Quantum recurrences in a one-dimensional gas of impenetrable bosons
Published in Physical Review E, 2015
Fano introduced the view of density matrices as vectors in Liouville space that can be projected along “axes” specified by operators satisfying a Lie algebra (related to symmetries in the system). This formulation captured my attention as something beautiful, making apparently simple what is complex.
How to choose these “axes” for the particle in a box problem? I had to figure it out. Fortunately, by reading Schwinger’s life and work at Columbia, I came across his elegant and unique formulation of quantum mechanics (Quantum Kinematics and Dynamic), from which I got a clue in a completely different context: take the elements of the Heisenberg group.
I then got my final view of the density matrix as a rotating vector, naturally explaining the back-and-forth motion of a free particle (with negligible dissipation) bouncing back off the walls of the box. It made me believe that it could be a simplistic description of the observations in the quantum Newton’s cradle experiment.