Ginzburg-Landau Equation Research Articles

Effect of defects on the thermomagnetic instabilities of superconducting radio-frequency cavities with a multilayer structure

Abstract Vortex motion can lead to significant energy dissipation, resulting in hot spots and thermomagnetic instabilities that are detrimental to the application of superconductors. This paper presents a theoretical examination of thermomagnetic instabilities triggered by vortex motion within a Nb$_{3}$Sn-I-Nb cavity featuring a multilayer structure. The investigation is conducted using Ginzburg-Landau theory in conjunction with the heat diffusion equation. The numerical simulations align well with experimental data from Nb$_{3}$Sn superconducting cavities. Given that the performance of SRF cavities is highly sensitive to various defects, this study also considers the interaction between vortices and these defects. It reveals the impact of edge cracks and impurities on temperature rise and the quality factor. The findings indicate that edge cracks significantly reduce the threshold field for thermomagnetic instability in superconducting radio-frequency (SRF) cavities. The performance of SRF cavities is influenced not only by the RF field amplitude and frequency but also by the length and number of edge cracks. These results offer valuable insights for evaluating the performance of SRF cavities subjected to RF fields.

Superconducting multi-vortices and a novel BPS bound in chiral perturbation theory

We derive a novel BPS bound from chiral perturbation theory minimally coupled to electrodynamics at finite isospin chemical potential. At a critical value of the isospin chemical potential, a system of three first-order differential field equations (which implies the second-order field equations) for the gauge field and the hadronic profile can be derived from the requirement to saturate the bound. These BPS configurations represent magnetic multi-vortices with quantized flux supported by a superconducting current. The corresponding topological charge density is related to the magnetic flux density, but is screened by the hadronic profile. Such a screening effect allows to derive the maximal value of the magnetic field generated by these BPS magnetic vortices, being Bmax = 2, 04 × 1014 G. The solution for a single BPS vortex is discussed in detail, and some physical consequences, together with the comparison with the magnetic vortices in the Ginzburg-Landau theory at critical coupling, are described.

Extrinsic dielectric response due to domain wall motion in ferroelectric BaTiO[formula omitted]

BaTiO3 (BTO) is a prototypical perovskite ferroelectric, whose dielectric permittivity and loss spectra – which are strongly temperature and frequency dependent – include contributions from inhomogeneous polarization patterns, with domain walls (DWs) being the most common types. In order to elucidate how DWs influence dielectric response, we utilized a continuum approach based on the Landau–Ginzburg theory to model field-dependent properties of polydomain tetragonal phase of BTO near room temperature and above. A system with 180∘ DWs was evaluated as a case study, with both position-resolved and volume-averaged dielectric susceptibility and loss computed at different temperatures for a range of applied field frequencies and amplitudes. Our results demonstrate that cooperative dipole fluctuations in the vicinity of the DW provide a large (extrinsic) contribution to the system dielectric response relative to the intrinsic contribution stemming from within the domain. Dynamics of the DW profile fluctuations under applied field can be represented by a combination of breathing and sliding vibrational motions, with each exhibiting distinct dependence on the field frequency and amplitude. The implications of this behavior are important for understanding and improving control of coupled functional properties in ferroelectric materials, including their dielectric, electromechanical, and electrooptical responses. Furthermore, this investigation provides a computational benchmark for future studies and can be readily extended to other topological polarization patterns in ferroelectrics.

Circularly polarized radiation to control the superconducting states: Stability analysis.

Recently, the use of circularly polarized radiation for on-demand switching between distinct quantum states in a superconducting nanoring exposed to half-quantum magnetic flux has been proposed. However, the effectiveness of this method depends on the system's stability against local variations in the superconducting characteristics of the ring and flux fluctuations. In this study, we utilize numerical simulations based on the time-dependent Ginzburg-Landau (TDGL) equation to evaluate the influence of these inevitable factors on the switching behavior. The results obtained demonstrate that the switching phenomena remain remarkably robust, providing confidence in their experimental observation.

