Correlations in Nonequilibrium Luttinger Liquid and Singular Fredholm Determinants

Protopopov, I. V.; Gutman, D. B.; Mirlin, A. D.

doi:10.1103/physrevlett.110.216404

Cited by 10 publications

(17 citation statements)

References 67 publications

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“…A full-scale non-equilibrium bosonization approach, 24,[39][40][41][42][43][44] describing interactions exactly, including also effects of interchannel interaction within the reservoir region, poses a particular challenge when tunneling through the dots and finite range interactions are accounted for simultaneously. Our perturbative treatment indicates which elements have to enter an attempt for a full bosonization solution that captures currents in triangles III and IV.…”

Section: Discussionmentioning

confidence: 99%

“…In the diagrams generated by (50), the phase proportional to x L − x L shifts the tunneling coordinate x L in the source channel to the coordinate x L in the reservoir channel, such that all currents become functions of the distance ∆x = x L − x R , as it is the case for intrachannel interaction (27), compare (39) and (44).…”

Section: Interactions Between Reservoir Region and Source Leadmentioning

confidence: 99%

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Interaction-induced charge transfer in a mesoscopic electron spectrometer

et al. 2019

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A novel mesoscopic electron spectrometer allows for the probing of relaxation processes in quantum Hall edge channels. The device is composed of an emitter quantum dot that injects energy-resolved electrons into the channel closest to the sample edge, to be subsequently probed downstream by a detector quantum dot of the same type. In addition to inelastic processes in the sample that stem from interactions inside the region between the quantum dot energy filters (inner region), anomalous signals are measured when the detector energy exceeds the emitter energy. Considering finite range Coulomb interactions in the sample, we find that energy exchange between electrons in the current inducing source channel and the inner region, similar to Auger recombination processes, is responsible for such anomalous currents. In addition, our perturbative treatment of interactions shows that electrons emitted from the source, which dissipate energy to the inner region before entering the detector, contribute to the current most strongly when emitter-detector energies are comparable. Charge transfer in which the emitted electron is exchanged for a charge carrier from the Fermi sea, on the other hand, preferentially occurs close to the Fermi level. arXiv:1906.11050v1 [cond-mat.mes-hall]

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Section: Discussionmentioning

confidence: 99%

Section: Interactions Between Reservoir Region and Source Leadmentioning

confidence: 99%

Interaction-induced charge transfer in a mesoscopic electron spectrometer

et al. 2019

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“…After linearization of the fermionic spectrum, it allows one to map the problem onto one of non-interacting bosons. For arbitrary distribution functions, the non-equilibrium bosonization yields results for LL correlation functions in terms of singular Fredholm determinants 9,10 .…”

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confidence: 99%

Dissipationless kinetics of one-dimensional interacting fermions

et al. 2014

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We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a non-linear single-particle spectrum. We show that, despite non-Fermi-liquid nature of the problem, non-equilibrium phenomena can be described in terms of a kinetic equation for certain quasiparticles related to the original fermions by a non-linear transformation which decouples the left-and right-moving excitations. Employing this approach, we investigate the kinetics of the phase space distribution of the quasiparticles and thus determine the time evolution of the density pulse. This allows us to explore a crossover from the essentially free-fermion evolution for weak or short-range interaction to hydrodynamics emerging in the case of sufficiently strong, long-range interaction.PACS numbers: 73.21.Hb, 73.22.Lp, 47.37.+q Understanding non-equilibrium phenomena is one of central themes in condensed matter physics. For Fermiliquid systems (e.g. electrons in metals) such phenomena are conventionally described in the framework of a quantum kinetic equation for quasiparticle excitations. According to Landau Fermi-liquid theory, it has the same form as for weakly interacting particles up to a renormalization of parameters (effective mass, interaction constants, and scattering integral). This equation governs the evolution of a single-particle density matrix (characterizing the quasiparticle phase space distribution) and readily yields various physical observables 1-3 .For a variety of strongly interacting fermionic systems, the Fermi liquid theory (at least, in its standard form) is not applicable: interaction destroys the quasiparticle pole. In these cases on has to find an alternative way to describe transport and non-equilibrium phenomena. This is usually done by formulating effective theories in terms of some collective degrees of freedom. A famous realization of a non-Fermi-liquid state is provided by one-dimensional (1D) interacting fermions. This system is characterized by a strongly correlated ground state-Luttinger liquid (LL) 4-8 -which exhibits an infrared divergence of an electronic self-energy, eliminating the quasiparticle pole from the spectral function. This manifests itself in a power-law suppression of the tunneling (zero-bias anomaly) and indicates that quasiparticle excitations are ill-defined. A well-known tool for dealing with such correlated 1D systems is bosonization 4-8 . After linearization of the fermionic spectrum, it allows one to map the problem onto one of non-interacting bosons. For arbitrary distribution functions, the non-equilibrium bosonization yields results for LL correlation functions in terms of singular Fredholm determinants 9,10 .In this work we explore kinetics of interacting 1D fermions, having in mind the following model setup. Initially, a hump (or a dip) in a fermionic density is created by an external potential. At time t = 0 the potential is switched off, and electronic pulses start to propagate to the right and to the left. The evolution of the electronic density as...

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“…Recent experiments have addressed nonequilibrium spectroscopy of carbon nanotubes 27 and quantum Hall edge states 28 as well as nonequilibrium edge state interferometry [29][30][31][32][33][34][35][36] . On the theory side, one of important recent theoretical advances was a development of the method of nonequilibrium bosonization [37][38][39][40] that permits, in particular, to treat Luttinger liquids with distribution functions of incoming electrons that have multiple Fermi edges. It was shown that this leads to a multiple-branch zero-bias anomaly with exponents and dephasing rates controlled by the nonequilibrium state of the system.…”

Section: Introductionmentioning

confidence: 99%

Interaction quench in nonequilibrium Luttinger liquids

2013

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We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a sudden interaction switch-on ("quench"), focussing on a double-step initial momentum distribution function. In the framework of the non-equilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasi-particle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.

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Correlations in Nonequilibrium Luttinger Liquid and Singular Fredholm Determinants

Cited by 10 publications

References 67 publications

Interaction-induced charge transfer in a mesoscopic electron spectrometer

Interaction-induced charge transfer in a mesoscopic electron spectrometer

Dissipationless kinetics of one-dimensional interacting fermions

Interaction quench in nonequilibrium Luttinger liquids

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