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

Abstract

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 ${\xi }_C^E$ in each of them. Besides the conductance $G$, we calculate the phase rigidity $\rho$ of the scattering wave function ${\Psi }_C^E$ 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 plateau-like enhanced in some energy regions of finite length while corridors with zero transmission (total reflection) 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 ${\xi }_C^E$ 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 $\rho$ of the scattering wave function. Averaged over energy in the considered energy window, $<G>$ is correlated with $1-<\rho >$. In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions ${\xi }_C^E$. They may be identified with traveling modes through the system. The remaining $M-2$ trapped narrow resonance states are well separated from one another.

arXiv commentResonance trapping mechanism explained in the captions of Figs. 7 to 11. Recent papers added in the list of references

References in corpus (18)

• Observation of resonance trapping in an open microwave cavity
• S-matrix theory for transmission through billiards in tight-binding approach
• Phase transitions in open quantum systems
• Conductance of Open Quantum Billiards and Classical Trajectories
• Fluctuating "order parameter" for a quantum chaotic system with partially broken time-reversal symmetry
• Phase rigidity and avoided level crossings in the complex energy plane
• Intensity Fluctuations in Closed and Open Systems
• Fano resonances in the overlapping regime
• Interfering resonances in a quantum billiard
• Wavefunction statistics in open chaotic billiards
• Influence of branch points in the complex plane on the transmission through double quantum dots
• Whispering gallery modes in open quantum billiards
• Measurement of long-range wavefunction correlations in an open microwave billiard
• Open system of interacting fermions: Statistical properties of cross sections and fluctuations
• Spectroscopic studies in open quantum systems
• Statistical aspects of nuclear coupling to continuum
• Effective Hamiltonian and unitarity of the S matrix
• The brachistochrone problem in open quantum systems

Cited by in corpus (13)

• A review of progress in the physics of open quantum systems: theory and experiment
• Resonances in open quantum systems
• Nearby states in non-Hermitian quantum systems
• Clustering of exceptional points and dynamical phase transitions
• Open quantum systems and Dicke superradiance
• Electronic transport in iron atomic contacts: from the infinite wire to realistic geometries
• Statistics of eigenfunctions in open chaotic systems: a perturbative approach
• Impact of non-Hemiticity on modal strength and correlation in transmission through random open cavities
• Non-Hermitian Hamiltonian and Lamb shift in circular dielectric microcavity
• Feshbach projection-operator formalism to resonance scattering on Bargmann-type potentials
• Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity
• Relative Entropy as a Measure of Difference Between Hermitian and Non-Hermitian Systems
• Critical points in two-channel quantum systems