Related papers: Localization of Eigenfunctions in the Stadium Bill…
From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such…
We study the thermal rectification phenomenon in ``billiard'' systems with interacting particles. This interaction induces a local dynamical response of the billiard to an external thermodynamic gradient. To explain this dynamical effect we…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance,…
A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are…
The impact of geometry on many body localization is studied on simple, exemplary systems amenable to exact diagonalization treatment. The crossover between ergodic and MBL phase for uniform as well as quasi-random disorder is analyzed using…
We describe the eigenvalues and the eigenspaces of the adjacency matrices of subgraphs of the Hamming cube induced by Hamming balls, and more generally, by a union of adjacent concentric Hamming spheres. As a corollary, we extend the range…
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…
The present work explores the potential for observing multiple reentrant localization behavior in a double-stranded helical (DSH) system, extending beyond the conventional nearest-neighbor hopping interaction. The DSH system is considered…
We study quantum diffusion of wavepackets in one-dimensional random binary subject to an applied electric field. We consider three different cases: Periodic, random, and random dimer (paired) lattices. We analyze the spatial extent of…
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…
A "drivebelt" stadium billiard with boundary consisting of circular arcs of differing radius connected by their common tangents shares many properties with the conventional "straight" stadium, including hyperbolicity and mixing, as well as…
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of…
Using the tight-binding model, we investigate the influence of vacancy disorder on electrical transport in graphene Hall bars in the presence of quantizing magnetic fields. Disorder, induced by a random distribution of monovacancies, breaks…
The eigenstates of one-dimensional Hermitian and non-Hermitian tight-binding systems (in the presence/absence of quasiperiodic potential) and an external electric field undergo complete localization with equally spaced eigenenergies, known…
We study many-body localization properties of the disordered XXZ spin chain in the Ising phase. Disorder is introduced via a random magnetic field in the $z$-direction. We prove a strong form of dynamical exponential clustering for…
We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-Andr\'{e} model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a…
We report the first direct experimental observation of scarring phenomenon in transverse vibrational modes of a thin metal plate. The plate has the shape of a full stadium and clamped boundary conditions. Normal modes are imaged using…
Motivated by the findings of logarithmic spreading of entanglement in a many-body localized system, we more closely examine the spreading of entanglement in the fully many-body localized phase, where all many-body eigenstates are localized.…
Light scattering and localization in strongly scattering disordered systems is governed by the nature of the underlying eigenmodes, specially their spatial extension within the system. One of the main challenges in studying experimentally…