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arXiv:cond-mat/0112099 · Physical review. B, Condensed matter

Aharonov-Bohm oscillations of a particle coupled to dissipative environments

F. Guinea

Published May 14, 2002• 38 citations
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Abstract

The amplitude of the Bohm-Aharonov oscillations of a particle moving around a ring threaded by a magnetic flux and coupled to different dissipative environments is studied. The decay of the oscillations on increasing the radius of the ring is shown to depend on the spatial features of the coupling. When the environment is modeled by the Caldeira-Leggett bath of oscillators, interference effects are suppressed beyond a finite length, even at zero temperature. A nontrivial renormalization of the Aharonov-Bohm oscillations is also found when the particle is coupled by the Coulomb potential to a dirty electron gas. A finite renormalization of the Aharonov-Bohm oscillations is obtained for other models of the environment.

DOI
10.1103/physrevb.65.205317

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The amplitude of the Bohm-Aharonov oscillations of a particle moving around a ring threaded by a magnetic flux and coupled to different dissipative environments is studied. The decay of the oscillations on increasing the radius of the ring is shown to depend on the spatial features of the coupling. When the environment is modeled by the Caldeira-Leggett bath of oscillators, interference effects are suppressed beyond a finite length, even at zero temperature. A nontrivial renormalization of the Aharonov-Bohm oscillations is also found when the particle is coupled by the Coulomb potential to a dirty electron gas. A finite renormalization of the Aharonov-Bohm oscillations is obtained for other models of the environment.
We study a particle on a ring in the presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces a two loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in $\ensuremath{-}{R}^{2}$, where RRR is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that the metal induces dissipation, however the AB amplitude is $\ensuremath{\sim}{R}^{\ensuremath{-}2}$ for large RRR, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.
Abstract.- We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate ∝ T 3/2, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence. Introduction. – The problem of dephasing of a particle coupled to a dissipative environment at temperature T, and in particular in the limit T → 0 has fascinated the mesoscopic community during the last two decades [1–7]. It has been shown [8,9] that the Caldeira-
We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty-metal environment. At low but finite temperatures we find a dephasing rate ∝ T 3/2 , and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence.
The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance ℓ<<L\ell << Lℓ<<L. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit (ℓ>>L\ell >> Lℓ>>L). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.
We study the dynamics of a quantum particle coupled to dissipative (Ohmic) environments, such as an electron liquid. For certain choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular case is the three-dimensional dirty electron liquid. In other environments, like the one described by the Caldeira-Leggett model, the effective mass diverges at low temperatures, and quantum effects are strongly suppressed. For interactions within this class, arbitrarily weak potentials lead to localized solutions. Particles bound to external potentials, or moving in closed orbits, can show a first-order transition, between strongly and weakly localized regimes.
We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low-frequency dominance. Our solution produces a renormalization-group (RG) transformation to all orders in the inverse dissipation strength and, in particular, reproduces known two-loop results. Our RG leads to a weak dissipation parameter, for which a weak-coupling expansion for the position correlation function shows a $1/{\ensuremath{\tau}}^{2}$ decay in imaginary time.