Related papers: Quantum linear algebra for disordered electrons
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The quantum kinetic theory for noninteracting electrons in a disordered solid is introduced and discussed. We first use many-body…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated…
We consider the problem of electron transport across a quasi-one-dimensional disordered multiply-scattering medium, and study the statistical properties of the electron density inside the system. In the physical setup that we contemplate,…
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization…
In the weak disordered regime we provide analytical expressions for the electron localization lengths in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. They are exact up to order $W^2$…
We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a coloured noise and the one-dimensional Anderson-type model with correlated diagonal disorder. It is rigorously shown that…
This paper reviews the physics of quantum disorder in relation with a series of experiments using laser-cooled atoms exposed to "kicks" of a standing wave, realizing a paradigmatic model of quantum chaos, the kicked rotor. This dynamical…
We apply the linear $\delta$-expansion (LDE), originally developed as a nonperturbative, analytical approximation scheme in quantum field theory, to problems involving noninteracting electrons in disordered solids. The initial idea that the…
We show that the tails of the asymptotic density distribution of a quantum wave packet that localizes in the the presence of random or quasiperiodic disorder can be described by the diagonal term of the projection over the eingenstates of…
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. Parallel numerical simulations and analytic theory demonstrate that the interplay between nonlinearity and…
Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of…
We report a study of a disorder-dependent real-space representation of the quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
The density of states of one-dimensional disordered electron systems with long range Coulomb interaction is studied in the weak pinning limit. The density of states is found to follow a power law with an exponent determined by localization…
These lectures provide an introduction to the theory of disordered interacting electron systems. In particular, we concentrate on those aspects which are fundamental for the problem of the metal-insulator transition due to the interplay of…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical…
There are still no interacting models of the Wightman axioms, suggesting that the axioms are too tightly drawn. Here a weakening of linearity for quantum fields is proposed, with the algebra still linear but with the quantum fields no…