Liu, Li, and Berakdar Reply:

Abstract

Reply: In the preceding Comment [1], Narozhny and Fedotov (NF) raise several points of criticism regarding the validity of our recent Letter [2] on the muon decay in a laser field. NF argue that the parameters eE 0 =m ! and E S m 2 c 3 =e@ are very small in our case, and hence there are no reasons for a noticeable change of the muon lifetime (here m 207m e , e is the electric charge, E 0 and ! are the electric field amplitude of the laser and its frequency). We agree on the smallness of these two parameters; physically, quantifies the velocity of the muon quiver motion in the laser field whereas the condition for the value of E S follows from the requirement that the energy transferred from the laser field to the muon within a Compton wave length of the muon should be comparable to the rest energy of the muon, i.e., e E S m c 2 [here h=m c]. In our case, the field is weak, and since the moun is heavy, the laser dressing of the moun plays only a minor role and is, therefore, as stated in our Letter, neglected altogether in [2]. As discussed in details in [2], we argued that the driving mechanism for the laserassisted decay is the laser dressing of the electronic states. So while we agree to the NF estimates of and E S and to the expectations based upon them, these parameters do not determine the nonlinear energy and momentum transfer from the laser field within our adopted framework. Furthermore, NF indicate that Ref.[3] should have been cited. We agree on this point, even though we referred to the related works (Refs. [14, 15] of [2]) where [3] is discussed. NF further discuss our Eq. (6) and draw attention to a missing 2 prefactor and that E in the integrand should read E . These two corrections are typographical errors. This can also be inferred from Fig. (2) of [2] where our low-field results coincide with the laser-free case, as NF expect. In an attempt to derive explicit expressions for the decay rate, NF drop in our equation (6) the terms 1 l altogether, and they obtain their expression (1) from which they conclude that there should be no laser-induced enhancement. We note that, as stated in [2], the functions 1 l and their interplay are decisive to accomplish our results [the cutoff on the allowed l and hence on the 1 l contributions is evident from Fig. (1)]. It is still to be clarified to which extent the formula Eq. (1) proposed by NF conforms to our full numerical calculations. As for the general validity of our model, we remark that, as explicitly stated in [2], we drop in the Volkov state the dependence on terms quadratic in the vector potential due to the relatively weak laser fields under consideration. We also ignored completely the direct laser influence on the moun, for the reasons mentioned above. At this stage, it is not clear whether and to which extent the incorporation of these additional factors in the calculations would alter the conclusions of [2].

Donor impurity states in elliptical quantum rings subjected to a magnetic field

“…The maximum energy is −0.94R B , and the oscillation period is 0.5γ . These results are consistent with previously published results [23]. The oscillations arise from the magnetic field and from the requirement that the electron wave function satisfy periodic boundary conditions on the elliptical path.…”

Generalized Lüscher’s formula in multichannel baryon-baryon scattering

“…only have two components with s = 1, ν = 0, and s = 0, ν = 0, and J = l, J ′ = l ′ When substituting these explicit expressions ofM andF into the general formula (27) and follow similar steps as in case a, we can obtain the two-channel scattering Lüscher's formula as…”

“…It has been generalized in various ways over the years: to the boosted frames [24][25][26], to the case of asymmetric boxes [27][28][29], with twisted boundary conditions [30][31][32][33], to the case of particles with spin, e.g. to the case of two baryons [29,[34][35][36][37][38][39][40] and beyond the inelastic threshold [41][42][43][44][45][46], and even to three-particle case [47][48][49][50].…”

Boosting Molecular Fluorescence with a Plasmonic Nanolauncher

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