Reply to “Comment on: ‘Multi-photon Rabi model: Generalized parity and its applications’ [Phys. Lett. A 377 (2013) 3205]” [Phys. Lett. A 378 (2014) 1969]

We show that the claims stated in the comment made by Chi-Fai Lo on our paper [Phys. Lett. A 377 (2013) 3205] neither contradict nor falsify our results.     

Comment on “Convergence of macrostates under reproducible processes” [Phys. Lett. A 374 (2010) 3715]

In this Letter, two counterexamples show that the superadditivity inequality of relative entropy is not true even for the full-ranked quantum states. Thus, an inequality of quantum channels and complementary channels is not also true. Finally, a conjecture of weak superadditivity inequality is presented.     

Comment on: “Entanglement in three coupled oscillators” [Phys. Lett. A 384 (2020) 126134]

In this comment we analyze a method for the solution of the eigenvalue equation for three coupled harmonic oscillators proposed recently. We argue that the authors did not obtain the frequencies and coordinates of the normal modes that make the Hamiltonian operator diagonal but merely six transcendental equations for the relevant parameters that they did not attempt to solve. We derive the conditions for the existence of bound states that the authors did not appear to be able to obtain probably because of the complexity exhibited by those equations.     

Comment on “Convergence towards asymptotic state in 1-D mappings: A scaling investigation” [Phys. Lett. A 379 (18–19) (2015) 1246–1250]

Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality class. Thus, it is important that the exponents are named and treated in a standardized framework. In this comment, we reinterpret the exponents obtained by Teixeira et al. [1] for the logistic and cubic maps in order to correctly state the universality class of their bifurcations, since these maps may describe the mean-field solution of stochastic spreading processes.     

Comment on: “Exposed-key weakness of αη” [Phys. Lett. A 370 (2007) 131]

We show that the insecurity claim of the αη cryptosystem made by C. Ahn and K. Birnbaum in [C. Ahn, K. Birnbaum, Phys. Lett. A 370 (2007) 131] under heterodyne attack is based on invalid extrapolations of Shannon's random cipher analysis and on an invalid statistical independence assumption. We show, both for standard ciphers and αη, that expressions of the kind given by Ahn and Birnbaum can at best be interpreted as security lower bounds.     

Reply to: “Comment on: ‘Exposed-key weakness of αη’ [Phys. Lett. A 370 (2007) 131]” [Phys. Lett. A 372 (2008) 7091]

We present simulations countering the claims in [R. Nair, H.P. Yuen, Phys. Lett. A 372 (2008) 7091] that the approximation given in [C. Ahn, K. Birnbaum, Phys. Lett. A 370 (2007) 131, quant-ph/0612058] for the eavesdropper's entropy on the encrypted key cannot be valid, and additionally discuss ways in which our views on security requirements differ from those given in [R. Nair, H.P. Yuen, Phys. Lett. A 372 (2008) 7091].     

Comment on: “Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics” [Phys. Lett. A 372 (2008) 6847]

The second of the two proofs of the Wigner theorem on symmetry in quantum mechanics given in Simon et al. (2008) [1] is reexamined and refined to remove a possible gap in the argument presented there.     

Comment on: “Multi-photon Rabi model: Generalized parity and its applications” by B. Gardas and J. Dajka [Phys. Lett. A 377 (2013) 3205]

Recently Gardas and Dajka examined the multi-photon Rabi model and showed that it had a discrete eigenenergy spectrum with normalizable eigenstates. However, their analysis is actually invalid because it has been rigorously proven that the model does not have eigenstates in the Hilbert space spanned by the photon number states.     

Comment on ‘Šilnikov-type orbits of Lorenz-family systems’ [Physica A 375 (2007) 438–446]

In the commented paper, the authors consider a four-parameter family of three-dimensional autonomous systems that includes the widely studied systems of Lorenz, Chen and Lü. Their goal is to rigorously prove the existence of Šilnikov chaos in this Lorenz-family via the Šilnikov criterion. They use an undetermined coefficient method to demonstrate the presence of heteroclinic orbits. In this comment we point out that their analysis is erroneous. The odd function they consider for the first component of the Šilnikov heteroclinic orbit cannot represent such global connection. Thus, the main result of their paper, Theorem 2, is incorrect.     

Comment on “Stabilization of trapless Bose-Einstein condensates without any management” [Phys. Lett. A 383 (17) (2019) 2033-2038]

A recent paper by T. Ramakrishnan and S. Subramaniyan shows that there is an enhancement of the stability of the trapless BECs due to the inclusion of the higher-order interaction along with the two-and three-body interactions. We point out and correct the erroneous results calculated by the authors concerning the effective potential of the trapless BECs. In addition we have shown that the incorrect expression used by authors leads to notable discrepancies between such results and exact ones. Moreover, our numerical results coincide with our theoretical predictions.