Landau Diamagnetism of Degenerate Collisional Plasma

半金属中的阿哈罗诺夫-玻姆磁性及朗道抗磁性

Aharonov-Bohm magnetism and Landau diamagnetism in semimetals

本文计算了中空半金属圆柱和环在轴向磁通下的磁响应，预测了阿哈罗诺夫-玻姆效应的消失、短石墨烯管的铁磁基态，以及体半金属抗磁磁化率对尺寸的对数依赖。

Thin domain limit and counterexamples to strong diamagnetism

We study the magnetic Laplacian and the Ginzburg-Landau functional in a thin planar, smooth, tubular domain and with a uniform applied magnetic field. We provide counterexamples to strong diamagnetism, and as a consequence, we prove that the transition from the superconducting to the normal state is non-monotone. In some non-linear regime, we determine the structure of the order parameter and compute the super-current along the boundary of the sample. Our results are in agreement with what was observed in the Little-Parks experiment, for a thin cylindrical sample.

The Vlasov--Poisson--Landau system in the weakly collisional regime

Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = νQ(F,F)(t,x,v),\\ E(t,x) = \nabla Δ^{-1} (\int_{\mathbb R^3} F(t,x,v)\, \mathrm{d} v - \frac{1}{(2π)^3}\int_{\mathbb T^3} \int_{\mathbb R^3} F(t,x,v)\, \mathrm{d} v \, \mathrm{d} x), \end{aligned}$$ with $ν\ll 1$. We prove that for $ε>0$ sufficiently small (but independent of $ν$), initial data which are $O(εν^{1/3})$-Sobolev space perturbations from the global Maxwellians …

Exact collisional moments for plasma fluid theories

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-o…

Fluid moments of the Landau collision operator

One important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multi-dimensional Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to weakly collisional and strong f…