Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator.

A detailed numerical study reveals that the asymptotic values of the standard-deviation-to-mean ratio of the out-of-time-ordered correlator in energy eigenstates can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely, the algebraic u(3) model, and demonstrate a clear correspondence between the energy-smoothed relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a chaos indicator.

Complex Density of Continuum States in Resonant Quantum Tunneling.

We introduce a complex-extended continuum level density and apply it to one-dimensional scattering problems involving tunneling through finite-range potentials. We show that the real part of the density is proportional to a real "time shift" of the transmitted particle, while the imaginary part reflects the imaginary time of an instantonlike tunneling trajectory. We confirm these assumptions for several potentials using the complex scaling method.

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit.

Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally.

Superradiance in finite quantum systems randomly coupled to continuum.

We study the effect of superradiance in open quantum systems, i.e., the separation of short- and long-living eigenstates when a certain subspace of states in the Hilbert space acquires an increasing decay width.

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems.

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems.

Exceptional points near first- and second-order quantum phase transitions.

We study the impact of quantum phase transitions (QPTs) on the distribution of exceptional points (EPs) of the Hamiltonian in the complex-extended parameter domain. Analyzing first- and second-order QPTs in the Lipkin-Meshkov-Glick model we find an exponentially and polynomially close approach of EPs to the respective critical point with increasing size of the system. If the critical Hamiltonian is subject to random perturbations of various kinds, the averaged distribution of EPs close to the critical point still carries decisive information on the QPT type.

Regularity-induced separation of intrinsic and collective dynamics.

We propose that the adiabatic separation of collective and intrinsic motions in many-body systems is related to increased regularity of the intrinsic dynamics. The surmise is verified on the separation of rotations from intrinsic vibrations in the interacting boson model of nuclear structure.

Quantum chaos in the nuclear collective model. II. Peres lattices.

This is a continuation of our paper [Phys. Rev. E 79, 046202 (2009)] devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei.

Quantum chaos in the nuclear collective model: Classical-quantum correspondence.

Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic classical features with energy and control parameters. Corresponding signatures are now verified also on the quantum level for different schemes of quantization and with a variable classicality constant.

Impact of quantum phase transitions on excited-level dynamics.

The influence of quantum phase transitions on the evolution of excited levels in the critical parameter region is discussed. The analysis is performed for one- and two-dimensional systems with first- and second-order ground-state transitions. Examples include the cusp and nuclear collective Hamiltonians.

Regular and chaotic vibrations of deformed nuclei with increasing gamma rigidity.

We study classical trajectories corresponding to L=0 vibrations in the geometric collective model of nuclei with stable axially symmetric quadrupole deformations. It is shown that with increasing stability against the onset of triaxiality the dynamics passes between a fully regular and semiregular limiting regime. In the transitional region, an interplay of chaotic and regular motions results in complex oscillatory dependence of the regular phase space on the Hamiltonian parameter and energy.