scholarly journals Charged fixed point in the Ginzburg–Landau superconductor and the role of the Ginzburg parameter κ

2003 ◽  
Vol 651 (3) ◽  
pp. 361-386 ◽  
Author(s):  
Hagen Kleinert ◽  
Flavio S. Nogueira
Keyword(s):  
Fixed Point ◽  
Ginzburg Landau

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

Decoupling of the CuO2 plane and superconductivity in Cu0.5Tl0.5Ba2(Ca2−ySry)Cu3O10−δ(y = 0–0.4) samples

2016 ◽  
Vol 30 (17) ◽  
pp. 1650097
Author(s):  
Nawazish A. Khan ◽  
M. Usman Muzaffar
Keyword(s):  
Flux Pinning ◽  
High Temperature Superconductors ◽  
Normal Pressure ◽  
Cuo2 Plane ◽  
Fermi Velocity ◽  
Orthorhombic Crystal ◽  
Ginzburg Landau ◽  
Orthorhombic Crystal Structure ◽  
Axis Length

[Formula: see text]–[Formula: see text] samples have been synthesized at normal pressure at 860[Formula: see text]C. The main objectives of these experiments to study the role of inter-plane decoupling in suppressing the superconductivity of high temperature superconductors (HTSC). These samples have shown orthorhombic crystal structure and the [Formula: see text]-axis length increases with increased Sr-doping. All the samples have shown metallic variations of resistivity [Formula: see text] from room temperature down to the onset of superconductivity. The magnitude of the superconductivity is suppressed and the apical oxygen modes are hardened with Sr-doping. These studies have shown that Sr-doping promotes decoupling of conducting [Formula: see text] planes which suppress the superconducting properties of final compound. The excess conductivity analyses have shown increases in the width of two-dimensional (2D) Lawrence–Doniach (LD) regime with Sr-doping. The coherence length along the [Formula: see text]-axis [Formula: see text], the inter-layer coupling [Formula: see text], the phase relaxation time of the carriers [Formula: see text] and the Fermi velocity [Formula: see text] of superconductor carriers is suppressed. The underlying reason for the suppression of superconductor properties is the decrease in the density of carriers in the superconductor planes. However, the values of [Formula: see text], [Formula: see text] and [Formula: see text] have been found to increase with the increased Sr-doping, which is suggested to be originating from the enhancement in the flux pinning character which is induced by Sr-doping. The values of magnetic field penetration depth [Formula: see text] and the Ginzburg–Landau (GL) parameter [Formula: see text] decrease with Sr-doping and it is also suggested to be originating from the increase of flux pinning character of the samples with Sr-doping.

scholarly journals Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 59
Author(s):  
Ahmed Salem ◽  
Mohammad Alnegga
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of A Solution ◽  
New Class ◽  
Research Article ◽  
Analysis Technique ◽  
Modern Analysis

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

scholarly journals Analytical holographic superconductors in AdSN-Lifshitz topological black holes

2015 ◽  
Vol 12 (02) ◽  
pp. 1550015 ◽  
Author(s):  
D. Momeni ◽  
R. Myrzakulov ◽  
L. Sebastiani ◽  
M. R. Setare
Keyword(s):  
Critical Temperature ◽  
Gauge Field ◽  
Field Model ◽  
Abelian Gauge ◽  
Ginzburg Landau ◽  
Holographic Superconductors ◽  
Energy Issue ◽  
Breaking Parameter ◽  
Second Order Phase Transition

We present the analytic Lifshitz solutions for a scalar field model minimally coupled with the abelian gauge field in N-dimensions. We also consider the presence of cosmological constant Λ. The Lifshitz parameter z appearing in the solution plays the role of the Lorentz breaking parameter of the model. We investigate the thermodynamical properties of the solutions and discuss the energy issue. Furthermore, we study the hairy black hole solutions in which the abelian gauge field breaks the symmetry near to the horizon. In the holographic picture, it is equivalent to a second-order phase transition. Explicitly we show that there exists a critical temperature which is a function of the Lifshitz parameter z. The system below the critical temperature becomes superconductor, but the critical exponent of the model remains the same of the usual holographic superconductors without the higher-order gravitational corrections, in agreement with Ginzburg–Landau theories.

Calorimetric properties of a superconducting anisotropic square: ZFC process

2020 ◽  
pp. 2150128
Author(s):  
C. A. Aguirre ◽  
Q. D. Martins ◽  
J. Barba-Ortega
Keyword(s):  
Specific Heat ◽  
Free Energy Density ◽  
Vortex State ◽  
Cooper Pairs ◽  
Zero Field ◽  
Cooling Process ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Zero Field Cooling

We analyzed the role of the inclusion of anti-dots on the vortex state and some calorimetric properties of a mesoscopic superconducting square immersed in an external applied magnetic field. We calculated the magnetization, entropy, Gibbs free energy, density of Cooper pairs and specific heat for this system in a zero field cooling process, solving the time-dependent Ginzburg–Landau equations. We found that the critical temperature is non-dependent on the number of anti-dots and dependent slightly on the size of the defects. Oscillations in the entropy and specific heat are found due the temperature dependence of the superconducting characteristics length.

scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

scholarly journals Solitonic Fixed Point Attractors in the Complex Ginzburg–Landau Equation for Associative Memories

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 24
Author(s):  
Alexey N. Pyrkov ◽  
Tim Byrnes ◽  
Valentin V. Cherny
Keyword(s):  
Fixed Point ◽  
Landau Equation ◽  
Photon Absorption ◽  
Ginzburg Landau ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Solitonic Solution ◽  
Fixed Point Attractor ◽  
Point Attractor ◽  
Gain Loss

It was recently shown that the nonlinear Schrodinger equation with a simplified dissipative perturbation features a zero-velocity solitonic solution of non-zero amplitude which can be used in analogy to attractors of Hopfield’s associative memory. In this work, we consider a more complex dissipative perturbation adding the effect of two-photon absorption and the quintic gain/loss effects that yields the complex Ginzburg–Landau equation (CGLE). We construct a perturbation theory for the CGLE with a small dissipative perturbation, define the behavior of the solitonic solutions with parameters of the system and compare the solution with numerical simulations of the CGLE. We show, in a similar way to the nonlinear Schrodinger equation with a simplified dissipation term, a zero-velocity solitonic solution of non-zero amplitude appears as an attractor for the CGLE. In this case, the amplitude and velocity of the solitonic fixed point attractor does not depend on the quintic gain/loss effects. Furthermore, the effect of two-photon absorption leads to an increase in the strength of the solitonic fixed point attractor.

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