Nonequilibrium Quantum Impurity Systems

We propose a hierarchical dynamics approach for evaluation of nonequilibrium dynamic response properties of quantum impurity systems. It is based on a hierarchical equations of motion formalism, in conjunction with a linear response theory established in the hierarchical Liouville space. This provides an accurate and universal tool for characterization of a variety of response and correlation functions of local impurities, as well as transport related response properties. The practicality of our proposed approach is demonstrated via the evaluation of various dynamical properties of a single-impurity Anderson model. These include the impurity spectral density, local charge fluctuation, local magnetic susceptibility, and current-voltage admittance, in both equilibrium and nonequilibrium situations. The numerical results are considered to be quantitatively accurate, as long as they converge quantitatively with respect to the truncation of the hierarchy.We propose a hierarchical dynamics approach for evaluation of nonequilibrium dynamic response properties of quantum impurity systems. It is based on a hierarchical equations of motion formalism, in conjunction with a linear response theory established in the hierarchical Liouville space. This provides an accurate and universal tool for characterization of a variety of response and correlation functions of local impurities, as well as transport related response properties. The practicality of our proposed approach is demonstrated via the evaluation of various dynamical properties of a single-impurity Anderson model. These include the impurity spectral density, local charge fluctuation, local magnetic susceptibility, and current-voltage admittance, in both equilibrium and nonequilibrium situations. The numerical results are considered to be quantitatively accurate, as long as they converge quantitatively with respect to the truncation of the hierarchy.

arXiv:1301.6850Physical Review BJul 22, 201345 citations

Stable nonequilibrium of quantum systems

V. V. Mityugov

Radiophysics and Quantum ElectronicsApr 1, 19890 citations

Nonequilibrium Transport in Quantum Impurity Models: The Bethe Ansatz for Open Systems

Pankaj Mehta, Natan Andrei

We develop an exact nonperturbative framework to compute steady-state properties of quantum impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe ansatz--the nonequilibrium Bethe ansatz--we explicitly construct the scattering eigenstates for the interacting resonance level model and derive exact, nonperturbative results for the steady-state properties of the system.We develop an exact nonperturbative framework to compute steady-state properties of quantum impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe ansatz--the nonequilibrium Bethe ansatz--we explicitly construct the scattering eigenstates for the interacting resonance level model and derive exact, nonperturbative results for the steady-state properties of the system.

arXiv:cond-mat/0508026Physical Review LettersJun 1, 2006226 citations

Quantum critical points in quantum impurity systems

Hyun Jung Lee, R. Bulla

arXiv:cond-mat/0406557Physica B Condensed MatterApr 1, 20050 citations

Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

HyungWon Kim, David A. Huse

We treat the nonequilibrium motion of a single-impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\ensuremath{\sim}{t}^{d/(d+1)}$ for the $d$ -dimensional system with $d\ensuremath{\ge}2$. For nonzero temperature $T$ , this crosses over to diffusive motion at long times with diffusivity $D\ensuremath{\sim}{T}^{\ensuremath{-}(d\ensuremath{-}1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.We treat the nonequilibrium motion of a single-impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\ensuremath{\sim}{t}^{d/(d+1)}$ for the $d$-dimensional system with $d\ensuremath{\ge}2$. For nonzero temperature $T$, this crosses over to diffusive motion at long times with diffusivity $D\ensuremath{\sim}{T}^{\ensuremath{-}(d\ensuremath{-}1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.

arXiv:1201.1055Physical Review AApr 6, 20127 citations

d

-dimensional system with $d\ensuremath{\ge}2$. For nonzero temperature

T

, this crosses over to diffusive motion at long times with diffusivity $D\ensuremath{\sim}{T}^{\ensuremath{-}(d\ensuremath{-}1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.