Conductance of open quantum billiards and classical trajectories

Abstract

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.

Shot noise and transport in small quantum cavities with large openings

“…The resonance wave function ͉⌽ R (x,y)͉ 2 displays a strong localization along the convex boundary, which is a characteristic feature of the WGM. 10 In the SIS, these trajectories almost exclusively correspond to one bounce at the convex boundary, while for the Bun1 billiard, there is also a small contribution of trajectories with two bounces. In the SIS the WGM accumulate Rϭ ͚⌫ WGM / ͚ i ⌫ i Ͼ98% of the total sum of widths ͚⌫ i of all states, while in the Bun1 billiard they accumulate a fraction Rϭ93% of the total sum.…”

“…As a consequence, the conductance of the quantum cavity significantly exceeds the prediction of RMT. 10 It is well established that shot noise ͑the zero-frequency current-current correlations caused by the discreteness of electric charge͒ provides valuable complementary information not contained in the conductance ͑for a review see Ref.11͒. It was found that correlations due to Fermi statistics suppress the shot-noise power P by a factor Fϭ P/ P 0 below the maximal value P 0 ϭ2eG 0 V of incoherent transport, with e the unit of charge, G 0 the series conductance of the two point contacts, and V the applied voltage.…”

“…As a consequence, the conductance of the quantum cavity significantly exceeds the prediction of RMT. 10 It is well established that shot noise ͑the zero-frequency current-current correlations caused by the discreteness of electric charge͒ provides valuable complementary information not contained in the conductance ͑for a review see Ref.…”

Resonance Trapping and Dynamical Phase Transitions

“…Both time scales are well separated from one another. An example are the short-lived whispering gallery modes in a microwave cavity with convex boundary which coexist with many long-lived states, for details see [5][6][7]. The dynamical phase transitions are surely the most interesting feature of non-Hermitian quantum physics [1,8].…”

Dynamical Phase Transitions in Quantum Systems

“…Both time scales are well separated from one another. A theoretical example are the shortlived whispering gallery modes in a small microwave cavity with convex boundary which coexist with many long-lived states, for details see [20][21][22]. An experimental example are the isobaric analogue resonances in medium -mass nuclei.…”