We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the ab initio band structure of silicon and the tight-binding spectrum of the alloy AlxGa1−xAs, and show that some of their statistical properties obey the universal predictions of quantum chaos derived from the theory of random matrices. Also, the Bloch momenta are int...

The neutron resonances, especially in heavy fissioning nuclei, were extensively studied during last 60 years. The renewed interest to their properties is related to the problem of quantum chaos. In the region of low neutron energies, the resonances are very narrow and well separated. The large lifetime and the small energy spread allow one to interpret a resonance as a fully equilibrated compou...

Sciences exist to demonstrate the fundamental order underlying nature. Chaos/complexity theory is a novel and amazing field of scientific inquiry. Notions of our everyday experiences are somehow in connection to the laws of nature through chaos/complexity theory’s concerns with the relationships between simplicity and complexity, between orderliness and randomness (Retrieved from http://www.inc...

Since the 2005 demonstration of optimal topological chaos in a particular instance of the 2-sector RSS model, the delineation of the optimal policy function for “small” discount factors has remained open. This paper (i) provides an explicit solution when the discount factor is less than the labor/capital-output ratio, (ii) establishes the existence of optimal topological chaos for a non-negligi...

The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the J − T scheme for 12 particles in the sd-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model bas...

Quantum systems with chaotic classical counterparts cannot be treated by perturbative techniques or any kind of adiabatic approximations. This is so, in spite of the quantum suppression of classical chaos. We explicitly calculate the adiabaticity parameter for the case of a Fermi Accelerator and show that the adiabatic expansion of the evolution operator is divergent. The relevance of this situ...

To elucidate the mechanism by which chaos is generated in the shell model, we compare three random–matrix ensembles: the Gaussian orthogonal ensemble, French’s two–body embedded ensemble, and the two–body random ensemble (TBRE) of the shell model. Of these, the last two take account of the two–body nature of the residual interaction, and only the last, of the existence of conserved quantum numb...

In the last decades, renormalization group (RG) ideas have been applied to describe universal properties of different routes to chaos (quasi-periodic, period doubling or tripling, Siegel disk boundaries, etc.). Each of the RG theories leads to universal scaling exponents which are related to the action of certain RG operators. The goal of this announcement is to show that there is a principle t...

We derive semiclassical approximations for wavefunctions, Green’s functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The wavefunctions, Green’s functions and expectation values of the unperturbed Hamiltonian are expressed in terms of the spectral determinant of the perturbed Hamilt...

Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations (perturbations in dynamics), as well as systems which are robust against mutation (perturbations in network structure). To achieve such a design, we apply a ...