Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noiss

Global well-posedness of complex Ginzburg-Landau equation with a space-time white noise

We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the dynamical $Φ_3^4$ model. We prove a priori $L^{2p}$ estimate for the paracontrolled solution as in the deterministic case [5].

Closed and exact functions in the context of Ginzburg-Landau models

For a general vector field we exhibit two Hilbert spaces, namely the space of so called closed functions and the space of exact functions and we calculate the codimension of the space of exact functions inside the larger space of closed functions. In particular we provide a new approach for the known cases: the Glauber field and the second-order Ginzburg-Landau field, and for the case of the fourth-order Ginzburg-Landau field.

A model for vortex nucleation in the Ginzburg-Landau equations

This paper studies questions related to the dynamic transition between local and global minimizers in the Ginzburg-Landau theory of superconductivity. We derive a heuristic equation governing the dynamics of vortices that are close to the boundary, and of dipoles with small inter vortex separation. We consider a small random perturbation of this equation, and study the asymptotic regime under which vortices nucleate.

Absence of Replica Symmetry Breaking in the Random Field Mixed-Spin Ginzburg-Landau Model

In this paper, an extension of the random field Ginzburg-Landau model on the hypercubic lattice is considered by adding $p$-spin ($p\geqslant 2$) interactions coupled to general disorders. This new model is called the random field mixed-spin Ginzburg-Landau model. We proved that, in the infinite volume limit of this model, the variance of spin overlap vanishes.

Ginzburg-Landau 场最大值的紧性

Tightness of the maximum of Ginzburg-Landau fields

本文在临界维数 $d=2$ 下，对满足一致凸性条件的离散 Ginzburg-Landau 场，证明了其边长为 $N$ 的盒子上的最大值经显式中心化后具有紧性。

Diffusive scaling in energy ginzburg-Landau dynamics

Ginzburg-Landau energy models arise as autonomous sto-chastic dynamics for the energies in coupled systems after a weak coupling limit (cf. [3, 6]). We prove here that, under certain conditions, the energy fluctuations of these stochastic dynamics are driven by the heat equation, under a diffusive space time scaling.

Coulomb Gases and Ginzburg-Landau Vortices

These are the lecture notes of a "Nachdiplomvorlesung" course taught at ETH Zurich in the Spring of 2013. They appeared in the EMS series Zurich Lectures in Advanced Mathematics.

Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.

长程相互作用下金兹堡-朗道动力学的宏观涨落理论

Macroscopic Fluctuation Theory for Ginzburg-Landau dynamics with long range interactions

本研究将宏观涨落理论推广至长程相互作用的金兹堡-朗道动力学系统，明确其宏观有效方程由非线性分数阶扩散方程描述，拓展了该理论的适用范围。