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Decoherence of a particle in a ring

Doron Cohen, Baruch Horovitz

Published Nov 27, 2012• 3 citations
OpenAlex

Abstract

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-

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Decoherence of a particle in a ring

Doron Cohen, B. Horovitz

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.

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Low-Temperature Dephasing and Renormalization in Model Systems

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We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath.Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects.In particular in the latter case dephasing should be distinguished from renormalization effects.For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spinboson models.Next we review Caldeira-Leggett models, with applications, e.g., to persistent currents in mesoscopic rings.Then, we analyze the more general problem of a particle which interacts with a quantum field V (t, r(t)), the fluctuations of which are characterized by a dielectric function (ω, k).Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.

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Aharonov-Bohm oscillations of a particle coupled to dissipative environments

F. Guinea

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.

arXiv:cond-mat/0112099•Physical review. B, Condensed matter•May 14, 2002•38 citations
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 zero-temperature spin dynamics of a particle confined to a ring in the presence of spin-orbit coupling and Ohmic electromagnetic fluctuations. We show that the dynamics of the angular position θ( t ) are decoupled from the spin dynamics and that the latter is mapped to certain correlations of a spinless particle. We find that the spin correlations in the z -direction (perpendicular to the ring) are finite at long times, i.e. do not dephase. The parallel (in-plane) components for spin do not dephase at weak dissipation but they probably decay as a power law with time at strong dissipation.
We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath.Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects.In particular in the latter case dephasing should be distinguished from renormalization effects.For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spinboson models.Next we review Caldeira-Leggett models, with applications, e.g., to persistent currents in mesoscopic rings.Then, we analyze the more general problem of a particle which interacts with a quantum field V (t, r(t)), the fluctuations of which are characterized by a dielectric function (ω, k).Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.
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.