Statistics of Wave Functions in Coupled Chaotic Systems

Abstract

Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wavefunctions in two coupled disordered or chaotic quantum billiards. We find novel spatial correlations that are absent in a single chaotic system. Our exact result can be interpreted for small coupling in terms of the hybridization of eigenstates of the isolated billiards. We show that the presented picture is universal, independent of microscopic details of the coupling.

4 pages, 2 figures; acknowledgements and references added

References in corpus (3)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Mesoscopic fluctuations of tunneling through double quantum dots

Cited by in corpus (3)

• Enhanced mesoscopic fluctuations in the crossover between random matrix ensembles
• On the scaling approach to electron-electron interactions in a chaotic quantum dot
• Interactions, superconducting $T_c$, and fluctuation magnetization for two coupled dots in the crossover between the Gaussian Orthogonal and Unitary ensembles