Introduction and theory

PHI is a multi-threaded software implementation of a hierarchy equation of motion (HEOM) integrator to run on shared memory parallel computers. The HEOM is a method to calculate the noise-averaged time evolution of density matrix that describes a quantum system in contact with a thermal environment. The dynamics of quantum systems in a thermal environment, sometimes called dissipative quantum dynamics or open quantum dynamics, is of interest in many areas of research and has been studied for many decades with various methods. This User's Guide gives a brief introduction of the specify a quantum system in the input parameter file, and then run PHIto calculate the density matrix evolution. For a thorough treatment of open quantum systems please read:

• H.P Breuer and F. Petruccione. ``The theory of open quantum systems.''
  Oxford University Press. 2002
• U. Weiss. ``Dissipative quantum systems.''
  World Scientific. 2008