Related papers: Statistical structural properties of many-body cha…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…
The fluctuation-dissipation theorem (FDT) is a fundamental result in statistical mechanics. It stipulates that, if perturbed out of equilibrium, a system responds at a rate proportional to a thermal-equilibrium property. Applications range…
We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a…
We develop a statistical theory of waveform shaping of incident waves that aim to efficiently deliver energy at weakly lossy targets which are embedded inside chaotic enclosures. Our approach utilizes the universal features of chaotic…
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop…
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.…
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid…
The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate…
The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization…
At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large…
The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems.…
It is often expected (and assumed) for a quantum chaotic system that the presence of correlated eigenvalues implies that all the other properties as dictated by random matrix theory are satisfied. We demonstrate using the spin-$1/2$ kicked…
The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in…
We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site…
Statistical mechanics assumes that a quantum many-body system at low temperature can be effectively described by its Gibbs state. However, many complex quantum systems exist only as metastable states of dissipative open system dynamics,…
Quantum simulators offer a new opportunity for the experimental exploration of non-equilibrium quantum many-body dynamics, which have traditionally been characterized through expectation values or entanglement measures, based on density…
We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann-Husimi representations for quantum states, as well as…