Toulouse limit for the nonequilibrium Kondo impurity: Currents, noise spectra, and magnetic properties

Schiller, Avraham; Hershfield, Selman

doi:10.1103/physrevb.58.14978

Cited by 125 publications

(232 citation statements)

References 44 publications

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“…To our knowledge, the only results on shot noise in the Kondo model are due to Schiller and Hershfield [311], = J RR z . As a function of the bias voltage, the Fano factor is zero at zero bias, and grows monotonically.…”

Section: B Anderson and Kondo Impuritiesmentioning

confidence: 99%

“…The frequency dependence of the shot noise is sensitive to the spectral function of the Kondo model, and exhibits structure at the inner scales of energy. The studies [311], though quite careful, do not, of course, exhaust the opportunities to investigate shot noise in strongly correlated systems, offered by the Kondo model.…”

Section: B Anderson and Kondo Impuritiesmentioning

confidence: 99%

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Shot noise in mesoscopic conductors

2000

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Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and BoltzmannLangevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

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Section: B Anderson and Kondo Impuritiesmentioning

confidence: 99%

Section: B Anderson and Kondo Impuritiesmentioning

confidence: 99%

Shot noise in mesoscopic conductors

2000

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“…The latter describes directly the expected end result just from "how the state looks" asymptotically far from the impurity. Hershfield's Y operator [5] (see also the studies [3,6,7]) gives a "steady-state density matrix" that encodes these scattering states. This is interesting, since a non-equilibrium steady state is not described by the usual density matrix, but it is still hard to apply to interacting systems.…”

mentioning

confidence: 99%

New Method for Studying Steady States in Quantum Impurity Problems: The Interacting Resonant Level Model

Doyon

2007

Phys. Rev. Lett.

101

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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 ).PACS numbers: 73.63. Kv, 72.15.Qm, 72.10.Fk Impurity models describe mesoscopic quantum objects in contact with large conducting leads. Quantum dots are much-studied examples, and experiments in a bias voltage [1] lead to accurate descriptions of their nonequilibrium steady-state properties. In impurity models, such states are of high interest as they pose the theoretical challenge of capturing the effect of non-equilibrium in a truly quantum system, yet they constitute the simplest non-equilibrium situation, where properties are time independent. At low energies, interactions between the leads' Landau quasi-particles and the impurity occur in the s-wave channel, and the spectrum may be linearised around the two Fermi points. Then, the universal behaviour is described by free massless fermions on the half line (bulk conformal field theory) with a non-conformal boundary interaction at the end-point. Many methods are known for studying equilibrium behaviors in such models, but understanding and accessing properties of non-equilibrium steady states is still a much harder task. Wilson's picture does not apply, and, for instance, the effect of a bias on low-energy processes (which determines the large-bias current) is still under study [2,3].Two calculational schemes exist:the real-time Schwinger-Keldysh formulation and the scattering-state Lippman-Schwinger formulation. The former relies on the infinite extent of the half line in order to absorb the energy released by relaxation from an appropriate "uninteracting" density matrix to the steady state. It requires relaxation mechanisms (see, e.g. [3]), whose absence may lead to pathologies in perturbative expansions [4]. The latter describes directly the expected end result just from "how the state looks" asymptotically far from the impurity. Hershfield's Y operator [5] (see also the studies [3,6,7]) gives a "steady-state density matrix" that encodes these scattering states. This is interesting, since a non-equilibrium steady state is not described by the usual density matrix, but it is still hard to apply to interacting systems. Exact results for integable models occur when the exact quasi-particles do not mix the bias...

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“…They are just two different ways of summing that series. For a non-interacting problem for which the series can be resumed exactly, the NEGF and the NE density matrix with the Y operators approach provide the same result [59,60]. For an interacting system, one must resort to approximations to partially resume the series, and, therefore, the two approaches are similar only when the same approximations are used.…”

Section: An Examplementioning

confidence: 97%

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

Ness

2017

Entropy

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Abstract:We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs-von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.

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Toulouse limit for the nonequilibrium Kondo impurity: Currents, noise spectra, and magnetic properties

Cited by 125 publications

References 44 publications

Shot noise in mesoscopic conductors

Shot noise in mesoscopic conductors

New Method for Studying Steady States in Quantum Impurity Problems: The Interacting Resonant Level Model

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

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