无序系统与神经网络

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance…

Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic…

The interaction between non-reciprocity and disorder-free localization has emerged as a fascinating open question. Here, we explore the effects of pseudo mobility edges (MEs) along with different types of eigenstates in a one-dimensional…

We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method,…

We study a Lindbladian generalization of the Anderson model of localization that describes disordered free fermions coupled to a disordered environment. From finite size scaling of both eigenvalue statistics and participation ratio, we…

The backpropagation method has enabled transformative uses of neural networks. Alternatively, for energy-based models, local learning methods involving only nearby neurons offer benefits in terms of decentralized training, and allow for the…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

In topological phases of matter for which the bulk and boundary support distinct electronic gaps, there exists the possibility of decoupled mobility gaps in the presence of disorder. This is in analogy with the well-studied problem of…

We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…

We report on the characterization of Pt-YBa$_2$Cu$_3$O$_{7-\delta}$ interfaces, focusing on how oxygen vacancies content ($\delta$) affects electrical transport mechanisms. Our study examines four Pt-YBa$_2$Cu$_3$O$_{7-\delta}$ samples with…

Scale-free localization in non-Hermitian systems is a distinctive type of localization where the localization length of certain eigenstates, known as scale-free localized (SFL) states, scales proportionally with the system size. Unlike skin…

Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…

The interplay of onsite quasiperiodic potential, superconductivity, and non-Hermiticity is explored in a non-Hermitian unconventional superconducting quasicrystal described by Aubry-Andr\'e-Harper (NHAAH) model with $p$-wave pairing. In…

We study the non-Hermitian Aubry-Andr\'e-Harper model, incorporating complex phase modulation, unmodulated and modulated nonreciprocal hopping. Using Avila's global theory, we derive analytical phase boundaries and map out the phase…

We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana--Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the…

Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…

Ising machines, hardware accelerators for combinatorial optimization and probabilistic sampling problems, have gained significant interest recently. A key element is stochasticity, which enables a wide exploration of configurations, thereby…

Precise asymptotics have revealed many surprises in high-dimensional regression. These advances, however, have not extended to perhaps the simplest estimator: direct Nadaraya-Watson (NW) kernel smoothing. Here, we describe how one can use…

Stark Many-Body Localization (MBL) is a phenomenon observed in quantum systems in the absence of disorder, where the presence of a linear potential, known as the Stark field, causes the localization. Our study aims to provide novel insight…

Wave propagation in time-varying media has attracted significant attention for its innovative potential to control wave-matter interactions and to develop versatile active materials. While most research has focused on electromagnetic waves,…