@article{Representation:3615,
      recid = {3615},
      author = {Ryu, Won Hee},
      title = {Reductionist Representation of Quantum Statistics and  Dynamics Using Coarse Graining},
      publisher = {University of Chicago},
      school = {Ph.D.},
      address = {2021-12},
      pages = {180},
      abstract = {Feynman’s imaginary time path integral formalism of  quantum statistical mechanics and the corresponding  quantum-classical isomorphism provides a theoretical  formalism to incorporate nuclear quantum effects (NQEs) in  simulations of condensed matter systems using  well-established classical methods such as molecular  dynamics (MD) or Monte Carlo (MC). Moreover, path integral  methods also have been extended into the dynamical realm to  calculate dynamic quantities such as vibrational spectra.  Despite the wide success of path integral methods in both  statistics and dynamics, they are not without rooms for  improvement. These challenges are innate to the classical  nature of the ring polymers, or discrete representation of  the imaginary time path. In quantum statistics, the path  integral methods provide a significant sampling challenge  due to the extended phase space of the ring polymers.  Moreover in quantum dynamics, the connection between the  dynamics of the ring polymer and the real time quantum  dynamics remain unclear. To address these distinct  challenges, we use ideas from classical statistical  mechanics in the context of path integral methods.  Coarse-graining of path integral (CG-PI) theory constructs  an alternative reductionist representation of the ring  polymer using coarse graining, greatly reducing the  dimensionality. In this dissertation, the many-body  generalization of the one-body CG-PI theory is discussed.  Moreover, we also introduce a numerical CG-PI (n-CG-PI)  method and modeling scheme that have shown to well capture  the structural correlations of realistic molecular systems.  In the realm of dynamics, the recently developed  generalized Langevin equation analysis of ring polymer  molecular dynamics theory (GLE/RPMD) provides an  alternative picture of the ring polymer dynamics by  directly mapping it into a GLE form. By doing so, we  analyze the two different contributions on the dynamics,  namely from the system and the bath. The numerical results  testify both the importance of the system potential and the  higher order interactions of the bath. },
      url = {http://knowledge.uchicago.edu/record/3615},
      doi = {https://doi.org/10.6082/uchicago.3615},
}