Analysis of universality in transient dynamics of coherent electronic transport

We study the charge transfer dynamics following the formation of a phase or voltage biased superconducting nano-junction using a full counting statistics analysis. We demonstrate that the evolution of the zeros of the generating function allows one to identify the population of different many body states much in the same way as the accumulation of Yang-Lee zeros of the partition function in equilibrium statistical mechanics is connected to phase transitions. We give an exact expression connecting the dynamical zeros to the charge transfer cumulants and discuss when an approximation based on "dominant" zeros is valid. We show that, for generic values of the parameters, the system gets trapped into a metastable state characterized by a non-equilibrium population of the many body states which is dependent on the initial conditions. We study in particular the effect of the switching rates in the dynamics showing that, in contrast to intuition, the deviation from thermal equilibrium increases for the slower rates. In the voltage biased case the steady state is reached independently of the initial conditions. Our method allows us to obtain accurate results for the steady state current and noise in quantitative agreement with steady state methods developed to describe the multiple Andreev reflections regime. Finally, we discuss the system dynamics after a sudden voltage drop showing the possibility of tuning the many body states population by an appropriate choice of the initial voltage, providing a feasible experimental way to access the quench dynamics and control the state of the system.

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“…In a previous work we derived exact expressions for the charge cumulants of arbitrary order [46]. In terms of the DYLZs these can be written as…”

Section: A Relation Between Dylzs and Cumulantsmentioning

confidence: 99%

Quench dynamics in superconducting nanojunctions: Metastability and dynamical Yang-Lee zeros

2017

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“…This is useful for distinguishing between rapid and slow current fluctuations which can, in turn, be addressed simultaneously at different frequencies and at different times. In these systems, not only the first moment of the single-particle observables but also current-current correlations and their associated frequency-dependent noise spectra have been considered [238,239,[340][341][342] as they contain more useful information about the transient dynamics. Generally, it has been established that these fluctuations do not follow simple monotonic relaxation processes which could be estimated from their equilibrium or steady-state properties.…”

Section: Electronic Transportmentioning

confidence: 99%

A many-body approach to transport in quantum systems: from the transient regime to the stationary state

Ridley

Talarico

Karlsson

et al. 2022

J. Phys. A: Math. Theor.

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We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive -- encompassing pump--probe scenarios as well as driven quantum systems -- we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron--phonon couplings, topological superconductors, and optically responsive molecular junctions where electron--photon couplings are relevant.

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“…On the theoretical side transport transient dynamics has been addressed using different methods valid for different regimes. Thus, the scattering approach or the non-equilibrium Green function formalism have been used for describing the dynamics in the coherent non-interacting regime [19][20][21][22][23][24][25][26][27][28][29][30]. However, the inclusion of interactions is essential to analyze the transport dynamics through localized states, as is the case of molecular junctions or semiconducting quantum dots.…”

Section: Introductionmentioning

confidence: 99%

Transient dynamics in interacting nanojunctions within self-consistent perturbation theory

et al. 2018

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We present an analysis of the transient electronic and transport properties of a nanojunction in the presence of electron-electron and electron-phonon interactions. We introduce a novel numerical approach which allows for an efficient evaluation of the non-equilibrium Green functions in the time domain. Within this approach we implement different self-consistent diagrammatic approximations in order to analyze the system evolution after a sudden connection to the leads and its convergence to the steady state. These approximations are tested by comparison with available numerically exact results, showing good agreement even for the case of large interaction strength. In addition to its methodological advantages, this approach allows us to study several issues of broad current interest like the build up in time of Kondo correlations and the presence or absence of bistability associated with electron-phonon interactions. We find that, in general, correlation effects tend to remove the possible appearance of charge bistability.

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Analysis of universality in transient dynamics of coherent electronic transport

Cited by 8 publications

References 24 publications

Quench dynamics in superconducting nanojunctions: Metastability and dynamical Yang-Lee zeros

Quench dynamics in superconducting nanojunctions: Metastability and dynamical Yang-Lee zeros

A many-body approach to transport in quantum systems: from the transient regime to the stationary state

Transient dynamics in interacting nanojunctions within self-consistent perturbation theory

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