Free evolution in the Ginzburg-Landau equation and other complex diffusion equations

Abstract New ordinary differential equations (ODEs) for the evolution of spectral components are derived from the complex Ginzburg-Landau equation (CGLe) for one-dimensional spatial domains without boundaries (free evolution) and with one fixed boundary (semi-free evolution). For such evolution, a complex or imaginary diffusion term creates a tendency for waves to lengthen. This requires a novel ansatz and auxiliary condition that treat wavenumbers as time-varying. The ansatz consists of a discrete spatial Fourier transform modified with a time-dependent wavenumber for the peak spectral component. The wavenumbers of the other components are fixed relative to this wavenumber. The new auxiliary condition is the terminal condition for complex diffusion (after wavenumbers evolve to zero, they remain at zero). The derived free and semi-free ODEs are solved along characteristic lines located symmetrically about a fixed spatial point. Waves lengthen with time away from this point in both directions. Laboratory experiments on the formation of channel sandbars, theoretically described by the CGLe, show two regions whose evolutionary behaviour is qualitatively predicted by the free and semi-free evolution equations. This analysis applies to other time-dependent partial differential equations with complex or imaginary diffusion terms. New freely evolving solutions are derived for the complex heat equation and Schrödinger equation (linear and nonlinear).

Dynamics of Vortex Matter in 2D Gapless Superconducting Materials with Impurities.

The recent interest in using ultrafast single-photon detectors in research and commercial applications has garnered significant attention from the scientific community. The dynamic event in the detection process consists of a photon causing local destruction of the order parameter, and then the applied current dissipates heat, bringing the material even more out of the superconducting state and then spiking a voltage peak in a measurement device. We investigated the role of superconducting and thermal parameters of the Generalized Time-Dependent Ginzburg-Landau (GTDGL) theory within the event of the first vortex penetration and the thermal dissipation in superconductors near the critical temperature. Moreover, in the vicinity of the Bogomolny point of the static Ginzburg-Landau theory, where κ ≈ 1/√2 and T → Tc, it has been found severely different vortex profiles. We point out that within the GTDGL theory, the presence of impurities (usual or paramagnetic) influences flux penetration and enhances the dissipation of heat, causing anomalous vortex configurations.

Thermal gradient-induced critical current degradation in mesoscopic superconducting thin film

Abstract Superconducting materials inevitably suffer from the sudden change of temperature in localized areas in practical applications, and the concomitant thermal gradient may be detrimental to their performance. Critical current density is a key factor affecting the performance of superconductors. However, the effect of thermal gradient on the critical current density has not been identified. Here, by combining the time-dependent Ginzburg–Landau equations and the heat transfer equation, the thermal gradient and magnetic field dependence of the critical current density are systematically investigated and rationalized by exploring the behavior of vortex and magnetization. For lower magnetic fields, it is found that the thermal gradients strongly reduce the local surface barriers, which inhibits vortex entry and movement, leading to a rapid deterioration of the current-carrying capability. Under moderate magnetic fields, the critical current density corresponding to higher thermal gradients decreases more slowly with increasing magnetic field, which results from the thermal gradient-induced entry and moving of vortices along the current direction. As the magnetic field continues to increase, the variation of the critical current density transitions into a platform period and even slightly rises. The enhanced critical current is primarily attributed to the excess entry of vortices, which increases the surface barrier of the sample. With the further increase in the magnetic field, the critical current density continues to decrease due to increased magnetic field penetration. These results unveil the fundamental interplay between thermal gradients, external magnetic field, vortex, magnetization and critical current density, and provide a theoretical basis for understanding the heat-induced quenching of mesoscopic superconducting thin films in practical applications.

Numerical Modeling of Vortex-Based Superconducting Memory Cells: Dynamics and Geometrical Optimization.

