Alternative proof for the localization of Sinai's walk

We give an alternative proof of the localization of Sinai's random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood

Integrable impurities in Hubbard chain with the open boundary condition

The Kondo problem of two impurities in 1D strongly correlated electron system within the framework of the open boundary Hubbard chain is solved and the impurities, coupled to the ends of the electron system, are introduced by their scattering matrices with electrons so that the boundary matrices satisfy the reflecting integrability condition. The finite size correction of the ground state energy is obtained due to the impurities. Exact expressions for the low temperature specific heat contributed by the charge and spin parts of the magnetic impurities are derived. The Pauli susceptibility and the Kondo temperature are given explicitly. The Kondo temperature is inversely proportional to the density of electrons.Comment: 6 pages, Revtex, To appear in Europhysics Letter

Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors

We consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling and mixed spin-singlet/triplet superconducting pairing in the context of mean-field theory. The Hamiltonian is diagonalized and exact eigenvalues are obtained, thus allowing us to write down the coupled gap equations for the different order parameters. Our results may then be applied to any model describing coexistence of any combination of these three phenomena. As a specific application of our results, we consider tunneling between a normal metal and a noncentrosymmetric superconductor with mixed singlet and triplet gaps. The conductance spectrum reveals information about these gaps in addition to how the influence of spin-orbit coupling is manifested. We also consider the coexistence of itinerant ferromagnetism and triplet superconductivity as a model for recently discovered ferromagnetic superconductors. The coupled gap equations are solved self-consistently, and we study the conditions necessary to obtain the coexistent regime of ferromagnetism and superconductivity. Analytical expressions are presented for the order parameters, and we provide an analysis of the free energy to identify the preferred system state. Moreover, we make specific predictions concerning the heat capacity for a ferromagnetic superconductor. In particular, we report a nonuniversal relative jump in the specific heat, depending on the magnetization of the system, at the uppermost superconducting phase transition. [Shortened abstract due to arXiv submission.]Comment: 19 pages, 15 figures (high quality figures available in published version). Accepted for publication in Phys. Rev.

Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters

Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $_{n}$ ($_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $_{n}$ ($_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure

Gravitational Waves in Bianchi Type-I Universes I: The Classical Theory

The propagation of classical gravitational waves in Bianchi Type-I universes is studied. We find that gravitational waves in Bianchi Type-I universes are not equivalent to two minimally coupled massless scalar fields as it is for the Robertson-Walker universe. Due to its tensorial nature, the gravitational wave is much more sensitive to the anisotropy of the spacetime than the scalar field is and it gains an effective mass term. Moreover, we find a coupling between the two polarization states of the gravitational wave which is also not present in the Robertson-Walker universe.Comment: 34 papers, written in ReVTeX, submitted to Physical Review