The presentation consists of two parts. We first propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1- dimensional space, creation and annihilation operators are defined such that the F+1- dimensional space is complete for any combined excitations. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the well-known Meyer-Miller model.
We then show a unified second-order scheme for constructing simple, robust and accurate algorithms for typical thermostats for exact quantum/classical statistics for the canonical ensemble. The scheme consistently improves the efficiency for evaluating all quantum thermodynamic properties for any type of thermostat. Even when the Born-Oppenheimer approximation is broken, the unified scheme offers a powerful and accurate tool for studying non-adiabatic systems in thermal equilibrium.
Professor Jian Liu received his B.S. at the University of Science & Technology of China in 2000 and Ph.D. at the University of Illinois at Urbana-Champaign in 2005. After working as a postdoc or research associate at the University of California, Berkeley and at Stanford University, he joined the College of Chemistry and Molecular Engineering, Peking University in December 2012.
Bi-Weekly Seminar Series by the NYU-ECNU Center for Computational Chemistry at NYU Shanghai