Quantum sticking of atoms on membranes

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The phonon-assisted sticking rate of slow moving atoms impinging on an elastic membrane at nonzero temperature is studied analytically using a model with linear atom-phonon interactions, valid in the weak coupling regime. A perturbative expansion of the adsorption rate in the atom-phonon coupling is infrared divergent at zero temperature, and this infrared problem is exacerbated by finite temperature. The use of a coherent state phonon basis in the calculation, however, yields infrared-finite results even at finite temperature. The sticking probability with the emission of any finite number of phonons is explicitly seen to be exponentially small, and it vanishes as the membrane size grows, a result that was previously found at zero temperature; in contrast to the zero temperature case, this exponential suppression of the sticking probability persists even with the emission of an infinite number of soft phonons. Explicit closed-form expressions are obtained for the effects of soft-phonon emission at finite temperature on the adsorption rate. For slowly moving atoms, the model predicts that there is zero probability of sticking to a large elastic membrane at nonzero temperature and weak coupling.Comment: 14 pages, 5 figure

Section: Discussionsupporting

confidence: 90%

Section: Introductionsupporting

confidence: 93%

See 1 more Smart Citation

Infrared problem in quantum acoustodynamics at finite temperature

Clougherty¹

2017

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“…We consider micromembranes whose size ranges from 100 nm to 10 µm. These values have been previously used to model [3][4][5] ultracold atomic hydrogen impinging at normal incidence on a suspended, circular sample of graphene.…”

Section: Adsorption Of Atomic Hydrogen On Graphenementioning

confidence: 99%

Radiative corrections to quantum sticking on graphene

Sengupta

Clougherty

2017

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We study the sticking rate of atomic hydrogen to suspended graphene using four different methods that include contributions from processes with multiphonon emission. We compare the numerical results of the atom self-energy obtained by: (1) the loop expansion of the atom self-energy, (2) the non-crossing approximation (NCA), (3) the independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). The loop expansion reveals an infrared problem, analogous to the infamous infrared problem in QED. The 2-loop contribution to the sticking rate gives a result that tends to diverge for large membranes. The latter three methods remedy this infrared problem and give results that are finite in the limit of an infinite membrane.We find that for micromembranes (sizes ranging 100 nm to 10 µm), the latter three methods give results that are in good agreement with each other and yield sticking rates that are mildly suppressed relative to the lowest-order golden rule rate. Lastly, we find that the SPR sticking rate decreases slowly to zero with increasing membrane size, while both the NCA and IBMA rates tend to a nonzero constant in this limit. Thus, approximations to the sticking rate can be sensitive to the effects of soft-phonon emission for large membranes.

“…It is important that we point out that within the simple model of IBM implemented for graphene physisorption, our work 1 has revealed that the zero adsorption rate predicted by Ref. [5,4] is only possible if one considers (i) contribution to adsorption rate from the long time regime, where the effects of Franck-Condon factor sets in and (ii) neglects the effects of thermal phonon emission. Points (i) and (ii) are indeed the regime of study in Ref.…”

mentioning

confidence: 90%

Theory of phonon-assisted adsorption in graphene: Many-body infrared dynamics

Sengupta

2019

Based on a new self-energy for atom-phonon interaction, preceding Comment argues about the insufficiency of the mathematical techniques within the Independent Boson Model (IBM) to study physisorption in graphene membranes. In this Reply, we show that the new self-energy reported in the Comment is a perturbative expansion approximated for a 2-phonon process, severely divergent for membrane sizes larger than 100 nm and within its current mathematical form, ill-suited for investigating the physics of physisorption in graphene micromembranes. Additionally, we provide with further evidence of the adsorption rate within the IBM that further reinforces the physical soundness of the mathematical techniques reported in Phys. Rev. B 100, 075429 (2019).The main point of our paper 1 is: adsorption rate of low-energy atoms impinging normally on suspended, µm sized graphene membranes is finite, approximately equal to the adsorption rate predicted by Fermi's golden rule. To arrive at this conclusion, we have used the Independent Boson Model (IBM) that captures the interaction between the incoming atom and the phonons of the graphene membrane. Our mathematical technique for the calculation of the adsorption rate includes a selfenergy formalism within the context of the IBM 1 .In the Comment 2 , author provides with a new selfenergy for the atom-phonon interaction which goes beyond the IBM and includes additional terms that are absent in our work 1 . Author then adapts our method for the calculation of the adsorption rate and extends it to this new self-energy. Within our formalism, he finds that the new self-energy fails to provide with a self-consistent solution. Author thus concludes that the failure of the new self-energy to give self-consistent solution must im-ply the invalidity of our mathematical formalism.Additionally, while the Comment dismisses our method as invalid, it does not provide with a mathematical technique that calculates the adsorption rate within this new self-energy. Thus, the Comment eludes the main point of our paper and remains inconclusive about the adsorption rate of incoming atoms.In this Reply, we will first discuss some of the fundamentally important features of the new self-energy reported in the Comment. We will then argue as to which one is invalid: our mathematical method to compute the adsorption rate or the new self-energy reported in the Comment. Finally, we will conclude our Reply with further evidence of the adsorption rate within the IBM that reinforces the physical soundness of the mathematical technique reported in Ref. [1].Let us begin with our analysis of the new self-energy reported in the Comment 2 . Throughout our Reply, we will refer to this self-energy as Σ c . Eq. (5) and Eq. (6) of the Comment (see Ref.[2]) gives the new self-energy as 2