Strong Tunneling in the Single-Electron Box

König, Jürgen; Schoeller, Herbert

doi:10.1103/physrevlett.81.3511

Cited by 60 publications

(53 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This idea has been applied to the single-electron box [10], coupled metallic islands [19], and the one-dimensional Polaron problem [20]. In the first two cases very good results have been obtained, even comparable to very time-consuming QMCsimulations.…”

Section: Discussionmentioning

confidence: 99%

An Introduction to Real-Time Renormalization Group

Schoeller

1999

Low-Dimensional Systems

Self Cite

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

An Introduction to Real-Time Renormalization Group

Schoeller

1999

Low-Dimensional Systems

Self Cite

View full text Add to dashboard Cite

“…The first and second diagram in Fig. 7 represent a correction to j − , 19) whereas the third and fourth diagram represent an additional renormalization of the distribution function for right moving fermions, which can be represented by a change in the relation between toG R and G R ,…”

Section: B Large Number Of Channelsmentioning

confidence: 99%

“…The other theoretical approach starts from an effective theory in which the primary dynamic variables are the potential differences between the quantum dot and the electrodes. 9 This approach has mainly been used to study metal grains coupled to the reservoirs via tunnel barriers with many channels, 10,11,12,13,14,15,16,17,18,19,20 , but recently it has been applied to semiconductor quantum dots, both without 21,22,23 and with 24 coherent scattering of electrons from inside the quantum dot. The general conclusions of both approaches are the same: For the incoherent case and ideal point contacts (no backscattering in the contact), it was found that all charge quantization effects completely vanishes.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium theory of Coulomb blockade in open quantum dots

Brouwer

Lamacraft

Flensberg³

2005

Phys. Rev. B

View full text Add to dashboard Cite

We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a simple picture for the conductance corrections in terms of renormalization of the dot's elastic scattering matrix, which is obtained also by elementary perturbation theory. For the case of ideal contacts, a symmetry argument immediately allows us to conclude that interactions give no signature in the averaged conductance. Non-equilibrium applications to the pumped current in a quantum pump are worked out in detail.

show abstract

“…This problem has been extensively investigated by instanton methods 14,15,16,17 , by RG methods 8,9,18 , and by Monte Carlo (MC) methods 9,10,19 . All methods show that B c increases exponentially with the dissipation strength α, i.e.…”

mentioning

confidence: 99%

Interference in the presence of dissipation

Horovitz

Doussal

2006

Phys. Rev. B

View full text Add to dashboard Cite

We study a particle on a ring in 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 2 loop RG for the CaldeiraLegget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in −R 2 where R 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 ∼ R −2 for large R, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.PACS numbers: 73.23. Ra, The problem of interference and dephasing in presence of dissipative environments is of significance for a variety of experimental systems and a fundamental theoretical issue. The experimental systems include mesoscopic rings embedded on various surfaces where Aharonov-Bohm (AB) oscillations can be measured 1,2 , and the related problem of decoherence at low temperatures 3 . A different type of experimental systems are cold atom traps created by atom chips 4,5,6 , or trapped excited atoms with huge electric dipoles 7 . The atom chip that produces a magnetic or electric trap for the cold atoms necessarily also produces noise. Our problem is then relevant for evaluating the interference amplitude of cold atoms or molecules in presence of such noise.As an efficient tool for monitoring the effect of the environment we follow a suggestion by Guinea 8 to find the AB oscillation amplitude as function of the radius R of the ring, as measured by the curvature 9,10 1/B c of the ground state energy E 0 at external flux φ x = 0, i.e. 1/B c = ∂ 2 E 0 /∂φ 2 x | 0 . For free particles of mass M this amplitude is the mean level spacing ∼ 1/M R 2 . Two types of environments were suggested to lead to an anomalous suppression, i.e. a stronger decrease of the oscillation amplitude than 1/R 2 : system (i) is that of a Caledeira Legget bath and system (ii) of a charge in a dirty metal environment.System (i) is relevant to the Coulomb blockade problem 9,10,11,12 as well as to quantum dots at a distance from metallic gates 13 . This problem has been extensively investigated by instanton methods 14,15,16,17 , by RG methods 8,9,18 , and by Monte Carlo (MC) methods 9,10,19 . All methods show that B c increases exponentially with the dissipation strength α, i.e. B c ∼ α −µ e π 2 α , with differences in the exponent µ. In 2nd order renormalization group 9 (RG) µ = 2 , real time RG gives 18 µ = 6.5, instanton methods give either 14 µ = 2 or 15,17 µ = 3, or 16 µ = 4, while MC suggests 19 µ = 5. This system was also studied by a variational approach 21 which was solved numerically showing a nonperturbative regime at strong α. Since α = γR 2 where γ is a friction coefficient, a length scale π/ √ γ is identified 8 , beyond which the AB oscillations decay.The system (ii) was investigated by RG methods 8 finding B c ∼ R 2+µ ′ with µ ′ 1 nonunivers...

show abstract

Strong Tunneling in the Single-Electron Box

Cited by 60 publications

References 23 publications

An Introduction to Real-Time Renormalization Group

An Introduction to Real-Time Renormalization Group

Nonequilibrium theory of Coulomb blockade in open quantum dots

Interference in the presence of dissipation

Contact Info

Product

Resources

About