无序系统与神经网络

Current research on the disordered topological quantum phases primarily focuses on the uncorrelated and short-range correlated disorder regime. These topological Anderson insulators are typically self-averaging. However, topological quantum…

State-of-the-art organic solar cells increasingly rely on low-offset semiconductor blends, challenging the traditional requirement of a large energetic driving force for efficient charge separation. In these systems, the energetic offset…

We study the critical dynamics of the quantum random-field Ising model using the nonperturbative functional renormalization group (NP-FRG). The static critical behavior is found to be controlled by the zero-temperature fixed point of the…

Quasiperiodic systems usually interpolate between extended, critical, and localized states as the quasiperiodic modulation is increased. Here we show that the magnetic Qi-Wu-Zhang Chern-insulator model realizes a distinct full-spectrum…

Physical reservoir computing offers an energy-efficient alternative to conventional neural networks, where the intrinsic memory capacity in the physical system plays a central role. We demonstrate that memory capacity can be engineered…

The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem. We formulate…

The statistics of stationary points are a powerful way to understand mean-field random landscapes, and the Kac--Rice formula is a general way to compute them. A longstanding technical barrier to these calculations is the presence of the…

We investigate Anderson localization in three-dimensional disordered systems by comparing scalar classical waves with mass and force-constant disorder to electronic tight-binding models with diagonal and off-diagonal disorder. We show that…

We develop a quantitative theory of the Random Language Model (RLM), an ensemble of stochastic context-free grammars, in a scaling limit where the number of hidden symbols $N \to \infty$ while the grammar temperature $\tilde{\epsilon}_d \to…

Context-free grammars are minimal models of hierarchical structure in human language, generating structured text from recursive production rules. The Random Language Model (RLM) [De Giuli, PRL 2019], an ensemble of such grammars with random…

A stochastic risk model is applied to simulating the behavior of a nuclear reactor in a situation where the neutron chain length is described by a distribution with heavy "tails," such as the Pareto distribution. Probabilities of a…

The quantum geometric tensor is a fundamental property of quantum states, with broad applications in condensed matter physics, topological phases, and quantum phase transitions. The eigenvalues characterize the scale, anisotropy, and…

We perform a large scale simulation of quantum annealing in the Sherrington-Kirkpatrick (SK) spin glass up to a system size $N=40000$ to estimate its ground state energy using the deGennes-Suzuki-Kubo mean-field Ising dynamics, extending…

The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the…

The Localization Landscape Theory (LLT) offers a classical analogy for understanding Anderson localization through an effective confining potential, whose percolation threshold has been proposed to mark the mobility edge. While this…

We prove a trade-off theorem for order and disorder parameters in one-dimensional quantum spin systems with quenched disorder. For a disordered ensemble with exact Ising symmetry and average translation symmetry, any gapped ensemble must…

Within the framework of non-Hermitian photonics, we investigate the spectral and dynamical properties of one- and two-dimensional non-Hermitian off-diagonal disordered optical lattices, where randomness is applied to the couplings rather…

We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean…

We performed parallel measurements of heat effects and shear modulus relaxation for glassy Te$_{75}$Ge$_{15}$Ga$_{10}$ taken as a representative of practically important non-metallic glasses with covalent bonding. It is shown that the heat…

We present a numerical study of the ultrametric properties of the set of RNA secondary structures with the maximum number of base pairs (energetically degenerate minima) within the maximum matching model (Nussinov algorithm). Using 18…