A comparative study of two phenomenological models of dephasing in series and parallel resistors

Abstract

We compare two phenomenological models of dephasing that are in use recently. We show that the stochastic absorption model leads to reasonable dephasing in series (double barrier) and parallel (ring) quantum resistors in presence and absence of magnetic flux. For large enough dephasing it leads to Ohm's law. On the other hand a random phase based statistical model that uses averaging over Gaussian random-phases, picked up by the propagators, leads to several inconsistencies. This can be attributed to the failure of this model to dephase interference between complementary electron waves each following time-reversed path of the other.

Feynman path description of the effects of dephasing of spatial coherences on the transmission and reflection probabilities through a one-dimensional potential

“…Statistical methods were shown to be consistent with experimentally observed Aharonov-Bohm oscillations in quantum rings [29]. However, it has been pointed out [30] that in the limit of complete incoherence, larger transmission probabilities in double-barrier structures are predicted using these phase randomization models than would have been predicted using Ohm's law; in contrast, Buttiker's dephasing probe model is consistent with Ohm's law in the limit of complete incoherence, which suggests that both complete phase and momentum randomization are required in the classical limit.…”

“…. It has been pointed out [30] that the use of normally distributed phase distributions give essentially identical results to periodic phase distributions when…”

Statistical model for the effects of phase and momentum randomization on electron transport

“…Regarding a fixed dephasing configuration as a series of incoherently coupled tunneling barrieres, its resistance in the limit of completely momentum randomizing dephasing (7) and completely momentum conserving dephasing (10) corresponds to the results in [6,11,19]. However, by ensemble averaging our statistical dephasing model provides a simple formula (18) for the additional resistance due to momentum randomizing dephasing, which is also valid for partial decoherence p < 1 and partial momentum randomization 0 < p r < 1.…”

“…Other models include the dephasing effects by stochastic absorption through an attenuating factor [16] or by random phase factors [17,18]. However, these models are still controversially discussed [19] and most of them are defined only in the limit of completely momentum randomizing or completely momentum conserving dephasing.…”