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arXiv:cond-mat/0512411

Comment on ``Influence Functional for Decoherence of Interacting Electrons in Disordered Conductors'' (cond-mat/0510563v1) and on related papers (cond-mat/0510556v1 and cond-mat/0510557v1)

Dmitry S. Golubev, Andrei D. Zaikin

Published Dec 16, 2005• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.cond-mat/0512411

Related papers

On a theory of low temperature electron decoherence in disordered conductors

Dmitry S. Golubev, Andrei D. Zaikin

Recently von Delft (JvD) attempted to revise our theory of low temperature decoherence of electrons in disordered conductors with electron-electron interactions [D.S. Golubev and A.D. Zaikin, Phys. Rev. B 59, 9195 (1999)] and argued [Intl. J. Mod. Phys. B 22, 727 (2008)] that by 'more accurate treatment of recoil efiects' he was able to obtain the electron decoherence rate that vanishes at T = 0. In this paper 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. While our theory has a simple and transparent relation to the well known P ( E ) theory (which exactly accounts for all recoil efiects) JvD's approach is inconsistent with this theory thus being unable to correctly treat even recoil efiects it was explicitly aimed at.

Journal of Physics Conference Series•Oct 1, 2008•2 citations

Reply to a Comment on "Quantum Decoherence in Disordered Mesoscopic Systems" (cond-mat/9808078, cond-mat/9808053)

Dmitry S. Golubev, Andrei D. Zaikin

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.

arXiv:cond-mat/9811185•Nov 13, 1998•0 citations

Decoherence in weak localization. I. Pauli principle in influence functional

Florian Marquardt, Jan von Delft, Robert A. L. Smith +1 more

This is the first in a series of two papers, in which we revisit the problem of decoherence in weak localization. The basic challenge addressed in our work is to calculate the decoherence of electrons interacting with a quantum-mechanical environment while taking proper account of the Pauli principle. First, we review the usual influence functional approach valid for decoherence of electrons due to classical noise, showing along the way how the quantitative accuracy can be improved by properly averaging over closed (rather than unrestricted) random walks. We then use a heuristic approach to show how the Pauli principle may be incorporated into a path-integral description of decoherence in weak localization. This is accomplished by introducing an effective modification of the quantum noise spectrum, after which the calculation proceeds analogous to the case of classical noise. Using this simple but efficient method, which is consistent with much more laborious diagrammatic calculations, we demonstrate how the Pauli principle serves to suppress the decohering effects of quantum fluctuations of the environment, and essentially confirm the classic result of Altshuler, Aronov, and Khmelnitskii [J. Phys. C 15, 7367 (1982)] for the energy-averaged decoherence rate, which vanishes at zero temperature. Going beyond that, we employ our method to calculate explicitly the leading quantum corrections to the classical decoherence rates and to provide a detailed analysis of the energy dependence of the decoherence rate. The basic idea of our approach is general enough to be applicable to the decoherence of degenerate Fermi systems in contexts other than weak localization as well. Paper II will provide a more rigorous diagrammatic basis for our results by rederiving them from a Bethe-Salpeter equation for the Cooperon.

arXiv:cond-mat/0510556•Physical Review B•Nov 30, 2007•30 citations

Decoherence of Interacting Electrons in Disordered Conductors: on the Relation between Influence Functional and Diagrammatic Approaches

Jan von Delft

We establish a connection between the influence functional approach of Golubev and Zaikin (GZ) and Keldysh diagrammatic perturbation theory for calculating the decoherence time τ ϕ of interacting electrons in disordered metals; we show how the standard diagrams for the Cooperon self energy can be recovered from GZ's influence functional e -(i SR + SI ) .This allows us to shed light on GZ's claim that SR is irrelevant for decoherence: SR generates as many important self energy diagrams as SI ; GZ's neglect of SR is permissible only at high temeratures (T /τ el ).

arXiv:cond-mat/0210644•Journal of the Physical Society of Japan•Jan 3, 2003•10 citations

