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Schoeller, Herbert; König, Jürgen; Kuczera, Frank; Schön, Gerd

doi:10.1023/a:1004650202717

Cited by 4 publications

(8 citation statements)

References 10 publications

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“…The discrepancy between perturbation theory and our data increases with g, indicating that higherorder corrections have to be included. With third-order perturbation theory 23 deviations for G min are reduced but still visible.…”

Section: Resultsmentioning

confidence: 97%

Conductance of the single-electron transistor: A comparison of experimental data with Monte Carlo calculations

et al. 2002

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We report on experimental results for the conductance of metallic single-electron transistors as a function of temperature, gate voltage and dimensionless conductance. In contrast to previous experiments our transistor layout allows for a direct measurement of the parallel conductance and no ad hoc assumptions on the symmetry of the transistors are necessary. Thus we can make a comparison between our data and theoretical predictions without any adjustable parameter. Even for rather weakly conducting transistors significant deviations from the perturbative results are noted. On the other hand, path integral Monte Carlo calculations show remarkable agreement with experiments for the whole range of temperatures and conductances.

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Section: Resultsmentioning

confidence: 97%

Conductance of the single-electron transistor: A comparison of experimental data with Monte Carlo calculations

et al. 2002

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“…of (315) leads to an increase of J, therefore this situation is called the relevant case. Due to the relations (39) and (40), we expect G Λ ∼ √ Γ Λ and we obtain…”

Section: Weak Coupling Limitmentioning

confidence: 89%

“…Instead of the bandwidth, the relative time of the reservoir Green's function was used as a cutoff parameter and the kernel of the kinetic equation was kept invariant during the RG flow by setting up a formally exact hierarchy of RG equations. The method has been applied to charge fluctuations in the single electron box [37], transport through metallic quantum dots [38,39], charge fluctuations in semiconductor quantum dots [1,40], the polaron problem [41], the influence of acoustic phonons on transport through coupled quantum dots [42], and to the dynamics of the spin boson problem [2]. Within all these applications, a linear coupling between the quantum system and the particle or heat reservoir was considered.…”

Section: Introductionmentioning

confidence: 99%

A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics

Schoeller

2009

Eur. Phys. J. Spec. Top.

165

417

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Abstract. We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoirsystem coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1,2,3,4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.

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“…of these equations which do not occur on the l.h.s.. We note that the overall sign on the r.h.s. differs from the one in [1] since we have included the factors −i into the vertices. Furthermore, we have generalized the RG equations to an arbitrary cutoff-function F (t/tc).…”

Section: Renormalization Groupmentioning

confidence: 99%

“…This article presents a tutorial introduction to a recently developed real-time renormalization group method [1]. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment.…”

Section: Introductionmentioning

confidence: 99%