J. Lages

Decoherence by a chaotic many-spin bath

We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the systems density matrix, the linear entropy, and the fidelity of the central system decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, and the baths spectral density of states) is not always sufficient, and much finer details of the baths dynamics can strongly affect the decoherence process.

Composition law for polarizers

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption—as in a Polaroid film—and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincare sphere as is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved, for example, by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.

Symplectic map description of Halley's comet dynamics

Abstract We determine the two-dimensional symplectic map describing 1P/Halley chaotic dynamics. We compute the Solar system kick function, i.e. the energy transfer to 1P/Halley along one passage through the Solar system. Each planet contribution to the Solar system kick function appears to be the sum of a Keplerian potential and of a rotating gravitational dipole potential due to the Sun movement around Solar system barycenter. The Halley map gives a reliable description of comet dynamics on time scales of 10 4 yr while on a larger scales the parameters of the map are slowly changing due to slow oscillations of orbital momentum.

Dark matter chaos in the Solar system

We study the capture of Galactic dark matter particles in the Solar system produced by rotation of Jupiter. It is shown that the capture cross-section is much larger than the area of the Jupiter orbit being inversely diverging at small particle energy. We show that the dynamics of captured particles is chaotic and is well described by a simple symplectic dark map. This dark map description allows us to simulate the scattering and dynamics of 10 14 dark matter particles during the lifetime of the Solar system and to determine the dark matter density profile as a function of distance from the Sun. The mass of captured dark matter in the radius of the Neptune orbit is estimated to be 2 × 10 15 g. The radial density of captured dark matter is found to be approximately constant behind the Jupiter orbit being similar to the density profile found in galaxies.

Phase of biparticle localized states for the Cooper problem in two-dimensional disordered systems

The Cooper problem is studied numerically for the Anderson model with disorder in two dimensions. It is shown that the attractive Hubbard interaction creates a phase of biparticle localized states in the regime where noninteracting states are delocalized. This phase cannot be obtained in the mean-field approximation and the pair coupling energy is strongly enhanced in this regime. The effects of magnetic field are studied and it is shown that under certain conditions they lead to delocalization.

Chaotic enhancement of dark matter density in binary systems and galaxies

Using symplectic map description we study the capture of galactic dark matter particles (DMP) in two-body and few-body galaxies. This approach allows to model scattering of

A new kind of geometric phases in open quantum systems and higher gauge theory

10^{16}

Suppression of quantum chaos in a quantum computer hardware

DMP following time evolution of captured particle on about

Geometric phase and Pancharatnam phase induced by light wave polarization

10^9

C*-geometric phase for mixed states: entanglement, decoherence and the spin system

orbital periods. We obtain DMP density distribution inside such galaxies and determine the enhancement factor of their density in galactic center compared to its inter-galactic value as a function of mass ratio of galactic bodies and a ratio of body velocity to velocity of galactic DMP wind. We find that the enhancement factor can be of the order of ten thousands.