Low Energy Asymptotics of the Spectral Shift Function for Pauli Operators with Nonconstant Magnetic Fields

Eigenvalues behaviours for self-adjoint Pauli operators with unsigned perturbations and admissible magnetic fields

We investigate the behaviour of the eigenvalues of two-dimensional Pauli operators with nonconstant magnetic fields perturbed by a sign-indefinite decaying electric potential V. We prove new eigenvalues asymptotics.

A simple criterion for the existence of nonreal eigenvalues for a class of 2D and 3D Pauli operators

In this work, we investigate the discrete spectrum generated by complex matrix-valued perturbations for a class of 2D and 3D Pauli operators with nonconstant magnetic fields. We establish a simple criterion for the potentials to produce discrete spectrum near the low ground energy of the operators. Moreover, in case of creation of nonreal eigenvalues, this criterion specifies also their location.

Spectral shift function and Resonances near the low ground state for Pauli and Schrödinger operators

We study the spectral shift function (SSF) $ξ(λ)$ and the resonances of the operator $H_V := \big( σ\cdot (-i\nabla - \textbf{A}) \big)^{2} + V$ in $L^2(\mathbb{R}^3)$ near the origin. Here $σ:= (σ_1,σ_2,σ_3)$ are the $2 \times 2$ Pauli matrices and $V$ is a hermitian potential decaying exponentially in the direction of the magnetic field $\textbf{B} := \text{curl} \hspace{0.6mm} \textbf{A}$. We give a representation of the derivative of the SSF as a sum of the imaginary part of a holomorphic function and a harmonic measure related to the resonances of $H_V$. This representation warrant the Br…

多频斜移薛定谔算子的李雅普诺夫指数的正性与log-Hölder连续性

Positivity and Continuity of Lyapunov Exponents for Multi-Frequency Skew-Shift Schrödinger Operators

针对多频斜移势的一维离散薛定谔算子，证明了在Diophantine频率和大耦合下李雅普诺夫指数一致正且关于能量log-Hölder连续，将结果从单频或简单拟周期模型推广到多频斜移情形。