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Adiabatic quantization of Andreev levels | | P.G.Silvestrov
; M.C.Goorden
; C.W.J.Beenakker
; | | Date: |
9 Aug 2002 | | Journal: | Phys. Rev. Lett. 90, 116801 (2003) DOI: 10.1103/PhysRevLett.90.116801 | | Subject: | Mesoscopic Systems and Quantum Hall Effect; Chaotic Dynamics | cond-mat.mes-hall nlin.CD | | Abstract: | We identify the time $T$ between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent $lambda$), coupled to a superconductor by an $N$-mode point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods $T_{n}$, which in turn generate a ladder of excited states $epsilon_{nm}=(m+1/2)pihbar/T_{n}$. The largest quantized period is the Ehrenfest time $T_{0}=lambda^{-1}ln N$. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension $W/sqrt{N}$, much below the width $W$ of the point contact. | | Source: | arXiv, cond-mat/0208192 | | Services: | Forum | Review | PDF | Favorites | |
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