Related papers: Random Matrices and Chaos in Nuclear Spectra
There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The first type controls the early-time physics, e.g. the thermal relaxation and the sensitivity of the system to initial conditions. It can be traced back to the…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
The random matrix ensembles (RME), especially Gaussian RME and Ginibre RME, are applied to nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum…
To show the existence of precursor phenomena of the transition order$\ to$chaos in atomic nuclei a simple analysis has been made, based on a recent criterion proposed by Pavli\-chenkov. The basic idea is that nonlinear effects in rotational…
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 study the relation between entanglement and quantum chaos in one- and two-dimensional spin-1/2 lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what…
The consequences of adding random perturbations (anarchy) to a baseline hierarchical model of quark masses and mixings are explored. Even small perturbations of the order of 5% of the smallest non-zero element can already give deviations…
We investigate the appearance of quantum chaos in a single many-body wave function by analyzing the statistical properties of the eigenvalues of its reduced density matrix $\rho_A$ of a spatial subsystem A. We find that the spectrum of…
The effect of residual interaction between nucleons (quasiparticles) on shell oscillations of the masses of spherical nuclei is considered. The singularity of the ground state energy of the system in the vicinity of nucleon magic numbers is…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…