2016
DOI: 10.3390/e18050180
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Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

Abstract: Abstract:We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions, within the differential equation for the populations, that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here, we show how care must be … Show more

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Cited by 11 publications
(16 citation statements)
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“…Since then, it has been generally believed that the imaginary part of the retarded self energy will continue to govern the relaxation processes, even in nonequilibrium. In fact, for the simplest version of an electron‐phonon coupled system, one can prove that this is the case …”
Section: Time‐resolved Dynamics Of the Normal Statementioning
confidence: 96%
See 1 more Smart Citation
“…Since then, it has been generally believed that the imaginary part of the retarded self energy will continue to govern the relaxation processes, even in nonequilibrium. In fact, for the simplest version of an electron‐phonon coupled system, one can prove that this is the case …”
Section: Time‐resolved Dynamics Of the Normal Statementioning
confidence: 96%
“…It has recently come to light, that the situation in nonequilibrium often is different from this simple behavior. This arises, from a mathematical standpoint, due to the fact that one needs to examine the evolution of the electron population nboldk as a function of time, which necessarily brings in the average time dependence of the lesser self‐energy, which may not behave the same way as the relative time dependence of the retarded self‐energy . Experimentally, this has already been seen clearly, as the decay of populations is governed by different time scales than the widths of ARPES peaks in equilibrium .…”
Section: Time‐resolved Dynamics Of the Normal Statementioning
confidence: 99%
“…The system is excited by a short pump pulse that directly deposits energy into the electrons by driving a current. The energy is subsequently transferred to the phonons until a balance is achieved between the electrons and the phonon bath ( 51 ). This naturally leads to a nontrivial time dependence of the deposited electron energy, that is, an exponential decay with a constant rate does not capture the physics.…”
Section: Resultsmentioning
confidence: 99%
“…4. For (elastic) electron-impurity scattering within the self-consistent Born approximation, the right hand side of the equation vanishes identically [16]. This is generically the case for any self-energy which has the form…”
Section: What Determines the Population Decay Rate?mentioning
confidence: 87%
“…The exact equations of motion may in limited cases be reduced to the former, but generally do not fit either of these [16]. Hence, one should not expect these simple behaviors to occur.…”
Section: A What Does Mathiessen's Rule Suggest?mentioning
confidence: 99%