Breit-Wigner width for two interacting particles in one-dimensional random potential

For two interacting particles (TIP) in one-dimensional random potential the dependence of the Breit-Wigner width $\Gamma$, the local density of states and the TIP localization length on system parameters is determined analytically. The theoretical predictions for $\Gamma$ are confirmed by numerical simulations.Comment: 10 pages Latex, 4 figures included. New version with extended numerical results and discussions of earlier result

Chaos Thresholds in finite Fermi systems

The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple Slater-determinant states. Nevertheless, the transition from Poisson to Wigner-Dyson statistics of energy levels is governed by the effective high order interaction between states very distant in the Fock space. The concrete form of the transition depends on the way one chooses to work out the problem of factorial divergency of the number of Feynman diagrams. In the proposed scheme the change of statistics has a form of narrow phase transition and may happen even below the direct interaction threshold.Comment: 9 pages, REVTEX, 2 eps figures. Enlarged versio

Local Spectral Density for a Periodically Driven System of Coupled Quantum States with Strong Imperfection in Unperturbed Energies

A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system is excited by an external periodic field, the temporal profile of which is close to monochromatic one. The shape of local spectral density is shown to be well described by the contour obtained from a relevant model of periodically driven two-states system with irreversible losses to an external thermal bath. The shape width and the inverse participation ratio are determined as functions both of the Rabi frequency and of parameters specifying the localization effect for our system in the absence of external field.Comment: 6 pages, 5 figures, submitted to Optics and Spectroscop

Emergence of Quantum Ergodicity in Rough Billiards

By analytical mapping of the eigenvalue problem in rough billiards on to a band random matrix model a new regime of Wigner ergodicity is found. There the eigenstates are extended over the whole energy surface but have a strongly peaked structure. The results of numerical simulations and implications for level statistics are also discussed.Comment: revtex, 4 pages, 4 figure

Renyi-Wehrl entropies as measures of localization in phase space

We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure states for spin systems. According to Lieb's conjecture the minimal values are provided by the spin coherent states. Though Lieb's conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Renyi-Wehrl entropies averaged over the natural measure in the space of pure quantum states.Comment: 18 pages, no figures, some improved versions of main proofs, added J.referenc

Energy level statistics of the two-dimensional Hubbard model at low filling

The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin and pseudospin symmetry) have been taken into account explicitly from the beginning of the calculation by projecting into symmetry invariant subspaces. The details of this group theoretical treatment are presented with special attention to the nongeneric case of L=4, where a particular complicated space group appears. For all the lattices studied, a significant amount of levels within each symmetry invariant subspaces remains degenerated, but except for L=4 the ground state is nondegenerate. We explain the remaining degeneracies, which occur only for very specific interaction independent states, and we disregard these states in the statistical spectral analysis. The intricate structure of the Hubbard spectra necessitates a careful unfolding procedure, which is thoroughly discussed. Finally, we present our results for the level spacing distribution, the number variance $\Sigma^2$, and the spectral rigidity $\Delta_3$, which essentially all are close to the corresponding statistics for random matrices of the Gaussian ensemble independent of the lattice size and the coupling strength. Even very small coupling strengths approaching the integrable zero coupling limit lead to the Gaussian ensemble statistics stressing the nonperturbative nature of the Hubbard model.Comment: 31 pages (1 Revtex file and 10 postscript figures

Two Interacting Electrons in a Quasiperiodic Chain

We study numerically the effect of on-site Hubbard interaction U between two electrons in the quasiperiodic Harper's equation. In the periodic chain limit by mapping the problem to that of one electron in two dimensions with a diagonal line of impurities of strength U we demonstrate a band of resonance two particle pairing states starting from E=U. In the ballistic (metallic) regime we show explicitly interaction-assisted extended pairing states and multifractal pairing states in the diffusive (critical) regime. We also obtain localized pairing states in the gaps and the created subband due to U, whose number increases when going to the localized regime, which are responsible for reducing the velocity and the diffusion coefficient in the qualitatively similar to the non-interacting case ballistic and diffusive dynamics. In the localized regime we find propagation enhancement for small U and stronger localization for larger U, as in disordered systems.Comment: 14 pages Revtex file, 8 figures (split into 19 jpg figures). (postscript versions of the jpg figures are also available upon request) submitted to PR

Effective charge-spin models for quantum dots

It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localised near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript file

The Gravitational Lens -- Galaxy Group Connection. II. Groups Associated with B2319+051 and B1600+434

We report on the results of a spectroscopic survey of the environments of the gravitational lens systems CLASS B1600+434 (z_l = 0.41, z_s = 1.59) and CLASS B2319+051 (z_l = 0.62). The B1600+434 system has a time delay measured for it, and we find the system to lie in a group with a velocity dispersion of 100 km/s and at least six members. B2319+051 has a large group in its immediate foreground with at least 10 members and a velocity dispersion of 460 km/s and another in the background of the lens with a velocity dispersion of 190 km/s. There are several other small groups in the fields of these lens systems, and we describe the properties of these moderate redshift groups. Furthermore, we quantify the effects of these group structures on the gravitational lenses and find a ~5% correction to the derived value of H_0 for B1600+434.Comment: 10 pages, 9 figures, submitted to A

The Star Formation Rate Density and Dust Attenuation Evolution over 12 Gyr with the VVDS Surveys

[Abridged] We investigate the global galaxy evolution over 12 Gyr (0.05<z<4.5), from the star formation rate density (SFRD), combining the VVDS Deep (17.5<=I<=24.0) and Ultra-Deep (23.00<=i<=24.75) surveys. We obtain a single homogeneous spectroscopic redshift sample, totalizing about 11000 galaxies. We estimate the rest-frame FUV luminosity function (LF) and luminosity density (LD), extract the dust attenuation of the FUV radiation using SED fitting, and derive the dust-corrected SFRD. We find a constant and flat faint-end slope alpha in the FUV LF at z1.7, we set alpha steepening with (1+z). The absolute magnitude M*_FUV brightens in the entire range 02 it is on average brighter than in the literature, while phi* is smaller. Our total LD shows a peak at z=2, present also when considering all sources of uncertainty. The SFRD history peaks as well at z=2. It rises by a factor of 6 during 2 Gyr (from z=4.5 to z=2), and then decreases by a factor of 12 during 10 Gyr down to z=0.05. This peak is mainly produced by a similar peak within the population of galaxies with -21.5<=M_FUV<=-19.5 mag. As times goes by, the total SFRD is dominated by fainter and fainter galaxies. The presence of a clear peak at z=2 and a fast rise at z>2 of the SFRD is compelling for models of galaxy formation. The mean dust attenuation A_FUV of the global galaxy population rises by 1 mag during 2 Gyr from z=4.5 to z=2, reaches its maximum at z=1 (A_FUV=2.2 mag), and then decreases by 1.1 mag during 7 Gyr down to z=0. The dust attenuation maximum is reached 2 Gyr after the SFRD peak, implying a contribution from the intermediate-mass stars to the dust production at z<2.Comment: 23 pages, 15 figures, accepted for publication in A&