无序系统与神经网络

Common belief, confirmed by existing experiments, is that arbitrarily weak disorder should lead to spatial localization of eigenmodes of scalar wave equations when wave propagation is two-dimensional (2D). We predict that contrary to this…

We investigate the robustness of unbound states in one-dimensional quasiperiodic models with near-infinitely deep potentials. By constructing a deeper extension of the Liu-Xia model and combining inverse participation ratio (IPR)…

Self-organizing memristive networks are physical circuits that dynamically reconfigure their circuitry in response to external input signals. Their adaptive behavior arises from intrinsic neuro-synaptic dynamics combined with a…

Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve…

Learning with physical systems is an emerging paradigm that seeks to harness the intrinsic nonlinear dynamics of physical substrates for learning. The impetus for a paradigm shift in how hardware is used for computational intelligence stems…

Energy efficient sampling with probabilistic neurons or p-bits has been demonstrated in the context of Boltzmann machines and it is natural to ask if these approaches can be extended to the field of generative AI where energy costs have…

One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…

We investigate the effect of a periodic electric field drive on the generalized Aubry-Andr\'e model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mobility edges. Our study of the Floquet spectrum…

Periodic boundary conditions are not always used in the study of disordered systems, but it can be advantageous to apply them to mimick thermodynamically large systems. In this case, polarization and its cumulants can not be obtained…

Structural glasses prepared by bulk quenching a liquid melt universally exhibit puzzling low-energy excitations commonly known as the ``two-level systems'' (TLSs). Recent studies indicate that ultrastable glassy films made by vapor…

In-context learning (ICL) is a key building block of modern large language models, yet its theoretical mechanisms remain poorly understood. It is particularly mysterious how ICL operates in real-world applications where tasks have a common…

Disorder in moire superlattices simultaneously degrades flat-band localization and induces Anderson localization, yet how these two regimes interact has remained unclear. Here, we introduce a combined framework linking localization-length…

The quantum metric is a fundamental ingredient of band quantum geometry and has recently at tracted intense interest, with most of its transport signatures appearing in the intrinsic second order nonlinear conductivity. In the clean limit,…

We extend the recently introduced strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains, to study excited states, and finite temperature…

The \emph{Daydreaming} algorithm was proposed as a learning rule that simultaneously reinforces stored patterns and suppresses spurious attractors to improve the storage capacity of the Hopfield model. Its effectiveness has been reported…

The fate of Many-Body Localization (MBL) in the thermodynamic limit remains elusive, partly because numerical studies suffer from unexplained finite-size effects. We introduce and numerically study the charge transport capacity (CTC) -- a…

We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…

We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case…

The spiked Wigner ensemble is a prototypical model for high-dimensional inference. We study the spectral properties of an inhomogeneous rank-one spiked Wigner model in which the variance of each entry of the noise matrix is itself a random…

Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here,…