The lack of dense random-access memory is one of the main obstacles to the development of digital superconducting computers. It has been suggested that AVRAM cells, based on the storage of a single Abrikosov vortex-the smallest quantized object in superconductors-can enable drastic miniaturization to the nanometer scale. In this work, we present the numerical modeling of such cells using time-dependent Ginzburg-Landau equations. The cell represents a fluxonic quantum dot containing a small superconducting island, an asymmetric notch for the vortex entrance, a guiding track, and a vortex trap. We determine the optimal geometrical parameters for operation at zero magnetic field and the conditions for controllable vortex manipulation by short current pulses. We report ultrafast vortex motion with velocities more than an order of magnitude faster than those expected for macroscopic superconductors. This phenomenon is attributed to strong interactions with the edges of a mesoscopic island, combined with the nonlinear reduction of flux-flow viscosity due to the nonequilibrium effects in the track. Our results show that such cells can be scaled down to sizes comparable to the London penetration depth, ∼100 nm, and can enable ultrafast switching on the picosecond scale with ultralow energy per operation, ∼10-19 J.

Analysis of a Crank–Nicolson fast element-free Galerkin method for the nonlinear complex Ginzburg–Landau equation

A fast element-free Galerkin (EFG) method is proposed in this paper for solving the nonlinear complex Ginzburg–Landau equation. A second-order accurate time semi-discrete system is presented by using the Crank–Nicolson scheme for the temporal discretization, and then a meshless fully discrete system is established by using the EFG method for the spatial discretization. In the proposed EFG method, Nitsche’s technique is used to impose the essential boundary conditions in a weak sense, and the reproducing kernel gradient smoothing integration is used to accelerate the calculation. Theoretical errors for the time semi-discrete system and the fully discrete EFG system are analyzed in detail. Optimal error estimates of the fully discrete Crank–Nicolson EFG method are obtained in both L2 and H1 norms. Numerical results validate the theoretical results and the effectiveness of the method.

Optical solitons of the (1+1)-dimensional perturbed complex Ginzburg–Landau equation having the Kerr law in the absence of the chromatic dispersion

Optical solitons of the (1+1)-dimensional perturbed complex Ginzburg–Landau equation having the Kerr law in the absence of the chromatic dispersion

Fully stabilized Minkowski vacua in the 26 Landau-Ginzburg model

We study moduli stabilization via fluxes in the 26 Landau-Ginzburg model. Fluxes not only give masses to scalar fields but can also induce higher order couplings that stabilize massless fields. We investigate this for several different flux choices in the 26 model and find two examples that are inconsistent with the Refined Tadpole Conjecture. We also present, to our knowledge, the first 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 Minkowski solution in string theory without any flat direction.

Impact of magnetic field variation on thermally annealed tantalum-filled vertical superconducting interconnects for scalable quantum computing systems

Efforts to scale down advanced quantum processors with more numbers of qubits offer challenges since the integration of qubits is a significant obstacle in the path. Superconducting vertical interconnects in 3D IC integration can provide a crucial solution for wiring complexities, as shorter interconnections reduce energy loss when working in cryogenic conditions with better signal fidelity. Using the time-dependent Ginzburg–Landau equation, this simulation study analyzes vertical superconducting interconnects filled with materials like tantalum, niobium, and thermally annealed tantalum. It also investigates how London penetration depth (temperature-dependent) and magnetic fields affect Cooper pair density and, consequently, current density.

Correction: Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

Correction: Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

Pseudo-proper two-dimensional electron gas formation

Abstract In spite of the interest in the two-dimensional electron gases (2DEGs) experimentally found at surfaces and interfaces, important uncertainties remain about the observed insulator–metal transitions (IMTs). Here we show how an explicit pseudo-proper coupling of carrier sources with a relevant soft mode significantly affects the transition. The analysis presented here for 2DEGs at polar interfaces is based on group theory, Landau–Ginzburg theory, and illustrated with first-principles calculations for the prototypical case of the LaAlO 3 / SrTiO 3 interface, for which such a structural transition has recently been observed. This direct coupling implies that the appearance of the soft mode is always accompanied by carriers. For sufficiently strong coupling an avalanche-like first-order IMT is predicted.

