[PhD Thesis Presentation_Zoom] ‐ Mr. Mathias Mikkelsen– “Quenched and driven dynamics in one-dimensional quantum systems”

  As a first example I investigate a gas of a strongly-interacting bosons in a one-dimensional ring lattice geometry, which is initially in an equilibrium phase and to which a constant rotation of the lattice is suddenly added. In a second project I explore the connection between non-equilibrium excitations described by the work statistics of a quench and the information scrambling defined by the squared commutator for relevant operators using analytic solutions for the paradigmatic example of two interacting particles in a harmonic trap. To be able to also describe larger systems, I then present an improved method of exact diagonalization in Fock space for multi-component few-body continuum systems incorporating an effective interaction and show some examples where this can be applied. Finally, I describe an investigation into the effects of nonlinear interactions in an open optomechanical setup, where a steady state is obtained due to the interplay between input and loss, using a Quantum Langevin formalism.