Transmission through quantum dots in the regime of overlapping resonances

Ingrid Rotter

Max-Planck-Institut für Physik komplexer Systeme, Germany

The embedding of a quantum system into an environment of scattering wavefunctions causes additional correlations of the quantum states via the continuum. These correlations are described by a second-order term of the effective non-Hermitian Hamilton operator. They are mostly approximated by taking into account only the Hermitian part of the Hamilton operator. The additional correlations are dominant in the neighborhood of branch (exceptional) points in the complex energy plane where the (complex) eigenvalues of two states avoid crossing when controlled by a parameter. In this regime, the non-Hermitian part of the effective Hamilton operator can not be neglected. Here, the levels avoid crossing, the phase rigidity of the (bi-orthogonal) eigenfunctions of the effective Hamilton operator is reduced and the transmission through the system is enhanced.