only quantum mechanics’ fundamental commutator but also other unexplored relations among quantum mechanics observables and Witt algebra. Full article

We will show, in any space dimension $d\ge 3$, the decay and scattering in the energy space for the solution to the damped nonlinear Schrödinger equation posed on ${\mathbb{R}}^d\times \mathbb{T}$ and initial data in $H^1({\mathbb{R}}^d\times \mathbb{T})$. We will also derive new bilinear Morawetz identities and corresponding localized Morawetz estimates. Full article

This research focuses on the theoretical asymptotic stability and long-time decay of the zero solution for a system of time-fractional nonlinear Schrödinger delay equations (NSDEs) in the context of the Caputo fractional derivative. Using the fractional Halanay inequality, we demonstrate theoretically when the considered system decays and behaves asymptotically, employing an energy function in the sense of the L₂ norm. Together with utilizing the finite difference method for the spatial variables, we investigate the long-time stability for the semi-discrete system. Furthermore, we operate the L1 scheme to approximate the Caputo fractional derivative and analyze the long-time stability of the fully discrete system through the discrete energy of the system. Moreover, we demonstrate that the proposed numerical technique energetically captures the long-time behavior of the original system of NSDEs. Finally, we provide numerical examples to validate the theoretical results. Full article

In the noisy intermediate-scale quantum (NISQ) era, as the scale of existing quantum hardware continues to expand, the demand for effective methods to schedule quantum gates and minimize the number of operations has become increasingly urgent. To address this demand, the Quantum Firefly Algorithm (QFA) has been designed by incorporating quantum information into the traditional firefly algorithm. This integration enables fireflies to explore multiple positions simultaneously, thereby increasing search space coverage and utilizing quantum tunneling effects to escape local optima. Through wave function evolution and collapse mechanisms described by the Schrödinger equation, a balance between exploring new solutions and exploiting known solutions is achieved by the QFA. Additionally, random perturbation steps are incorporated into the algorithm to enhance search diversity and prevent the algorithm from being trapped in local optima. In quantum circuit scheduling problems, the QFA optimizes quantum gate operation sequences by evaluating the fitness of scheduling schemes, reducing circuit depth and movement operations, while improving parallelism. Experimental results demonstrate that, compared to traditional algorithms, the QFA reduces SWAP gates by an average of 44% and CNOT gates by an average of 16%. When compared to modern algorithms, it reduces SWAP gates by an average of 7% and CNOT gates by an average of 12%. Full article

This study presents the synthesis of manganese molybdenum tetraoxide (MnMoO₄)-based nanoparticles and then their experimental demonstration as saturable absorbers (SAs) in erbium-doped fiber lasers (EDFLs). The MnMoO₄ nanoparticles were prepared and then embedded between the fiber ferrule to act as an SA to generate Q-switched pulsed operation in EDFLs. For the characterization, scanning electron microscopy (SEM) was employed to confirm the particle size of the prepared MnMoO₄ nanoparticles, and the SA optical properties were further investigated by measuring their modulation depth and saturation intensity. By implementing the prepared SA within the cavity, the measured results revealed that under pump power ranging from 28 to 312.5 mW, the laser exhibited Q-switched pulse durations varying from 15.22 to 2.35 µs and repetition rates spanning from 24.98 to 88.11 kHz. The proposed EDFL system delivered an average output power between 0.128 and 2.95 mW, pulse energies ranging from 5.12 to 33.49 nJ, and peak power from 0.281 to 6.26 mW. The laser stability was also confirmed by continuously noticing the pulse duration, emission wavelengths, and pulse repetition rates for 4 h. Finally, a numerical model based on a nonlinear Schrödinger equation (NLSE) was employed to validate both experimental and theoretical results of the passive Q-switched EDFL. These findings highlight the potential of EDFLs utilizing MnMoO₄-based SAs for potential applications in pulsed laser sources. Full article

This second part of this companion paper the Carnot cycle is analyzed trying to investigate the similarities and differences between a framework related to thermodynamics and one related to information theory. The parametric Schrodinger equations are the starting point for the framing. In the thermodynamics frame, a new interpretation of the free energy in the isothermal expansion and a new interpretation of the entropy in the adiabatic phase are highlighted. The same Schrodinger equations are then applied in an information theory framework. Again, it is shown that a cycle can be constructed with a diagram that presents the Lagrange parameter and the average codeword length as coordinates. In this case the adiabatic phase consists of a transcoding operation and the cycle as a whole shows a positive or negative balance of information. In conclusion, the Carnot cycle continues to be a source of knowledge of complex systems in which entropy plays a central role. Full article

