Semiclassical typicality in open quantum systems

• Applicant: Professor Dr. Frank Thomas Großmann
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Theoretical Chemistry: Electronic Structure, Dynamics, Simulation ; Theoretical Condensed Matter Physics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 399787697

• Final Report Year: 2022

Final Report Abstract

The scientific outcome of the proposed project was twofold. Firstly, the original goal of finding thermalization using classical trajectories was reached for a model system of general interest: the symmetric double well potential. The original plan of using the Herman-Kluk semiclassical propagator had to be abandonned, but we could still rest the calculations on classical trajectories by using the coupled coherent states methodology of Shalashilin and Child. This method propagates the expansion coefficients of the wavefunction using a fully quantum mechanical scheme and thus can (at least in principle) be converged to the exact quantum result. We stress that also Herman-Kluk calculations have been performed, however, and thereby the semiclassical determination of correlation functions has been generalized to the case of autocorrelations of Gaussian wavepackets. Furthermore, the so-called Davydov Ansatz has proven to be very useful in the investigation of (non-Markovian) vibrational relaxation on solid surfaces. As a moral of these findings it turns out that a relatively small number of bath degrees of freedom is enough to account for thermalization of a central, nonlinear degree of freedom. Secondly, by exploring the foundations of Gaussian wavepacket methods starting from a variational principle (it turned out that the Dirac-Frenkel variational principle was most favorable), we could show that intricate differences between Gaussian methods based on a variational principle, like the fully variational VCS method (similar to vMCG: variational multi configuration Gaussians) and the CCS method, and the Herman-Kluk method exist. They are due to the fact that the Gaussians, although (over-)complete, do not form an orthogonal system. In the future, this finding could eventually lead to the development of new methods, where, e. g., the inverse overlap is also used in the Herman-Kluk method in order to decrease the number of trajectories needed to converge the results. Finally, not only the standard, so-called Glauber coherent states, but also the generalized coherent states put forth by Perelomov and Gilmore are worthwhile basis functions for quantum dynamical calculations. A first study in this direction has already been undertaken but a lot more work in the realm of lattice Hamiltonian (Bose-Hubbard model) waits to be done.

Publications

• Apoptosis of moving non-orthogonal basis functions in many-particle quantum dynamics. Physical Review B 101, 174315 (2020)
  M. Werther and F. Großmann
  
• On the Husimi version of the classical limit of quantum correlation functions. Cond. Matt. 5, 3 (2020)
  S. Loho Choudhury and F. Großmann
  
• Strong coupling to a phonon bath enhances adiabatic population transfer. Physical Review A 102, 063710 (2020)
  M. Werther and F. Großmann
  
• Exact variational dynamics of the multimode Bose-Hubbard model based on SU(M ) coherent states. Physical Review A 103, 042209 (2021)
  Yulong Qiao, and F. Großmann
  
• Review: Coherent state based solutions of the time-dependent Schrödinger equation: Hierarchy of approximations to the variational principle International. Reviews in Physical Chemistry 40, 81 (2021)
  M. Werther, S. Loho Choudhury, and F. Großmann
  
• Non-Markovian Vibrational Relaxation Dynamics at Surfaces. The Journal of Chemical Physics 156, 214702 (2022)
  E. W. Fischer, M. Werther, F. Bouakline, F. Großmann, and P. Saalfrank
  
• Quantum approach to the thermalization of the toppling pencil interacting with a finite bath. Physical Review A 105, 022201 (2022)
  S. Loho Choudhury, F. Großmann