Gibbs attractor: a chaotic nearly Hamiltonian system, driven by external harmonic force

A chaotic autonomous Hamiltonian systems, perturbed by small damping and small external force, harmonically dependent on time, can acquire a strange attractor with properties similar to that of the canonical distribution - the Gibbs attractor. The evolution of the energy in such systems can be described as the energy diffusion. For the nonlinear Pullen - Edmonds oscillator with two degrees of freedom the properties of the Gibbs attractor and their dependence on parameters of the perturbation are studied both analytically and numerically.Comment: 8 pages RevTeX, 3 figure

Energy diffusion in strongly driven quantum chaotic systems

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule exceeds the frequency of perturbation. It is shown that the energy evolution retains its diffusive character, with the diffusion coefficient that is asymptotically proportional to the magnitude of perturbation and to the square root of the density of states. The results are supported by numerical calculation. They imply the absence of the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit $\hbar \to 0$.Comment: 12 pages, 3 figures, RevTe

Bright solitons in Bose-Fermi mixtures

We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi ($^{87}$Rb -$^{40}$K in our case) scattering length.Comment: 6 pages, 6 figures, 1 tabl

A pulsed atomic soliton laser

It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a non-dispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments.Comment: 11 pages, 4 figure

On the interaction of a single-photon wave packet with an excited atom

The interaction of a single-photon wave packet with an initially excited two-level atom in free space is studied in semiclassical and quantum approaches. It is shown that the final state of the field does not contain doubly occupied modes. The process of the atom's transition to the ground state may be accelerated, decelerated or even reversed by the incoming photon, depending on parameters. The spectrum of emitted radiation is close to the sum of the spectrum of the incoming single-photon wave packet and the natural line shape, with small and complicated deviations.Comment: 17 pages, 5 figure

Models of the Pseudogap State of Two-Dimensional Systems

We analyze a number of ``nearly exactly'' solvable models of electronic spectrum of two-dimensional systems with well-developed fluctuations of short range order of ``dielectric'' (e.g. antiferromagnetic) or ``superconducting'' type, which lead to the formation of anisotropic pseudogap state on certain parts of the Fermi surface. We formulate a recurrence procedure to calculate one-electron Green's function which takes into account all Feynman diagrams in perturbation series and is based upon the approximate Ansatz for higher-order terms in this series. Detailed results for spectral densities and density of states are presented. We also discuss some important points concerning the justification of our Ansatz for higher-order contributions.Comment: 22 pages, 15 figures, RevTeX 3.0, Postscript figures attache

On the influence of noise on chaos in nearly Hamiltonian systems

The simultaneous influence of small damping and white noise on Hamiltonian systems with chaotic motion is studied on the model of periodically kicked rotor. In the region of parameters where damping alone turns the motion into regular, the level of noise that can restore the chaos is studied. This restoration is created by two mechanisms: by fluctuation induced transfer of the phase trajectory to domains of local instability, that can be described by the averaging of the local instability index, and by destabilization of motion within the islands of stability by fluctuation induced parametric modulation of the stability matrix, that can be described by the methods developed in the theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP