3

We introduce an extension of the non-equilibrium dynamical mean field theory to incorporate the effects of static random disorder in the dynamics of a many-particle system by integrating out different disorder configurations resulting in an effective time-dependent density-density interaction.

We present a method employing non-equilibrium dynamical mean-field theory and coherent potential approximation on the Schwinger-Keldysh contour to calculate the OTOC for disordered and interacting correlated fermionic systems.

We propose a non-Hermitian 2nd order topological insulator in 2D quasi-crystalline lattice with gapless corner states. We also engineer more exotic topo phases where corner states can be localized at designated corners.

We construct a measure for the adiabatic contribution to quantum transitions in an arbitrary basis, tackling the generic complex case where dynamics is only partially adiabatic, simultaneously populates several eigenstates and transitions between non-eigenstates are of key interest.