Advancing superconductivity research: Insights from numerical simulations of potassium fullerenide-60 and gold and with Ginzburg-Landau theory

There are many types of superconductors, including gold ormus and some fullerene derivatives. Gold can become a superconductor at extremely low temperatures (<1 K), allowing it to conduct electricity without resistance. While not as commonly used as materials like niobium or lead, gold superconductors are valuable for research and development in superconductivity. Fullerene derivatives like potassium fullerenide-60 also exhibit high superconductivity. Limited studies have been conducted on both gold ormus and superconducting fullerene derivatives. Our study of numerical simulations of the Ginzburg-Landau theory in superconductors for gold ormus and potassium fullerenide-60 has yielded important results. We have successfully simulated class-I and class-II superconducting gold ormus, as well as potassium fullerenide-60, using the Runge-Kutta fourth order method. Our analysis demonstrates the convergence of our simulation outcomes and highlights the importance of considering truncation error and selecting appropriate step sizes for accurate results. The periodic factor of penetration (PFP) for each superconductor has been determined, with class-I superconducting gold having a PFP of 250 nm, class-II superconducting gold having a PFP of 566.2 nm, and potassium fullerenide-60 having a PFP of 1.374 nm. Additionally, our study reveals the relationship between the periodic penetration factor and the length of the penetration depth, showing that the PFP reaches a minimum value at a penetration depth length of 130 nm. Overall, our findings contribute to a better understanding of superconductivity in gold ormus and potassium fullerenide-60, emphasizing the importance of accurate numerical simulations for studying complex physical phenomena. Our study confirmed the accuracy of the Runge-Kutta fourth-order method in simulating superconductors. By examining the PFP for various superconducting materials, we identified trends in penetration depth, shedding light on superconductivity. Our simulations give valuable insights for advancing research in this field, with the Runge-Kutta fourth-order method striking a balance between accuracy and efficiency. Careful parameter adjustment ensures reliable simulations and contributes to progress in superconductivity research.

Dynamics of N-elastically longitudinal coupled rotating pendulums with smooth and discontinuous nonlinearities: Generation of chaotic bursting with many orbits as a solution

The dynamics of a mechanical network, consisting of a certain number (N) of cells, in which each unit cell consists of the irrational coupling of a simple pendulum and inclined mass-spring oscillator, is investigated. The single cell was recently introduced by Ning Han and Qingjie Cao, and it has strong irrational nonlinearity, exhibiting smooth and discontinuous characteristics due to the geometry configuration. The obtained network has a large degree of freedom and consequently has richer dynamics as compared to a single one. The set of discrete equations of this network is found, while the first equation is driven by an external sinusoidal force; the variables here are the angles between the vertical direction and the directions of mass in each unit cell. By using the non-driven version of this set of equations, the equilibrium points are found as well as their stability using the Jacobian matrix. Then, by using the multiple time scale method, the solutions of the set of the network equations are found for weak amplitude oscillations of the system, while the large amplitude solutions are found numerically, showing the ability of the network to transform the shape of some solutions at the input to other forms as the signals evolve in the network. One notices the generation of simple chaotic signals as well as the train of impulse signals. What is important here is the generation of the chaotic bursting with many orbits by the system, which are the simultaneous oscillations around several fixed points. For the case of numerous cells, the system can be used as a waveguide; this is why the set of the equation of the network is reduced to the extended complex Ginzburg Landau (ECGL) equation, with complex nonlinear dispersion and nonlocality terms, using the Tanuiti's reduction perturbation methods. The dissipative dark compacton and peakon as solutions for the ECGL equation are then found. The input-output matching of the network is next investigated via the transfer function of the system near the equilibrium points. The inverse Fourier transform of the transfer function multiplied by the Fourier transform of the input sinusoidal force gives the solution of the network equation for low amplitude oscillations. Finally, the supratransmission condition is studied, leading to the fact that the input sinusoidal signal with frequency nearly inside the forbidden gap zone gradually transforms into the train of chaotic bursting.

