2013
DOI: 10.1007/s10825-013-0464-9
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Time-dependent factorial cumulants in interacting nano-scale systems

Abstract: We discuss time-dependent factorial cumulants in interacting nano-scale systems. Recent theoretical work has shown that the full counting statistics of non-interacting electrons in a two-terminal conductor is always generalized binomial and the zeros of the generating function are consequently real and negative. However, as interactions are introduced in the transport, the zeros of the generating function may become complex. This has measurable consequences: With the zeros of the generating function moving awa… Show more

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Cited by 28 publications
(33 citation statements)
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“…[29,30]. It can be obtained from the Taylor expansions of Z(χ ) = tr R(χ ) and of the generalized master equation (4) which read…”
Section: Hierarchy Of Equations For the Momentsmentioning
confidence: 99%
See 1 more Smart Citation
“…[29,30]. It can be obtained from the Taylor expansions of Z(χ ) = tr R(χ ) and of the generalized master equation (4) which read…”
Section: Hierarchy Of Equations For the Momentsmentioning
confidence: 99%
“…Notice that in contrast to Refs. [29,30], we do not consider number cumulants, but current cumulants. Therefore one first has to compute the time derivatives of the moments,…”
Section: Hierarchy Of Equations For the Momentsmentioning
confidence: 99%
“…Factorial moments are derived from the generating function MFfalse(z,tfalse):=Nfalse(z+1false)NPNfalse(tfalse), via the derivatives Nfalse(mfalse)false(tfalse)=zmMFfalse(z,tfalse)|z=0 taken at z=0. The corresponding factorial cumulants CnormalF,mfalse(tfalse):=Nfalse(mfalse)false(tfalse) are obtained from CnormalF,mfalse(tfalse):=mzmlnMFfalse(z,tfalse)-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 ().…”
Section: Stochastic Systemsmentioning
confidence: 99%
“…In the context of single-electron tunneling, the use of factorial rather than ordinary cumulants has been suggested [35,36] as a convenient tool to identify interactions in the system. Furthermore, factorial and generalized factorial cumulants [37] have been analyzed in the short-time limit to detect the presence of fundamental tunneling processes (such as Andreev tunneling) of two electrons simultaneously [38].…”
Section: Full Counting Statisticsmentioning
confidence: 99%
“…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 . The existence of a universal scaling law for the higher order cumulants has been reported in both, the incoherent and the coherent regimes.…”
Section: Introductionmentioning
confidence: 99%