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 existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean–field theory) plus ...

How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be used for some complex computations, while the precise information of initial conditions which vanishes in the course of iterations deos not matter for this kin...

Spatiotemporal chaos, or disorder in space and chaos in time, is studied in direct numerical simulations of Rayleigh-Bénard convection. In particular, the following results pertaining to spiral defect chaos are discussed. First, in the absence of the mean flow, spiral defect chaos is found to collapse to a stationary pattern comprising textures of stripes with angular bends. The quenched patter...

The mean-field limit of a bosonic quantum many-body system is described by (mostly) nonlinear equations motion which may exhibit chaos very much in the spirit classical particle chaos, i.e., an exponential separation trajectories Hilbert space with rate given positive Lyapunov exponent $\ensuremath{\lambda}$. question now whether $\ensuremath{\lambda}$ imprints itself onto measurable observable...

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise stochastic or chaotic . It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activi...

We study the statistical distribution of quantum energy splittings due to a dynamical tunneling. The system, the annular billiard, has whispering quasimodes due to a discrete symmetry that exists even when chaos is present in the underlying classical dynamics. Symmetric and antisymmetric combinations of these quasimodes correspond to quantum doublet states whose degeneracies decrease as the cir...