无序系统与神经网络

Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…

We investigate multi-component metallic glass systems using a hybrid Molecular Dynamics (MD) and Variance-Constrained Semi-Grand Canonical approach. This method enables us to generate samples with properties consistent with experimental…

Optimization problems are central to many important cross-disciplinary applications.In their conventional implementations, the sequential nature of operations imposes strict limitations on the computational efficiency. Here, we discuss how…

Recent years have seen a rise in the application of machine learning techniques to aid the simulation of hard-to-sample systems that cannot be studied using traditional methods. Despite the introduction of many different architectures and…

We use tools based on the modern theory of polarization for a numerical study of the localization transition of the Aubry-Andr\'{e} model. In this model the spatial modulation of the potential, $\alpha$, is an irrational number, which we…

We analytically solve the critical dynamics of the Kob-Andersen kinetically constrained model of supercooled liquids on the Bethe lattice, employing a combinatorial argument based on the cavity method. For arbitrary values of graph…

The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation…

An entanglement spectrum encodes statistics beyond the entanglement entropy, of which several have been studied in the context of many-body localization. We numerically study the extreme value statistics of entanglement spectra of many-body…

We propose a geometric series modulated non-Hermitian quasiperiodic lattice model, and explore its localization and topological properties. The results show that with the ever-increasing summation terms of the geometric series, multiple…

In many condensed matter systems, long range order emerges at low temperatures as thermal fluctuations subside. In the presence of competing interactions or quenched disorder, however, some systems can show unusual configurations that…

The precise modulation of activity through inhibitory signals ensures that both insect colonies and neural circuits operate efficiently and adaptively, highlighting the fundamental importance of inhibition in biological systems. Modulatory…

We have calculated wave functions and matrix elements of the dipole operator in the two- and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In particular, we…

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov…

The majority of analysis of interacting systems is done for weak and well-balanced interactions, when in fact topology and rare event factors often result in strong and sign-biased interactions when considering real systems. We analyse the…

We conduct a numerical study of wave localization in disordered three-dimensional non-Hermitian systems featuring exceptional points. The energy spectrum of a disordered non-Hermitian Hamiltonian, exhibiting both parity-time and…

Glass materials, as quintessential non-equilibrium systems, exhibit properties such as energy dissipation that are highly sensitive to their preparation histories. A key challenge has been identifying a unified order parameter to…

We consider an unsupervised classifying agent that evolves by enforcing self-consistency of its labels under continual exposure to a data-generating environment. Because the agent's predictions feed back into its own regularized updates,…

In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…

Recent studies have revealed reentrant localization transitions in quasi-periodic one-dimensional lattices, where the competition between dimerized hopping and staggered disorder plays a central role. Yet the extent to which such reentrant…

Deep neural networks and brains both learn and share superficial similarities: processing nodes are likened to neurons and adjustable weights are likened to modifiable synapses. But can a unified theoretical framework be found to underlie…