An investigation of rapid surface melting in nanowires

The investigation into virtual melting phenomena in nanowires holds significant relevance owing to its profound impact on material durability under extreme loading conditions. Thus, the exploration of this pivotal plastic deformation mechanism is undertaken utilizing the phase-field methodology. Employing a monolithic solver, we solve the coupled highly nonlinear time-dependent Ginzburg–Landau equation and dynamic elasticity equation. Our analysis encompasses the consideration of surface tension stress in conjunction with a coherent solid–liquid interface subjected to uniaxial transformation strain, thereby unveiling intriguing facets of melting phenomena. The investigation delves into the influence of transformation strain, kinetic coefficient, and temperature on the thickness of the solid–liquid interface and its corresponding velocity. This analysis is conducted through meticulous comparison with existing experimental data and analytical solutions. Moreover, employing the phase-field method yields precise descriptions of the system kinetics, capturing virtual melting phenomena in both pristine and flawed nanowire configurations.

Non-Hermitian mode management in periodically modulated waveguide amplifiers

We propose an efficient mode management scheme in active nonlinear multimode fibers based on non-Hermitian potentials in the longitudinal direction with an antisymmetric transverse profile. The proposal takes advantage of the nonlinear saturation toward particular mode configurations, which can be tuned by the non-Hermitian potential. We demonstrate flexible control of the beam profile within the parameter space of the applied potential with various possibilities, such as improving the beam quality by condensing photons to the lowest order Hermite mode, exciting higher order modes, or engineering a desired mode profile as a combination of modes. The effect is also analytically predicted using a mode-expansion approach, showing good agreement with the full model calculations based on the complex Ginzburg–Landau equation. This study was performed for 1D planar guiding structures, yet the results can be extended to 2D fibers and could be very useful in applications of fiber amplifiers and lasers.

The role of temperature-dependent solubility in the stability of thermohaline convection within a Voigt-fluid layer

The study focuses on both linear and weakly nonlinear stability analyses of thermohaline convection within a Voigt-fluid layer, considering the effects of temperature-dependent solubility. Analytical methods are employed to derive conditions for the onset of both stationary and oscillatory convection. The linear stability analysis is performed using normal mode analysis to explore how various physical parameters influence the initiation of convection. Notably, unlike Newtonian fluids, the Navier-Stokes-Voigt fluid suppresses the typical quasiperiodic bifurcation from a steady state. To gain deeper insight into the onset of convection, a weakly nonlinear stability analysis is conducted using a modified perturbation method, leading to the Ginzburg-Landau equation. This reveals the potential for subcritical instability, a phenomenon not fully captured by linear analysis alone. Additionally, the study examines how different physical parameters affect convective heat and mass transfer, with findings that align with previous studies in specific limiting cases.

Non trivial solutions for a system of coupled Ginzburg-Landau equations

This article addresses both the existence and properties of non-trivial solutions for a system of coupled Ginzburg-Landau equations derived from nematic-superconducting models. Its main goal is to provide a thorough numerical description of the region in the parameter space containing solutions that behave as a mixed (non trivial) nematic-superconducting state along with a rigorous proof for the existence of this region. More precisely, the rigorous approach establishes that the parameter space is divided into two regions with qualitatively different properties, according to the magnitude of the coupling constant: for small values (weak coupling), there is a unique non-trivial solution, and for large values (strong coupling), only trivial solutions exist. In addition, using a shooting method-based numerical approach, the profiles for the nematic and superconducting components of the non trivial solution are given, together with an algorithm computing the transition values representing the boundaries for the weak coupling region: from superconducting to mixed, and from mixed to nematic. Finally, numerical evidence is given for the existence of a third region, related to neither a small nor a strong coupling parameter (medium coupling) for which multiple non trivial solutions exist.