## Mathematical Physics and Operator Algebras

•  Jacob Gloe, MSU
•  Diffusion for a Quantum Particle in a Lindbladian Environment with a Periodic Hamiltonian
•  10/11/2022
•  11:00 AM - 12:00 PM
•  C304 Wells Hall
•  Jeffrey Hudson Schenker (schenke6@msu.edu)

A quantum particle restricted to a lattice of points has been well studied in many different contexts. In the absence of disorder or environmental interaction, the particle simply undergoes ballistic transport for many suitable Hamiltonian operators. Recently, progress has been made on introducing a Lindbladian interaction term to the model, which drastically changes the dynamics in the large time limit. We prove that indeed diffusion is present in this context for an arbitrary periodic Hamiltonian. Additionally, we show that the diffusion constant is inversely proportional to the particles' coupling strength with its environment.

## Contact

Department of Mathematics
Michigan State University