Related papers: Energy localization in two chaotically coupled sys…
Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…
Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering…
We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across…
This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs,…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
Despite the periodic kicks, a linear kicked rotor (LKR) is an integrable and exactly solvable model in which the kinetic energy term is linear in momentum. It was recently shown that spatially interacting LKRs are also integrable, and…
Electromagnetic (EM) wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first principles, study of this process is usually computationally expensive and the results exhibit…
We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle…
Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This…
In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model…
We study theoretically transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
We investigate the dynamics of highly polydispersed finite granular chains. From the spatio-spectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a…
The thermodynamic formalism of Ruelle, Sinai, and Bowen, in which chaotic properties of dynamical systems are expressed in terms of a free energy-type function - called the topological pressure - is applied to a Lorentz Lattice Gas, as…
The paper suggests a new stochastic model for energy producing, dispatching, and storing in the multi-battery setting that takes into account the topology of the system of the links between the batteries, the transmission and storage…
We study a system of two coupled kicked rotors, both classically and quantum mechanically, for a wide range of coupling parameters. This was motivated by two published reports, one of which reported quantum localization, while the other…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
We combine theoretical and experimental efforts to propose a method for studying energy fluctuations, in particular, to obtain the related bi-stochastic matrix of transition probabilities by means of simple measurements at the end of a…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…