无序系统与神经网络
Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical…
We study a quantum particle hopping on an infinite Cayley tree with nearest-neighbor hopping amplitudes drawn from a distribution singular as $|t|^{-a}$ near weak links and no on-site disorder. Because the graph is bipartite, the model has…
A three-body Hopfield model defined on sparse random graphs with finite mean connectivity is studied using a replica-symmetric (RS) analysis. By extending the functional replica framework for conventional two-body finite-connectivity…
We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle $\calE = \calM \times \R^d$. Beginning from a…
We investigate a one-dimensional lattice with spin-orbit coupling (SOC) and a Zeeman potential containing uniform and quasiperiodic components. By tuning SOC, anomalous mobility edges emerge that separate critical from non-critical states,…
Magnetoresistance hysteresis is often used to estimate the coercive field of a magnetic material. We reanalyse our published magnetotransport and magnetometry data on compacted powders of the half-metallic ferromagnet CrO2 and show that…
Equivariant graph neural networks have proven effective tools for inference of material's properties directly from their structure. Traditionally, these have been applied such that they respect full $O(3)$ equivariance, so that any rotation…
Self-assemblies of tunable units are being intensively studied as physical systems with signal-processing capabilities. Specifically, silver nanowire networks (AgNWNs) have demonstrated accumulation, non-linearity, and memory retention with…
Does thermal averaging preserve signatures of eigenstate complexity? We study the entropic complexity C = S_1 - S_2 (Shannon minus second-order Renyi entropy) across the ergodic-to-localized crossover of three disordered models: the…
Charge transport (CT) in biological systems is of great interest due to its role in various functional activities like photobiology, bioenergetics, redox catalytic and other metabolic activities, etc. It has been observed by various studies…
We derive a rigorous sufficient condition for the absence of spin-glass order in the Ising spin glass with symmetric binary couplings on Migdal--Kadanoff (MK) hierarchical lattices with even branching number. The key observation is that a…
We study a duality analysis in conjunction with the star-triangle transformation for symmetric-group permutation models on the triangular and honeycomb lattices. The calculation is motivated by the permutation-model description of random…
This work demonstrates that sparse long-range random bonds on a one-dimensional lattice alone can generate quantum-chaotic spectral correlations and also drive a localization transition in a noninteracting single-particle Hamiltonian. The…
We investigate localization transitions and spectral topology in a one-dimensional non-Hermitian generalization of the Aubry-Andr\'{e} model in which both the nearest-neighbor and the next-nearest-neighbor hopping amplitudes are…
We formulate feature learning as a geometric critical phenomenon of the lifted tensor-product learning metric. The central object is not a scalar overlap, but the target-active geometry of \[ \mathcal…
We study optimization-induced matrix ensembles generated by Gibbs measures. The same quenched disorder that weights configurations also supplies the matrix entries observed on them. For glassy Gibbs measures this raises a natural question:…
We propose a distinct type of long-range ordered phase that can occur in classical and quantum many-particle systems. It is induced by impurities and defects that locally break a subset of the order-parameter symmetries, i.e., by…
Understanding the dynamical properties of coupled phase oscillator systems with heterogeneous oscillator frequencies has been a long-standing challenge of complex systems theory. While the seminal work of Ott and Antonsen dramatically…
The Rosenzweig--Porter (RP) random matrix ensemble has emerged as a minimal model for the integrability-to-chaos crossover in quantum many-body systems. Its phase diagram features a region with fractal eigenstates, exhibiting intermediate…
The attention matrix of a causal transformer is row-stochastic, iterated over depth, and non-normal by construction. For non-normal operators, eigenvalues control only asymptotic behavior; finite-depth behavior is controlled by resolvent…