Scattering and Non-Equilbrium Transport in Quantum Importity Systems

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Non-Technical AbstractThis grant supports theoretical research involving the influence of impurities on the properties of systems such as quantum dots and nanoelectronics. In particular, the properties of these systems under nonequlibrium conditions will be studied. Most past work has been on equilibrium systems. However, nonequilibrium conditions are more realistic in actual applications. The project will involve the participation of graduate students and postdoctoral researchers.Technical AbstractIntellectual Merit: The study of non-equilibrium quantum impurity systems lies at theintersection of mesoscopic and strongly correlated physics. The dramatic recent advances in experimental techniques have allowed for the realization of impurity models in nanoscale devices such as quantum dots where quantum fluctuations are greatly enhanced due to low dimensionality. Describing the interplay between non-equilibrium conditions and strong correlations is a formidable intellectual challenge. This proposal addresses the issue of non-equilibrium steady states, a small corner of the more general problem . A new conceptual framework is proposed that allows for exact and explicit computations of the nonequilibrium steady state properties of quantum impurity models. In particular, it allows for the calculation of many experimentally measurable quantities such as the current across the dot and the nonequilibrium impurity density of states. The proposed framework also allows for the exact computation of scattering properties in quantum impurity models and consequently has strong implications for explaining such physical phenomena as decoherence and anomalous energy relaxation in metallic wires.Broader Impact: Non-equilibrium phenomena are ubiquitous in nature, and yet relativelypoorly understood. This stands in marked difference to equilibrium phenomena where a universal framework has been provided by Boltzmann more than a century ago. Steady states are the simplest among the great variety of non-equilibrium phenomena. This work will forge conceptual and practical tools to provide an exact description of steady-state dynamics in quantum impurity models. In the past, exact solutions have played an important role in increasing our understanding of equilibrium statistical mechanics. It is expected, therefore, that the proposed research will help point the way towards a general formulation of nonequilibrium steady-states by providing exact solutions for a set of models with important experimental realization. On a more practical level, the proposed research will help clarify the limits of applicability of nanodevices operating under temperature and voltage gradients. This has direct practical consequence for modern quantum electronics.The following projects will be studied:. Quantum impurities out of equilibrium: A new conceptual framework is proposedthat allows for the exact computation of the differential conductance and non-equilibriumdensity of states for a quantum dot described by the non-equilibrium Kondo or the Anderson models at all temperatures and bias voltages.. Scattering properties of quantum impurity systems: Exact computation of elastic and inelastic scattering amplitudes of an electron off a magnetic impurity is proposed.Precise predictions, valid for all temperatures and energy scales, will be available to describe: (i) the dephasing time as measured in experiments on magnetoresistance, and (ii) the anomalous energy relaxation rate observed in metallic wires under large bias voltage.. Extended 1D systems out of equilibrium: The development of a conceptual frameworkto describe some extended one-dimensional quantum systems out of equilibrium isproposed.