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arXiv:cond-mat/9810297

On loss of quantum coherence in an interacting Fermi gas

Kasper Astrup Eriksen, Per Hedegård

Published Oct 22, 1998• 0 citations
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Abstract

We clarify the path integral calculation, recently suggested by Golubev and Zaikin, and show, contrary to their claim, that quasiparticles become fully coherent quantum particles in the $T \to 0$ limit. The important physical point is the inclusion of the recoil of the quasiparticle when interacting with fluctuations in the rest of the Fermi gas.

DOI
10.48550/arxiv.cond-mat/9810297

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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

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
We clarify the path integral calculation, recently suggested by Golubev and Zaikin, and show, contrary to their claim, that quasiparticles become fully coherent quantum particles in the T→0T \to 0T→0 limit. The important physical point is the inclusion of the recoil of the quasiparticle when interacting with fluctuations in the rest of the Fermi gas.
The authors provide a comprehensive theoretical investigation of the validity of the Fermi-liquid quasiparticle description in a two-dimensional electron gas interacting via the long-range Coulomb interaction. Contrary to popular belief, they find that quasiparticles are robust far above the Fermi momentum, perhaps providing a clue as to why the energy-band description works well far from the Fermi surface. The authors also find that there exists a small region around a critical wave vector where the quasiparticles become fragile due to their coupling to the collective modes. They also provide three-dimensional results.
The quasiparticle description makes sense only if the relaxation rate of the quasiparticles is much smaller than their energy. The relaxation of quasiparticle excitations is due to their mutual collisions and consequent decay into several others. Physically, the effect of the Pauli exclusion principle is felt only when the occupation probability of a given quantum state is of the order of unity. In the Maxwell-Boltzmann case, the probability of occupation of any quantum state is always small and hence Pauli's principle is not important. A natural question arises as to how the properties of a degenerate Fermi gas would change if the fermions interacted mutually. In the excited state, the momentum distribution of the particles will be different. The properties of a degenerate Fermi gas were first studied by Wilson-Sommerfeld in 1927. They turn out to be very different from a classical ideal gas.
In periodic systems of interacting electrons, Fermi and Luttinger surfaces refer to the locations within the Brillouin zone of poles and zeros, respectively, of the single-particle Green's function at zero energy and temperature. Such difference in analytic properties underlies the emergence of well-defined quasiparticles close to a Fermi surface, in contrast to their supposed non-existence close to a Luttinger surface, where the single-particle density-of-states vanishes at zero energy. We here show that, contrary to such common belief, coherent `quasiparticles' do exist also approaching a Luttinger surface in compressible interacting electron systems. Thermodynamic and dynamic properties of such 'quasiparticles' are just those of conventional ones. For instance, they yield well defined quantum oscillations in Luttinger's surface and linear in temperature specific heat, which is striking given the vanishing density of states of physical electrons, but actually not uncommon in strongly correlated materials.
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.
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 ).