Dr. Amartya Bose
Chemistry in Solution and at Interfaces, Department of Chemistry, Princeton University
Quantum Dynamics: Path Integrals and Phase Space Methods
August 6, 2021 at 4.00 PM through MICROSOFT TEAMS
The Teams link is below
Quantum dynamics is essential to understanding various condensed phase processes like charge and exciton transfer dynamics. In fact, even primarily classical processes such as diffusion can often be enhanced by quantum dispersion effects. However, owing to its exponential scaling, simulations of quantum dynamics in the condensed phase pose severe computational challenges. Approximations become necessary to ensure feasibility of simulations. In this respect, path integrals provide an extremely lucrative framework for developing approximations that are broadly of two types — methods based on classical trajectories and methods involving system-solvent decomposition.
In phenomena where deep tunneling effects are absent, such as calculation of infrared spectra and diffusion coefficent, useful information can be obtained directly from classical trajectory simulations. In such situations, the Wigner phase space distribution is often used for quantizing the initial conditions to account for zero-point energy effects. However, this Wigner distribution involves a multidimensional Fourier transform, which makes the accurate evaluation a challenging task. Some approximate[2, 3] and rigorous methods[4, 5] for evaluating it and simulating the corresponding quasiclassical dynamics will be presented.
On the other hand, for processes with deep tunneling effects like charge or exciton transfer reactions, classical trajectories may not give sufficient accuracy. A low-dimensional subspace constitutes the quantum system, and the rest of the degrees of freedom are relegated to a different level of treatment. Path integrals are essential for enabling a rigorous description of the interaction between the quantum “system” and the “solvent” or “environment.” I will present various developments on the quasi-adiabatic propagator path integral (QuAPI)[6, 7] and quantum-classical path integral (QCPI)[8, 9] frameworks that make the methods more efficient and facilitate the use of rate theory[10, 11]. Applications to the dynamics of bacteriochlorophyll dimer and charge transfer complexes will be shown. Finally, a promising framework[13, 14] that combines the generality of Feynman-Vernon influence functional with the flexibility of tensor network methods to study the dynamics in large dimensional systems will be presented along with some future research directions.
 E. