Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium

Stegmann, Philipp; Sothmann, Björn; Hucht, Alfred; König, Jürgen

doi:10.1103/physrevb.92.155413

Cited by 52 publications

(52 citation statements)

References 49 publications

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“…As shown in Ref. (), the generating function yielding

C_{normalF, m}^{in}

via Eq. can, then, be expressed as

M_{F}^{in} false(z, t false) = {bold e}^{T} \cdot exp false({bold W}_{z + 1}^{in} t false) {bold P}_{stat},

with the vector

{bold e}^{T} = false(1, 1, \dots, 1 false)

.…”

Section: Stochastic Systemsmentioning

confidence: 99%

“…The corresponding factorial cumulants

C_{normalF, m} false(t false) : = 〈 〈 N^{false(m false)} 〉 〉 false(t false)

are obtained from

C_{normalF, m} false(t false) : = \frac{\partial^{m}}{\partial z^{m}} ln M_{F} false(z, t false) {-2 |}_{z = 0} .

In the context of single‐electron tunneling, the use of factorial rather than ordinary cumulants has been suggested as a convenient tool to identify interactions in the system. Furthermore, factorial and generalized factorial cumulants () have been analyzed in the short‐time limit to detect the presence of fundamental tunneling processes (such as Andreev tunneling) of two electrons simultaneously (). Here, we are going to use factorial cumulants to probe the violation of detailed balance by comparing

C_{normalF, m}^{in} false(t false)

with

C_{normalF, m}^{out} false(t false)

.…”

Section: Stochastic Systemsmentioning

confidence: 99%

“…To evaluate the generating function for a given stochastic system, we follow along the lines described in Ref. (). First, we construct a matrix

{bold W}_{z}^{in}

in which the matrix element

{((), {bold W}_{z}^{in})}_{χ^{'} χ}

is associated with the transition from state

χ

χ^{'}

.…”

Section: Stochastic Systemsmentioning

confidence: 99%

See 2 more Smart Citations

Violation of detailed balance for charge‐transfer statistics in Coulomb‐blockade systems

Stegmann

König

2016

Physica Status Solidi (b)

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We discuss the possibility to generate in Coulomb‐blockade systems steady states that violate detailed balance. This includes both voltage biased and non‐biased scenarios. The violation of detailed balance yields that the charge‐transfer statistics for electrons tunneling into an island experiencing strong Coulomb interaction is different from the statistics for tunneling out. This can be experimentally tested by time‐resolved measurement of the island's charge state. We demonstrate this claim for two model systems.

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“…As shown in Ref. (), the generating function yielding

C_{normalF, m}^{in}

via Eq. can, then, be expressed as

M_{F}^{in} false(z, t false) = {bold e}^{T} \cdot exp false({bold W}_{z + 1}^{in} t false) {bold P}_{stat},

with the vector

{bold e}^{T} = false(1, 1, \dots, 1 false)

.…”

Section: Stochastic Systemsmentioning

confidence: 99%

“…The corresponding factorial cumulants

C_{normalF, m} false(t false) : = 〈 〈 N^{false(m false)} 〉 〉 false(t false)

are obtained from

C_{normalF, m} false(t false) : = \frac{\partial^{m}}{\partial z^{m}} ln M_{F} false(z, t false) {-2 |}_{z = 0} .

C_{normalF, m}^{in} false(t false)

with

C_{normalF, m}^{out} false(t false)

.…”

Section: Stochastic Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Violation of detailed balance for charge‐transfer statistics in Coulomb‐blockade systems

Stegmann

König

2016

Physica Status Solidi (b)

Self Cite

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show abstract

“…It is well known that a super-Poissonian Fano factor (equivalent to a positive second-order factorial cumulant C 1,2 >0) indicates interaction-induced correlations between the transferred electrons. One of the advantages of using factorial cumulants is that its sign can be used as an indicator of correlations not only for the second-but also for higher-order cumulants [30][31][32]. Furthermore, the possibility to choose the parameter s different from 1 increases the sensitivity to detect correlations [32].…”

Section: Introductionmentioning

confidence: 99%

Revealing attractive electron–electron interaction in a quantum dot by full counting statistics

2018

Self Cite

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Recent experiments (2015 Nature 521 196; 2017 Nat. Commun. 8 395) have presented evidence for electron pairing in a quantum dot beyond the superconducting regime. Here, we show that the impact of an attractive electron-electron interaction on the full counting statistics of electron transfer through a quantum dot is qualitatively different from the case of a repulsive interaction. In particular, the sign of higher-order (generalized) factorial cumulants reveals more pronounced correlations, which even survive in the limit of fast spin relaxation.

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“…In this context, some works have recently analyzed the time‐dependent transport statistics, studying the charge transferred cumulants and the factorial cumulants in the incoherent regime. However, the coherent regime has been much less investigated .…”

Section: Introductionmentioning

confidence: 99%

Analysis of universality in transient dynamics of coherent electronic transport

Souto

Martín‐Rodero

Yeyati

2016

Fortschritte der Physik

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We analyze the time-dependent full-counting statistics of charges transmitted through a quantum dot in the coherent regime. The generating function for the time-dependent charge transfer statistics is evaluated numerically by discretizing the Keldysh time contour, which allows us to compute the higher order charge and current cumulants. We also develop an analytic expression for all order cumulants at any time given as a function of the zeros of the generating function, finding that the short time universality is due to the presence of a dominant single zero. The robustness of the universal features at short times is studied in both the sequential and coherent regimes.

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Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium

Cited by 52 publications

References 49 publications

Violation of detailed balance for charge‐transfer statistics in Coulomb‐blockade systems

Violation of detailed balance for charge‐transfer statistics in Coulomb‐blockade systems

Revealing attractive electron–electron interaction in a quantum dot by full counting statistics

Analysis of universality in transient dynamics of coherent electronic transport

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