Related papers: From quantum disorder to quantum chaos
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
The Bohigas--Giannoni--Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory is proved. For this purpose a new semiclassical field theory…
We review the construction of the supersymmetric sigma model for unitary maps, using the color- flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique…
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…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
We investigate the role of quantum monitoring in the dynamical manifestations of Hamiltonian quantum chaos. Specifically, we analyze the generalized spectral form factor, defined as the survival probability of a coherent Gibbs state under…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is…
The interaction of a quantized electromagnetic field in a cavity with a set of two-level atoms inside can be described with algebraic Hamiltonians of increasing complexity, from the Rabi to the Dicke models. Their algebraic character…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
Chaos-based potentials are defined and implemented in the one-dimensional tight-binding model as a way of simulating disorder-controlled crystalline lattices. In this setting, disorder is handled with the aid of the chaoticity parameter.…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
Understanding how physical systems are influenced by disorder is a fundamental challenge in quantum science. Addressing its effects often involves numerical averaging over a large number of samples, and it is not always easy to gain an…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition,…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…