相关论文: Support set of random wave-functions on the Bethe …

We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree) from the central site ("root") to the boundary ("leaves"). We show that the eigenfunction moments $P_q=N \left<|\psi|^{2q}(i)\right>$ exhibit a…

We study numerically Anderson localization on lattices that are tree-like except for the presence of one loop of varying length $L$. The resulting expressions allow us to compute corrections to the Bethe lattice solution on i)…

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus ("arithmetic random waves"). We study…

Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…

We study the length of the nodal set of eigenfunctions of the Laplacian on the $\spheredim$-dimensional sphere. It is well known that the eigenspaces corresponding to $\eigval=n(n+\spheredim-1)$ are the spaces $\eigspc$ of spherical…

We combine numerical diagonalization with a semi-analytical calculations to prove the existence of the intermediate non-ergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized…

From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…

We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…

We present a new large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the…

We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both…

We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: $D$, which determines the range of the coefficients of the on-site potentials, and $W$, which defines…

We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…

Wave localization is a fundamental phenomenon that appears universally in both natural materials and artificial structures and plays a crucial role in understanding the various physical properties of a system. Usually, a localized state has…

We study transient patterns appearing in a class of SPDE using the framework of quasi-stationary and quasi-ergodic measures. In particular, we prove the existence and uniqueness of quasi-stationary and quasi-ergodic measures for a class of…

We introduce the Weighted Planar Stochastic Porous Lattice (WPSPL), a geometrically disordered substrate generated by iteratively subdividing a unit square. At each step a block is selected with probability proportional to its area, divided…

We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically we consider one-dimensional stub and two-dimensional kagome lattices that have a random scalar potential and a…

Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely…

This paper investigates the dynamics of compact localized modes in one-dimensional flat-band elastic lattices. Flat dispersion arises from destructive interference between neighboring elements, resulting in a zero group velocity across all…

We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special band-gap scaling of the spectral surface of genus $N$ so that the…

We present here for the first time a unifying perspective for the lack of equipartition in non-linear ordered systems and the low temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two…