Influence of branch points in the complex plane on the transmission through double quantum dots

Rotter, I.; Sadreev, Almas F.

doi:10.1103/physreve.69.066201

Cited by 41 publications

(50 citation statements)

References 27 publications

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“…[19][20][21] Considering the coupling strength v as control parameter, the phenomenon of resonance trapping 3,22 appears, i.e., the wave functions of a few resonance states align each with one of the channel wave functions while the other resonance states decouple from the continuum ͑become trapped͒. The resonance trapping occurs hierarchically.…”

Section: ͑2͒mentioning

confidence: 99%

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

2007

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We study the transmission through different small systems as a function of the coupling strength v to the two attached leads. The leads are identical with only one propagating mode C E in each of them. In addition to the conductance G, we calculate the phase rigidity of the scattering wave function ⌿ C E in the interior of the system. Most interesting results are obtained in the regime of strongly overlapping resonance states where the crossover from staying to traveling modes takes place. The crossover is characterized by collective effects.Here, the conductance is plateaulike enhanced in some energy regions of finite length while corridors with zero transmission ͑total reflection͒ appear in other energy regions. This transmission picture depends only weakly on the spectrum of the closed system. It is caused by the alignment of some resonance states of the system with the propagating modes C E in the leads. The alignment of resonance states takes place stepwise by resonance trapping, i.e., it is accompanied by the decoupling of other resonance states from the continuum of propagating modes. This process is quantitatively described by the phase rigidity of the scattering wave function. Averaged over energy in the considered energy window, ͗G͘ is correlated with 1 − ͗͘. In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions C E . They may be identified with traveling modes through the system. The remaining M − 2 trapped narrow resonance states are well separated from one another.

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Section: ͑2͒mentioning

confidence: 99%

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

2007

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“…Such a redistribution is studied first numerically in a nucleus [7] and then analytically, by using statistical assumptions and neglecting the energy dependence of the z λ , in a large chaotic system [8]. It is caused by branch points in the complex energy plane [9]. That means, the eigenvalues z λ of H eff determine the time scale of the transmission.…”

Section: A Eigenvalues and Transmissionmentioning

confidence: 99%

“…Therefore again, as for non-overlapping resonances, A λ → 1 and r λ → 1 at the energies E = E λ of the long-lived states. In the transmission through the cavity, the short-lived states determine the smooth 'background' while the long-lived states cause the superposed peaks (fluctuations) in the transmission probability [9].…”

Section: Eigenfunctions Of the Effective Hamiltonian And Phase Rmentioning

confidence: 99%

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Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

Bulgakov

Rotter

2006

Phys. Rev. E

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The spectroscopic properties of an open large Bunimovich cavity are studied numerically in the framework of the effective Hamiltonian formalism. The cavity is opened by attaching two leads to it in four different ways. In some cases, the transmission takes place via standing waves with an intensity that closely follows the profile of the resonances. In other cases, short-lived and long-lived resonance states coexist. The short-lived states cause traveling waves in the transmission while the long-lived ones generate superposed fluctuations. The traveling waves oscillate as a function of energy. They are not localized in the interior of the large chaotic cavity. In all considered cases, the phase rigidity fluctuates with energy. It is mostly near to its maximum value and agrees well with the theoretical value for the two-channel case.

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“…The discussion bases on the results obtained in Refs. [2][3][4], where also the further references can be found.…”

Section: Avoided Level Crossings Of Discrete and Narrow Resonance Statesmentioning

confidence: 99%

Avoided level crossings and singular points

Rotter

2005

Czech J Phys

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Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points (BPs) which are singular points in the complex energy plane. They cannot be identified with exceptional points. At a BP width bifurcation occurs, different Riemann sheets evolve and the levels do not cross anymore when the system is still further opened. The BPs are physically meaningful: they influence the dynamics of open as well as of closed quantum systems. The geometric phase that arises by encircling a BP, is different from the phase that appears by encircling a diabolic point. This is found to be true even for the two BPs into which the diabolic point is unfolded by opening the system.PACS : 05.45.Mt, 03.65.Yz

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Influence of branch points in the complex plane on the transmission through double quantum dots

Cited by 41 publications

References 27 publications

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

Avoided level crossings and singular points

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