无序系统与神经网络

Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…

In sparse signal processing, this study investigates the effect of the global shrinkage parameter $\tau$ of a horseshoe prior, one of the global-local shrinkage prior, on the linear regression. Statistical mechanics methods are employed to…

Anderson localization provides a challenge to numerical approaches due to the inherent randomness, and hence absence of simple symmetries, in its discrete Hamiltonian representation. Numerous algorithmic approaches have been developed or…

The Ising spin-glass model on the three-dimensional (d=3) hierarchical lattice with long-range ferromagnetic or spin-glass interactions is studied by the exact renormalization-group solution of the hierarchical lattice. The chaotic…

Quantum localization (single-body or many-body) comes with the emergence of local conserved quantities -- whose conservation is precisely at the heart of the absence of transport through the system. In the case of fermionic systems and…

The FitzHugh-Nagumo (FHN) model serves as a fundamental neuronal model which is extensively studied across various dynamical scenarios, we explore the dynamics of a scalar FHN oscillator under the influence of white noise. Unlike previous…

Avalanches in mean-field models can be mapped to memoryless branching processes defining a universality class. We present a reduced expression mapping a broad family of critical and subcriticial avalanches in mean-field models at the…

Potential disorder in 1D leads to Anderson localization of the entire spectrum. Upon sacrificing hermiticity by adding non-reciprocal hopping, the non-Hermitian skin effect competes with localization. We find another route for…

We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{\'e}-Harper model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity…

We study the connection between damage spreading, a phenomenon long discussed in the physics literature, and the coupling of Markov chains, a technique used to bound the mixing time. We discuss in parallel the Edwards-Anderson spin glass…

The Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to…

How a closed system thermalizes, especially in the absence of global conservation laws but in the presence of disorder and interactions, is one of the central questions in non-equilibrium statistical mechanics. We explore this for a…

A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the high temperature disordered phase, for number…

A complexity classification scheme is developed from the fractal spectra of spin-glass chaos and demonstrated with multigeographic multicultural music and brain electroencephalogram signals. Systematic patterns are found to emerge. Chaos…

The human structural connectome has a complex internal community organization, characterized by a high degree of overlap and related to functional and cognitive phenomena. We explored connectivity properties in connectome networks and…

In non-Hermitian systems, the energy spectra and eigenstates exhibit high sensitivity to boundary conditions, lattice geometries, and local impurities. In this paper, we study the effect of long-range impurity coupling, located far from the…

The non-Hermitian systems exhibit extreme sensitivity to the boundary conditions. The change in the eigenspectrum with tunning boundary parameter is intimately connected to the non-Hermitian skin effect. The single-particle systems are…

Multiple trapping and release (MTR) is a typical transport mechanism of electron carriers in amorphous and other disordered semiconductors where localized states are significant. Quantitative description of MTR, however, has been based on…

The interplay between disorder and quantum interference leads to a wide variety of physical phenomena including celebrated Anderson localization -- the complete absence of diffusive transport due to quantum interference between different…

Previous studies have established that quasiperiodic lattice models with unbounded potentials can exhibit localized and multifractal states, yet preclude the existence of extended states. In this work, we introduce a quasiperiodic system…