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New method for studying steady states in quantum impurity problems: The interacting resonant level model

Benjamin Doyon
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Abstract

We develop a new perturbative method for studying any steady states of quantum impurities, in or out of equilibrium. We show that steady-state averages are completely fixed by basic properties of the steady-state (Hershfield's) density matrix along with dynamical "impurity conditions". This gives the full perturbative expansion without Feynman diagrams (matrix products instead are used), and "re-sums" into an equilibrium average that may lend itself to numerical procedures. We calculate the universal current in the interacting resonant level model (IRLM) at finite bias V to first order in Coulomb repulsion U for all V and temperatures. We find that the bias, like the temperature, cuts off low-energy processes. In the IRLM, this implies a power-law decay of the current at large V (also recently observed by Boulat and Saleur at some finite value of U).

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Benjamin Doyon. 2007-08-31. New method for studying steady states in quantum impurity problems: The interacting resonant level model. https://doi.org/10.1103/physrevlett.99.076806

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