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Journal of the Physical Society of Japan

Low-Temperature Dephasing and Renormalization in Model Systems

Dmitry S. Golubev, Gerd Schön, Andrei D. Zaikin

Published Jan 3, 2003• 8 citations
Publisher

Abstract

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.

DOI
10.1143/jpsjs.72sa.30

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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.
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 spin-boson 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 epsilon(omega,k). Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.
We study the dynamics in low dimensional correlated quantum systems. Advances in this thesis are three-fold. First, as a methodical point we extend the real-time formulation of the functional renormalization group approach introduced in [1]. Describing the transient time dependence of a given microscopic model prepared in an initial non-equilibrium state poses a formidable challenge in the presence of interaction. We successfully extend the functional renormalization group approach of [1] to finite temperature as well as extended interacting geometries. Furthermore, for both extensions we test the validity of the perturbatively motivated treatment by explicitly benchmarking to complementary methods and find that for not too large interactions the functional renormalization group proves to be quantitatively accurate. Second, we examine the non-equilibrium dynamics of open as well as closed quantum systems in the presence of correlations. We study a prominent prototype model for coherence in small quantum systems coupled to dissipative environments, namely the spin-boson model. We reveal that prevailing literature does not cover the full complexity of the dynamics encountered. The relaxation dynamics formerly classified as coherent and incoherent should be refined according to the results presented in this thesis: we propose a subdivision of the coherent regime into partially and asymptotically coherent. For the former the coherence signature of the dynamics is restricted only to intermediate times, while in the latter it extends in the asymptotic regime. Interestingly, we explicitly show that elevating temperature might be conducive to coherence, which is opposite to the expected behavior. For those closed quantum systems known to fall into the so called Luttinger Liquid universality class in equilibrium, we provide evidence that the equilibrium concept of universality seemingly carries over to the non-equilibrium steady-state. This is rather counter-intuitive, as universality is usually attributed to the low energy degrees of freedom only. Third, we study the thermoelectric transport properties of quantum dots. Quantum dots are promising candidates for highly efficient thermoelectric devices as they are not bounded by the Wiedemann-Franz law which strongly limits the efficiency of ordinary bulk systems. For this we study a charge fluctuating model and a model which additionally allows for spin fluctuations and phononic degrees of freedom. We find that in certain regimes quantum dots show very high efficiency when operated as power engines. [1] D. M. Kennes, ‘A Renormalization Group Approach to the Time Evolution of Correlated Quantum Dots’ Master’s thesis, RWTH Aachen (2011).
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.
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 analyze quantal Brownian motion in ddd dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an equivalent Master equation. Unlike the case of the Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest themselves due to the disordered nature of the environment. Using Wigner picture of the dynamics we distinguish between two different mechanisms for destruction of coherence. The analysis of dephasing is extended to the low temperature regime by using a semiclassical strategy. Various results are derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion. We also analyze loss of coherence at the limit of zero temperature and clarify the limitations of the semiclassical approach. The condition for having coherent effect due to scattering by low-frequency fluctuations is also pointed out. It is interesting that the dephasing rate can be either larger or smaller than the dissipation rate, depending on the physical circumstances.