In his recent paper, Vlatko Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called ‘local factors’ in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, the Schrödinger-picture locality ultimately depends on the explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined. Full article

C+L+S multiband (MB) optical transmission has the potential to increase the capacity of optical transport networks, and thus, it is a possible solution to cope with the traffic increase expected in the years to come. However, the introduction of MB optical technology needs to come together with the needed tools that support network planning and operation. In particular, quality of transmission (QoT) estimation is needed for provisioning optical MB connections. In this paper, we concentrate on modelling MB optical transmission for provide fast and accurate QoT estimation and propose machine learning (ML) approaches based on neural networks, which can be easily integrated into an optical layer digital twin (DT) solution. We start by considering approaches that can be used for accurate signal propagation modelling. Even though solutions such as the split-step Fourier method (SSFM) for solving the nonlinear Schrödinger equation (NLSE) have limited application for QoT estimation during provisioning because of their very high complexity and time consumption, they could be used to generate datasets for ML model creation. However, even that can be hard to carry out on a fully loaded MB system with hundreds of channels. In addition, in MB optical transmission, interchannel stimulated Raman scattering (ISRS) becomes a major effect, which adds more complexity. In view of that, the fourth-order Runge–Kutta in the interaction picture (RK4IP) method, complemented with an adaptive step size algorithm to further reduce the computation time, is evaluated as an alternative to reduce time complexity. We show that RK4IP provided an accuracy comparable to that of the SSFM with reduced computation time, which enables its application for MB optical transmission simulation. Once datasets were generated using the adaptive step size RK4IP method, two ML modelling approaches were considered to be integrated in the OCATA DT, where models predict optical signal propagation in the time domain. Being able to predict the optical signal in the time domain, as it will be received after propagation, opens opportunities for automating network operation, including connection provisioning and failure management. In this paper, we focus on comparing the proposed ML modelling approaches in terms of the models’ general and QoT estimation accuracy. Full article

We investigate the nonstationary parabolic Anderson problem ${\displaystyle \frac{\partial u}{\partial t}}=\varkappa \mathcal{L}u(t,x)+{\xi }_t(x)u(t,x),u(0,x)\equiv 1,(t,x)\in [0,\infty )\times Z^d$ where $\varkappa \mathcal{L}$ denotes a nonlocal Laplacian and ${\xi }_t(x)$ is a correlated white-noise potential. The irregularity of the solution is linked to the upper spectrum of certain multiparticle Schrödinger operators that govern the moment functions $m_p(t,x_1,x_2,\cdots ,x_p)=⟨u(t,x_1)u(t,x_2)\cdots u(t,x_p)⟩$. First, we establish a weak form of intermittency under broad assumptions on $\mathcal{L}$ and on a positive-definite noise correlator $B=B(x)$. We then examine strong intermittency, which emerges from the existence of a positive eigenvalue in a related lattice Schrödinger-type operator with potential B. Here, B does not have to be positive definite but must satisfy $\sum B(x)\ge 0$. The presence of such an eigenvalue intensifies the growth properties of the second moment $m_2$, revealing a more pronounced intermittent regime. Full article

We study an interesting superization problem of integrable nonlinear dynamical systems on functional manifolds. As an example, we considered a quantum many-particle Schrödinger–Davydov model on the axis, whose quasi-classical reduction proved to be a completely integrable Hamiltonian system on a smooth functional manifold. We checked that the so-called “naive” approach, based on the superization of the related phase space variables via extending the corresponding Poisson brackets upon the related functional supermanifold, fails to retain the dynamical system super-integrability. Moreover, we demonstrated that there exists a wide class of classical Lax-type integrable nonlinear dynamical systems on axes in relation to which a superization scheme consists in a reasonable superization of the related Lax-type representation by means of passing from the basic algebra of pseudo-differential operators on the axis to the corresponding superalgebra of super-pseudodifferential operators on the superaxis. Full article