Transient behavior of full counting statistics in thermal transport

The generating function of energy counting statistics is derived for phononic junction systems. It is expressed in terms of the contour-ordered self-energy of the lead with shifted arguments, $Σ^A(τ, τ') = Σ_L\bigl(τ+\hbar x(τ), τ' + \hbar x(τ')\bigr) - Σ_L(τ, τ')$, where $Σ_L(τ,τ')$ is the usual contour-ordered self-energy of the left lead. The cumulants of the energy transferred in a given time $t_M$ from the lead to the center is obtained by taking derivatives. A transient result of the first four cumulants of a graphene junction is presented. It is found that measurements cause the energy to flow into the lead.

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