无序系统与神经网络

Constraint Satisfaction Problems (CSPs) lie at the heart of complexity theory and find application in a plethora of prominent tasks ranging from cryptography to genetics. Classical approaches use Hopfield networks to find approximate…

Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…

Using functional methods, we investigate the sound quanta arising from quantized hydrodynamic fields in simple liquids at low temperatures, under the influence of high-energy processes, coming from non-hydrodynamic degrees of freedom. To…

We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…

We investigate localization and reentrance in a dimerized Su-Schrieffer-Heeger (SSH) tight-binding chain whose on-site energies are given by a quasiperiodic cosine masked by a deterministic Thue-Morse sequence. Working with non-interacting,…

We investigate localization and persistent currents in a helical tight-binding lattice subject to two independent magnetic fluxes and a quasiperiodic on-site potential. Working with non-interacting, spinless fermions under periodic boundary…

We study the localization properties of the quasiperiodic one-dimensional helical chain with two tunneling paths: nearest-neighbor and a long-range hop that connects sites of consecutive helical turns. Using exact diagonalization, we…

Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…

Disordered quantum magnets are not only experimentally relevant, but offer efficient computational methodologies to calculate the low energy states as well as various measures of quantum correlations. Here, we present a systematic analysis…

We study the $\pm J$ SK model for small $N$'s up to $N=9$. We sort the $2^{N(N-1)/2}$ possible realizations of the coupling matrix into equivalence classes according to the gauge symmetry and permutation symmetry and determine the energy…

Combinatorial optimization problems have a broad range of applications and map to physical systems with complex dynamics. Among them, the 3-SAT problem is prominent due to its NP-complete nature. In physics terms, its solution corresponds…

We investigate how much bias in the initial configuration is required to drive global agreement in synchronous, deterministic majority dynamics on large random $d$-regular graphs. Nodes take values $\pm 1$ and update their states at each…

Hyperuniformity, which is a type of long-range order that is characterized by the suppression of long-range density fluctuations in comparison to the fluctuations in standard disordered systems, has emerged as a powerful concept to aid in…

Glassy systems reveal a wide variety of generic behaviors, which lack a unified theoretical description. Here, we study a mean-field model, recently shown to reproduce the universal non-phononic vibrational spectra of glasses, under…

Despite considerable efforts over the last decade, the high-energy phase diagram of the random-field Heisenberg chain still eludes our understanding, in particular the nature of the non-ergodic many-body localized (MBL) regime expected at…

Models of interacting hysteretic elements, called hysterons, capture the sequential response and complex memory effects in a wide range of complex systems and can guide the design of intelligent metamaterials. However, even simple models…

The study of spectrum statistics, such as the consecutive-gap ratio distribution, has revealed many interesting properties of many-body complex systems. Here we propose a two-parameter surmise expression for such distribution to describe…

Inspired by striking advances in language modeling, there has recently been much interest in developing autogressive sequence models that are amenable to analytical study. In this short note, we consider extensions of simple disordered…

In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool…

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…