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U. Zuelicke
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In two recent articles [PRL 90, 026802 (2003); PRB 69, 085307 (2004)], we developed a transport theory for an extended tunnel junction between two interacting fractional-quantum-Hall edge channels, obtaining analytical results for the conductance. Ponomarenko and Averin (PA) have expressed disagreement with our theoretical approach and question the validity of our results (cond-mat/0602532). Here we show why PAs critique is unwarranted.
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In this note, we reply to the comment made by E.I.Kats and V.V.Lebedev [arXiv:1407.4298] on our recent work Thermodynamics of quantum crystalline membranes [Phys. Rev. B 89, 224307 (2014)]. Kats and Lebedev question the validity of the calculation presented in our work, in particular on the use of a Debye momentum as a ultra-violet regulator for the theory. We address and counter argue the criticisms made by Kats and Lebedev to our work.
The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems belonging to a special, though ubiquitous, class of strong correlations. It focuses on three inter-related aspects, namely (i) we exhibit strong numerical indications which suggest that the standard exponential probability law is asymptotically replaced by a power-law as its dominant term for large $N$; (ii) the subdominant term appears to be consistent with the $q$-exponential behavior typical of systems following $q$-statistics, thus reinforcing the thermodynamically extensive entropic nature of the exponent of the $q$-exponential, basically $N$ times the $q$-generalized rate function; (iii) the class of strong correlations that we have focused on corresponds to attractors in the sense of the Central Limit Theorem which are $Q$-Gaussian distributions (in principle $1 < Q < 3$), which relevantly differ from (symmetric) Levy distributions, with the unique exception of Cauchy-Lorentz distributions (which correspond to $Q = 2$), where they coincide, as well known. In his Comment, Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) have, as we detail here, visibly escaped to his analysis. Consequently, his conclusion claiming the absence of special connection with $q$-exponentials is unjustified.
A recent comment on our work (Phys. Rev. Lett., vol. 110, 016601 (2013)) by A.A.Aligia claims that we made mistakes in the evaluation of the lesser quantities. It is further claimed that the distribution function of the single-particle selfenergy of the interacting region in the Fermi liquid regime, e.g. at small bias voltage, low temperature, and small frequency, is continuous. These claims are based on a comparison of the particle-hole symmetric case with results obtained from the approach of A.A.Aligia. We disagree with these claims and show that the discrepancies that the comment alludes to originate from a violation of Ward identities by the method employed in the comment. A comparison of our approach with the numerical renormalization group shows perfect agreement for the symmetric case.
The above comment [E. I. Lashin, D. Dou, arXiv:1606.04738] claims that the paper Quantum Raychaudhuri Equation by S. Das, Phys. Rev. D89 (2014) 084068 [arXiv:1404.3093] has problematic points with regards to its derivation and implications. We show below that the above claim is incorrect, and that there are no problems with results of the above paper or its implications.
In this Reply we propose a modified security proof of the Quantum Dense Key Distribution protocol detecting also the eavesdropping attack proposed by Wojcik in his Comment.
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