Related papers: Difficulties with the Scars Model of Quantum Local…
We investigate scarred resonances of a stadium-shaped chaotic microcavity. It is shown that two components with different chirality of the scarring pattern are slightly rotated in opposite ways from the underlying unstable periodic orbit,…
We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two--dimensional area--preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of…
We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two…
In classical systems, chaos is clearly defined via the behavior of trajectories. In quantum systems with a classical analogue one finds that the transition from regular to chaotic dynamics is signified by a change in the spectral…
The Wigner function is a phase space quasi-probability distribution whose negative regions provide a direct, local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we introduce local positive- and…
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by…
Numerical calculation and analysis of extremely high-lying energy spectra, containing thousands of levels with sequential quantum number up to 62,000 per symmetry class, of a generic chaotic 3D quantum billiard is reported. The shape of the…
The eigenstate thermalization hypothesis describes how most isolated many-body quantum systems reach thermal equilibrium. However, the hypothesis is violated by phenomena such as many-body localization and quantum many-body scars. In this…
Quantum many-body scars are nonthermal states exhibiting persistent revivals in an otherwise ergodic, nonintegrable quantum system. Here we leverage the phenomenon of kinetic frustration -- the destructive interference of multiple quantum…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
Quantum many-body scars are rare eigenstates hidden within the chaotic spectra of many-body systems, representing a weak violation of the eigenstate thermalization hypothesis (ETH). Identifying these scars, as well as other non-thermal…
We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate…
A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker's map as a prototype example of a chaotic map.
It was recently shown (Keating & Prado, {\it Proc. R. Soc. Lond. A} {\bf 457}, 1855-1872 (2001)) that, in the semiclassical limit, the scarring of quantum eigenfunctions by classical periodic orbits in chaotic systems may be dramatically…
We apply periodic orbit theory to a quantum billiard on a torus with a variable number N of small circular scatterers distributed randomly. Provided these scatterers are much smaller than the wave length they may be regarded as sources of…
Understanding properties of quantum matter is an outstanding challenge in science. In this paper, we demonstrate how machine-learning methods can be successfully applied for the classification of various regimes in single-particle and…
The chaotic or ordered character of orbits in galactic models is an important issue, since it can influence dynamical evolution. This distinction can be achieved with the help of the Smaller Alingment Index - (SALI). We describe here…
We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of…
The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is…
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wavefunctions localized around unstable periodic orbits. The formalism applies to the description of…