Level Statistics and Localization for Two Interacting Particles in a Random Potential

We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define the symmetry breaking parameter $\mu \propto U^{-2}$ associated to the statistical invariance under change of basis. We show that the Wigner-Dyson rigidity of the energy levels is maintained up to an energy $E_{\mu}$. We find that $E_{\mu} \propto 1/\sqrt{\mu}$ when $\Gamma$ (the inverse lifetime of the states of the preferential basis) is smaller than $\Delta_2$ (the level spacing), and $E_{\mu} \propto 1/\mu$ when $\Gamma > \Delta_2$. This implies that the two-particle localization length $L_2$ first increases as $|U|$ before eventually behaving as $U^2$.Comment: 4 pages REVTEX, 4 Figures EPS, UUENCODE

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

Properties of the chiral spin liquid state in generalized spin ladders

We study zero temperature properties of a system of two coupled quantum spin chains subject to fields explicitly breaking time reversal symmetry and parity. Suitable choice of the strength of these fields gives a model soluble by Bethe Ansatz methods which allows to determine the complete magnetic phase diagram of the system and the asymptotics of correlation functions from the finite size spectrum. The chiral properties of the system for both the integrable and the nonintegrable case are studied using numerical techniques.Comment: 19 pages, 9eps figures, Late

Quantum error correction of coherent errors by randomization

A general error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomization of static imperfections in a many-qubit system by the repeated application of Pauli operators which change the computational basis. This Pauli-Random-Error-Correction (PAREC)-method eliminates coherent errors produced by static imperfections and increases significantly the maximum time over which realistic quantum computations can be performed reliably. Furthermore, it does not require redundancy so that all physical qubits involved can be used for logical purposes.Comment: revtex 4 pages, 3 fig

Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for publication in Phys. Rev.

Persistent currents in diffusive metallic cavities: Large values and anomalous scaling with disorder

The effect of disorder on confined metallic cavities with an Aharonov-Bohm flux line is addressed. We find that, even deep in the diffusive regime, large values of persistent currents may arise for a wide variety of geometries. We present numerical results supporting an anomalous scaling law of the average typical current $$ with the strength of disorder $w$, $\sim w^{- \gamma}$ with $\gamma < 2$. This is contrasted with previously reported results obtained for cylindrical samples where a scaling $\sim w^{-2}$ has been found. Possible links to, up to date, unexplained experimental data are finally discussed.Comment: 5 pages, 4 figure

Thermodynamics of an integrable model for electrons with correlated hopping

A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state and excitations of the model as a function of the interaction parameter, electronic density and magnetization. Using arguments from conformal field theory we can study the critical exponents describing the asymptotic behaviour of correlation functions at long distances.Comment: 24 pp., latex+epsf, figures include

Doping Induced Magnetization Plateaus

The low temperature magnetization process of antiferromagnetic spin-S chains doped with mobile spin-(S-1/2) carriers is studied in an exactly solvable model. For sufficiently high magnetic fields the system is in a metallic phase with a finite gap for magnetic excitations. In this phase which exists for a large range of carrier concentrations x the zero temperature magnetization is determined by x alone. This leads to plateaus in the magnetization curve at a tunable fraction of the saturation magnetization. The critical behaviour at the edges of these plateaus is studied in detail.Comment: RevTeX, 4 pp. incl. 3 figure

Critical exponents of the degenerate Hubbard model

We study the critical behaviour of the \SUN{} generalization of the one-dimensional Hubbard model with arbitrary degeneracy $N$. Using the integrability of this model by Bethe Ansatz we are able to compute the spectrum of the low-lying excitations in a large but finite box for arbitrary values of the electron density and of the Coulomb interaction. This information is used to determine the asymptotic behaviour of correlation functions at zero temperature in the presence of external fields lifting the degeneracy. The critical exponents depend on the system parameters through a $N\times N$ dressed charge matrix implying the relevance of the interaction of charge- and spin-density waves.Comment: 18 page

Time evolution of Wikipedia network ranking

We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80 percents of top universities of Shanghai ranking during the considered time period.Comment: 10 pages, 11 figures. Accepted for publication in EPJ