Related papers: My Random Walks in Anderson's Garden
This dissertation focuses on a theoretical study of interacting electrons in one dimension. The research elucidates the ground state (zero temperature) electronic phase diagram of an aluminum arsenide quantum wire which is an example of an…
The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher…
We estimate the conjectured interaction between the Earth gravitational field and a superconductor immersed in external, static electric and magnetic field. The latter is close to the sample upper critical field and generates the presence…
The aim of this paper is to study asymptotic geometric properties almost surely or/and in probability of extreme order statistics of an i.i.d. random field (potential) indexed by sites of multidimensional lattice cube, the volume of which…
When first proposed in 1957, the BCS theory for superconductivity, which explained the quasi-totality of its thermodynamic and transport properties, was greeted with great circumspection, before it became the play ground of particle…
We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition of the…
Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius $\rho_0$ in the superposition of the longitudinal uniform magnetic field $\bf B$ and Aharonov-Bohm flux…
Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids (QSL). Here, we show that excitations related to…
Superconductivity is a phenomenon where electrical current flows without friction. The current standard theory for it is the BCS (Bardeen-Cooper-Schrieffer) theory, which explains it as due to the energy gap formation by the…
We combine a recent mapping of the Anderson-Mott metal-insulator transition on a random-field problem with scaling concepts for random-field magnets to argue that disordered electrons near an Anderson-Mott transition show glass-like…
We present a phenomenological Green's function to characterize the superconducting and pseudogap phases of the cuprates based on a microscopic theory of doped Mott insulators. In this framework, the "Fermi arc" and "kink" phenomena observed…
We investigate the conductance through and the spectrum of ballistic chaotic quantum dots attached to two s-wave superconductors, as a function of the phase difference $\phi$ between the two order parameters. A combination of analytical…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
In this work we investigate a class of random walks that interacts with its environment called Tree Builder Random Walk (TBRW). In our settings, at each step, the walker adds a random number of vertices to its position sampled according to…
In high transition temperature (T_c) superconductivity, charge doping is a natural tuning parameter that takes copper oxides from the antiferromagnet to the superconducting region. In the metallic state above T_c the standard Landau's…
This paper treats a number of issues of the cuprates, ranging from the spin resonance peak and the linear one-particle scattering rate to the superconducting transition, in the frame of a Fermi liquid model. Recent ARPES expts. by Valla et…
Superconductivity and quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of quantum Hall effect with a superconductor can…
The infinite-U Anderson model is applied to transport through a quantum dot. The current and density of states are obtained via the non-crossing approximation for two spin-degenerate levels weakly coupled to two leads. At low temperatures,…
We solve by Dynamical Mean Field Theory a toy-model which has a phase diagram strikingly similar to that of high $T_c$ superconductors: a bell-shaped superconducting region adjacent the Mott insulator and a normal phase that evolves from a…
The Gutzwiller-projected mean field theory, also called Plain Vanilla or RMFT, is explained and its successes and possible extensions in describing the phenomenology of the cuprate superconductors are discussed. Throughout we emphasize that…