College of Science & Engineering
Twin Cities
This group is working on development of quantum mechanical theory of stationary driven dissipative systems, which are described by non-hermitian Hamiltonians. One example of such system is a random laser, where amplification and dissipation are randomly distributed on a lattice.
The group previously studied a lattice where sites amplify or dissipate independently from each other. But there are systems in nature where dissipation happens as a result of the collaboration of neighboring sites. This project will study whether spatial disorder leads to localization of oscillation modes in such disordered stationary systems. For this purpose, the researchers will diagonalize many realizations of corresponding non-hermitian Hamiltonians to study statistics of nearest neighbor distances of resulting complex eigenvalues, and verify whether disorder leads to transition between delocalized eigenmodes to localized, which is called the Anderson transition.