Open quantum dots: Physics of the non-Hermitian Hamiltonian

Quantum dots provide a natural system in which to study both classical and quantum features of transport, as they possess a very rich set of eigenstates. When coupled to the environment through a pair of quantum point contacts, these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. In this latter case, many of the eigenstates are decohered through interaction with the environment, but many survive and are referred to as the set of pointer states. These latter states are described by a projected, non-Hermitian Hamiltonian which describes their dissipation through many-body interactions with particles in the external environment.