arXiv subjects

Y. Alipour Fakhri

Publications and source records attributed to Y. Alipour Fakhri.

5 recordsLinked to original sources

arXiv2025

Finsler geometry in anisotropic superconductivity: a Ginzburg-Landau approach

We present a rigorous generalization of the classical Ginzburg--Landau model to smooth, compact Finsler manifolds without boundary. This framework provides a natural analytic setting for describing anisotropic superconductivity within Finsler geometry. The model is constructed via the Finsler--Laplacian, defined through the Legendre transform associated with the fundamental function F, and by employing canonical Finsler measures such as the Busemann--Hausdorff and Holmes--Thompson volume forms. We introduce an anisotropic Ginzburg--Landau functional for complex scalar fields coupled to gauge potentials and establish the existence of minimizers in the appropriate Finsler--Sobolev spaces by the direct method in the calculus of variations. Furthermore, we analyze the asymptotic regime as the Ginzburg--Landau parameter epsilon to 0 and prove a precise Gamma--convergence result: the rescaled energies converge to the Finslerian length functional associated with the limiting vortex filaments. In particular, the limiting vortex energy is shown to equal $π$ times the Finslerian length of the corresponding current, thereby extending the classical Bethuel--Brezis--He'lein result to anisotropic settings. These findings demonstrate that Finsler geometry unifies metric anisotropy and variational principles in gauge-field models, broadening the geometric scope of the Ginzburg--Landau theory beyond the Riemannian framework.

math-ph↗

arXiv2025

Non-Tonelli Finsler Geometry of Exotic Superconductivity: Metastable Vortex Phases and Geometric Phase Transitions

We develop a thermally coupled Ginzburg-Landau theory on \emph{Weakly Non-Tonelli (WNT) Finsler manifolds}, extending classical vortex analysis beyond the Tonelli convexity paradigm. The WNT framework weakens global $1$-homogeneity and strict convexity while preserving superlinearity and local ellipticity, enabling a geometric treatment of superconductors whose anisotropic energy landscapes are nonconvex and temperature-dependent. Within this setting, we construct the generalized Legendre correspondence, Hamiltonian metric, and WNT Laplacian, proving existence and sharp Coulomb asymptotics of the three-dimensional Green kernel. We then establish the $Γ$--convergence of the WNT-GL energy and identify metastable vortex filaments minimizing a renormalized geometric functional. Finally, a dynamic $Γ$-limit yields an effective filament flow governed by the WNT Finsler curvature and thermally induced geometric forces, predicting curvature focusing and phase bifurcation at a critical transition temperature $T_c$. This theory unifies convex-analytic, geometric, and physical perspectives, showing that Non-Tonelli Finsler structures form a natural analytic bridge between classical Finsler geometry, anisotropic variational models, and the nonlinear thermodynamics of exotic superconductivity.

math-ph↗

arXiv2025

Control-Translated Finsler-type structure and Anisotropic Ginzburg-Landau models

This paper develops a geometric and analytical extension of the Finsler--Ginzburg--Landau framework by introducing a distributed control field acting as a translation in the tangent bundle. Within this formulation, the classical Tonelli Lagrangian is deformed into a control--translated Finsler structure, whose Legendre dual induces a uniformly elliptic operator and a convex energy functional preserving the essential variational features of the anisotropic model. This approach provides a rigorous analytical setting for coupling external control fields with the intrinsic Finsler geometry of anisotropic superconductors. The study establishes the convexity, coercivity, and regularity properties of the induced energy functional and proves the existence of controlled minimizers through variational arguments on admissible configurations. In the asymptotic regime as the Ginzburg--Landau parameter tends to zero, a detailed $Γ$--convergence analysis yields a renormalized energy $W_u$ governing vortex interactions under control translation, quantifying the modification of the Green kernel and the self-energy due to the field $u(x)$. The results demonstrate that the control translation preserves the underlying Finsler structure while introducing a new geometric degree of freedom for manipulating and stabilizing vortex configurations.

math-ph↗

arXiv2025

Renormalized Energy and Vortex Interaction in Finsler Ginzburg-Landau Models

We develop a Finsler Ginzburg--Landau framework for the analysis of vortex interactions in anisotropic superconductors. Within this setting, the Finsler structure encodes directional dependence of the condensate energy, yielding a renormalized energy W_F that governs both equilibrium and dynamics of vortices. We derive the Gamma--limit, establish the analytical structure and stability of W_F, and show that vortex motion follows a Finsler gradient flow exhibiting anisotropic dissipation and drift. This approach provides a unified geometric and physical model for anisotropic superconductivity.

math-ph↗

arXiv2024

Kinematics and Generalized Raychaudhuri equation in f(G) gravity in imperfect fluid case

The equation of motion is the important equation for obtain the extra force and Raychaudhuri equation. By considering an explicitly coupling between an arbitrary function of the scalar Gauss-Bonnet, G and the Lagrangian density of matter, it is shown that an extra force normal to their four-velocities arises. In this paper, we obtain the extra force and the generalized Raychaudhuri equation in F(G) modified theory of gravity in an imperfect fluid for the massive particle by divergence of energy momentum tensor so we earn extra force an Raychaudhuri equation in a compared with f(R) modified gravity for perfect fluid this conclusion giving the evolution of the kinematical quantities and describing the relative accelerations of nearby particles .

gr-qc↗