Dynamical localization for polynomial long-range hopping random operators on $\mathbb{Z}^d$

具有幂律长程跳跃的$\mathbb{Z}^d$上准周期算子的格林函数估计

Green's function estimates for quasi-periodic operators on $\mathbb{Z}^d$ with power-law long-range hopping

本文针对$\mathbb{Z}^d$上具有幂律长程跳跃和解析余弦型位势的准周期算子建立定量格林函数估计，并由此证明局部化的算术版本、IDS的有限体积Hölder连续性及Aubry对偶算子无特征值。

单形上的安德森局域化

Anderson localization on a simplex

本文导出了广义安德森模型本征态矩的场论表示。该表示是准确的，可以用于安德森模型与一般的非随机跳跃元素在任何维度。我们将这种方法应用到单纯形模型，其中任何两个格点之间的跳跃幅度是相同的，并发现本征态是本地化在任何强度的无序。我们的分析预测与数值模拟的结果非常一致。

Localization for random coupled harmonic oscillators on $\mathbb{Z}^d$

In this paper we consider the localization properties of coupled harmonic oscillators in random media. Each of these oscillators is restricted to the lattice $\mathbb{Z}^d$. We show that for most states and an arbitrary choice of the random media, the long time localization for the coupled system holds in a time scale larger than the polynomial one.

Many-Body Localization Landscape

We generalize the notion of "localization landscape," introduced by M. Filoche and S. Mayboroda [Proc. Natl. Acad. Sci. USA 109, 14761 (2012)] for the single-particle Schrodinger operator, to a wide class of interacting many-body Hamiltonians. The many-body localization landscape (MBLL) is defined on a graph in the Fock space, whose nodes represent the basis vectors in the Fock space and edges correspond to transitions between the nodes connected by the hopping term in the Hamiltonian. It is shown that in analogy to the single-particle case, the inverse MBLL plays the role of an effective pote…

1D Mott variable-range hopping with external field

Mott variable-range hopping is a fundamental mechanism for electron transport in disordered solids in the regime of strong Anderson localization. We give a brief description of this mechanism, recall some results concerning the behavior of the conductivity at low temperature and describe in more detail recent results (obtained in collaboration with N. Gantert and M. Salvi) concerning the one-dimensional Mott variable-range hopping under an external field.

Localization in interacting fermionic chains with quasi-random disorder

We consider a system of fermions with a quasi-random almost-Mathieu disorder interacting through a many-body short range potential. We establish exponential decay of the zero temperature correlations, indicating localization of the interacting ground state, for weak hopping and interaction and almost everywhere in the frequency and phase; this extends the analysis in \cite{M} to chemical potentials outside spectral gaps. The proof is based on Renormalization Group and is inspired by techniques developed to deal with KAM Lindstedt series.

多粒子跳跃非对称扩散模型的电流分布

The current distribution of the multiparticle hopping asymmetric diffusion model

在本文中，我们处理的\textit{multiparticle hopping asymmetric diffusion model}（MADM）的$\mathbb{Z}$介绍了Sasamoto和Wadati在1998年。利用Bethe方法计算了含有$N$粒子的MADM的跃迁几率。转移概率表示为$N$维轮廓积分的总和，其中轮廓是以原点为中心的圆，并对其半径进行限制。通过使用跃迁概率，我们找到了$\mathbb{P}(x_m(t) =x)$，即从左数第$m$个粒子在时间$t$处于$x$的概率。概率$\mathbb{P}(x_m(t) =x)$被表示为在所有具有$|S| \geq m$的$S \subset \{1,...,N\}$上的$|S|$维轮廓积分的和，并且用于给出系统的当前分布。讨论了MADM与推非对称简单排斥过程（PushASEP）之间的映射.

树上随机薛定谔算子的Lifshitz尾扩张态

Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees

我们解决了一个现有的问题，关于移动边缘的位置与跳跃项和随机潜在的Bethe格上的运营商。该模型是最早研究安德森局域化的模型之一，并且由于与许多粒子系统的局域化问题的类比而继续引起人们的关注。我们发现，扩展状态出现通过无序使能共振远远超出运营商的跳跃项的能带。对于弱无序，这包括非常低密度的状态的Lifshits尾制度。

Anderson localization for multi-frequency quasi-periodic operators on $\mathbb{Z}^d$

We establish Anderson localization for general analytic $k$-frequency quasi-periodic operators on $\mathbb{Z}^d$ for \textit{arbitrary} $k,d$.

Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$

We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical localization (SDL). In particular, given the recent progress at the bottom of the spectrum for the $\mathbb{Z}^2$ and $\mathbb{Z}^3$ cases with Bernoulli single site probability distribution, our results imply SDL in these regimes.

Mott变程跳变及其它点上行走过程的不变原理

Invariance principle for Mott variable range hopping and other walks on point processes

考虑带能量标志的齐次Poisson点过程上的随机游动.跳跃率在跳跃长度的A次方中呈指数衰减，并通过玻尔兹曼因子依赖于能量标记。A=1的情况对应于强安德森局域化状态下无序固体中声子诱导的莫特变程跳跃。我们证明了，对于几乎每一个实现的标记过程，扩散重标度随机游动，与任意的起点，收敛到布朗运动的扩散矩阵是正定的，和独立的环境。最后，我们将上述结果推广到包括稀释格在内的其他点过程。

Incomplete Localization for Disordered Chiral Strips

We prove that a disordered analog of the Su-Schrieffer-Heeger model exhibits dynamical localization (i.e. the fractional moments condition) at all energies except possibly zero energy, which is singled out by chiral symmetry. Localization occurs at arbitrarily weak disorder, provided it is sufficiently random. If furthermore the hopping probability measures are properly tuned so that the zero energy Lyapunov spectrum does not contain zero, then the system exhibits localization also at that energy, which is of relevance for topological insulators. The method also applies to the usual Anderson m…