Comment on ``On loss of quantum coherence in an interacting Fermi gas'' (cond-mat/9810297)

Dmitry S. Golubev, Andrei D. Zaikin

In a recent paper \cite{EH} Eriksen and Hedegard (EH) claimed that they ``clarified'' our path integral calculation \cite{GZ1} and found an error in our analysis. Here we will demonstrate that this claim is based on mathematically incorrect and physically meaningless procedure invented by the authors \cite{EH}. The main problem in the EH analysis is due to their erroneous calculation of Gaussian path integrals and has nothing to do with the momentum recoil of a particle interacting with an external bath.

arXiv:cond-mat/9810368•Oct 27, 1998•0 citations

Decoherence of interacting electrons in disordered conductors: on the relation between influence functional and diagrammatic approaches (Proceedings of the International Conference on Quantum Transport and Quantum Coherence(Localisation 2002))

Jan von Delft

Journal of the Physical Society of Japan•Jan 1, 2003•1 citation
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.
Recently von Delft (JvD) attempted to revise our theory of low temperature decoherence of electrons in disordered conductors with electron-electron interactions [D.S. Golubev and A.D. Zaikin, Phys. Rev. B 59, 9195 (1999)] and argued [Intl. J. Mod. Phys. B 22, 727 (2008)] that by 'more accurate treatment of recoil efiects' he was able to obtain the electron decoherence rate that vanishes at T = 0. In this paper 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. While our theory has a simple and transparent relation to the well known P ( E ) theory (which exactly accounts for all recoil efiects) JvD's approach is inconsistent with this theory thus being unable to correctly treat even recoil efiects it was explicitly aimed at.
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.
This is the first in a series of two papers, in which we revisit the problem of decoherence in weak localization. The basic challenge addressed in our work is to calculate the decoherence of electrons interacting with a quantum-mechanical environment while taking proper account of the Pauli principle. First, we review the usual influence functional approach valid for decoherence of electrons due to classical noise, showing along the way how the quantitative accuracy can be improved by properly averaging over closed (rather than unrestricted) random walks. We then use a heuristic approach to show how the Pauli principle may be incorporated into a path-integral description of decoherence in weak localization. This is accomplished by introducing an effective modification of the quantum noise spectrum, after which the calculation proceeds analogous to the case of classical noise. Using this simple but efficient method, which is consistent with much more laborious diagrammatic calculations, we demonstrate how the Pauli principle serves to suppress the decohering effects of quantum fluctuations of the environment, and essentially confirm the classic result of Altshuler, Aronov, and Khmelnitskii [J. Phys. C 15, 7367 (1982)] for the energy-averaged decoherence rate, which vanishes at zero temperature. Going beyond that, we employ our method to calculate explicitly the leading quantum corrections to the classical decoherence rates and to provide a detailed analysis of the energy dependence of the decoherence rate. The basic idea of our approach is general enough to be applicable to the decoherence of degenerate Fermi systems in contexts other than weak localization as well. Paper II will provide a more rigorous diagrammatic basis for our results by rederiving them from a Bethe-Salpeter equation for the Cooperon.
We establish a connection between the influence functional approach of Golubev and Zaikin (GZ) and Keldysh diagrammatic perturbation theory for calculating the decoherence time τ ϕ of interacting electrons in disordered metals; we show how the standard diagrams for the Cooperon self energy can be recovered from GZ's influence functional e -(i SR + SI ) .This allows us to shed light on GZ's claim that SR is irrelevant for decoherence: SR generates as many important self energy diagrams as SI ; GZ's neglect of SR is permissible only at high temeratures (T /τ el ).
In a recent paper \cite{EH} Eriksen and Hedegard (EH) claimed that they ``clarified'' our path integral calculation \cite{GZ1} and found an error in our analysis. Here we will demonstrate that this claim is based on mathematically incorrect and physically meaningless procedure invented by the authors \cite{EH}. The main problem in the EH analysis is due to their erroneous calculation of Gaussian path integrals and has nothing to do with the momentum recoil of a particle interacting with an external bath.