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The collected works in the "cond-mat.mes-hall" category primarily engage with debates surrounding theoretical approaches to understanding electron interactions in mesoscopic systems, decoherence, and quantum transport phenomena. Central themes include the validity and limitations of approximation methods, such as the influence functional and equation of motion methods, in capturing low-temperature behaviors and electron decoherence rates, especially at T=0. The discourse highlights the contentious nature of theoretical predictions and underscores the importance of methodological rigor, as criticisms often focus on perceived misapplications of quantum principles and approximations that lead to inconsistent or incorrect physical interpretations. This body of research is significant as it refines theoretical models that are crucial for advancing our understanding of quantum coherence and transport in disordered and mesoscopic systems, impacting future experimental validations and applications in quantum computing and materials science.
Recently von Delft (cond-mat/0510563v1)(JvD) has successfully re-derived our influence functional for interacting electrons and claimed that within our approach he was able to obtain the electron decoherence rate that vanishes at T=0. In this Comment we demonstrate that this JvD's claim is in error, as it is based on ambiguous and uncontrolled manipulations violating basic principles of quantum theory, such as energy-time uncertainty relation, causality, fluctuation-dissipation theorem, detailed balance and the like. We also briefly address insufficient approximations employed by Marquardt {\it et al.} (cond-mat/0510556v1) and by von Delft {\it et al.} (cond-mat/0510557v1) and demonstrate that the results of all three papers in the limit T=0 are inconsistent with simple rules of algebra.
The generalized Lyapunov exponents describe the growth of the second moments for a particular solution of the quasi-1D Schroedinger equation with initial conditions on the left end. Their possible application in the Anderson transition theory became recently a subject for controversy in the literature. The approach to the problem of the second moments advanced by Markos et al (cond-mat/0402068) is shown to be trivially incorrect. The difference of approaches by Kuzovkov et al (cond-mat/0212036, cond-mat/0501446) and the present author (cond-mat/0504557, cond-mat/0512708) is discussed.
The equation of motion method (EOM) is one of the approximations to calculate transport coefficients of interacting electron systems. The method is known to be useful to examine high-temperature properties. However, sometimes a naive application of the EOM fails to capture an important physics at low-energy scale, and it happens in recent preprints cond-mat/0309458 and cond-mat/0308413 which study a series of quantum dots. These preprints concluded that a unitarity-limit transport due to the Kondo resonance, which has been deduced from a Fermi-liquid behavior of the self-energy at T=0, $Ο=0$ [A.O., PRB {\bf 63}, 115305 (2001)], does not occur. We show that the EOM self-energy obtained with a finite cluster has accidentally a singular $1/Ο$ dependence around the Fermi energy, and it misleads one to the result incompatible with a Fermi-liquid ground state.
We reply to the critique of our results raised by Aleiner, Altshuler and Gershenzon (AAG) in cond-mat/9808078 and cond-mat/9808053. We demonstrate that our path integral analysis fully reproduces the results of AAG if analyzed on a perturbative level. This should settle the issue of "missing diagrams" in our calculation. We, furthermore, demonstrate that our approach allows us to proceed beyond the Golden-rule-type perturbation theory employed by AAG. This explains the difference between our and AAG's results. We also comment on the comparison of our results with the experiments presented by AAG.
In references cond-mat/9907171 and cond-mat/9606206 (Phys.Rev.B.53, 4927 (1996)) by You-Quan Li and Bin Chen, was considered a mesoscopic LC circuit with charge discreteness. So, it was proposed a finite difference Schroedinger equation for the charge time behavior. In this comment, we generalize the corresponding mesoscopic Hamiltonian in order to taken into account the dissipative effects (resistance R). Namely, a quantum term RI, proportional to the current, is added to the mesoscopic LC circuit equation. This is carried-out in analogy with the theory of Caldirola-Kanai for quantum one particle damping.
In the preprint cond-mat/0408050 M. V. Cheremisin noticed that some results (namely Fig. 4) of our recent work (cond-mat/0407364) have been taken from his paper cond-mat/0405176. As clear from the caption to Fig. 4 as well as from the text of our paper, we did not consider the curves shown in that Figure as our original results, but emphasized that they have been obtained in the well known paper Chiu and Quinn, Phys. Rev. B 9, 4724 (1974) 30 years ago. It is a surprise, that M. V. Cheremisin presents the 30-years-old results of Chiu and Quinn as his own results, obtained for the first time in cond-mat/0405176.
A short reply to Jarzynski's comment cond-mat/0509344 on my paper ``Flaw of Jarzynski's equality when applied to systems with several degrees of freedom'' (cond--mat/0508721) is presented.
Claims by Kroha and Zawadowski in cond-mat/0105026 on inadequate approximations and an incorrect statement in cond-mat/0102150 are shown to be based on oversimplified estimates and a false quotation.
In the present work we reply to the Comment by Catalan and Scott (cond-mat/0607500) on two of our papers. This Comment has been rejected from publication in Physical Review Letters and, hence, our Reply is based on the cond-mat version.
We show that the choice of the sign of the hopping matrix in our impurity band model for disordered III-V diluted magnetic semiconductors [PRL 87, 107293 (2000); cond-mat/0111045] is justified: with this choice, the impurity band is placed inside the gap and it has a mobility edge, as expected for a disordered system. The other sign choice, suggested in cond-mat/0111504, leads to an unphysical description of the occupied states of the impurity band (extremely long tail, no mobility edge, no bulk ferromagnetism).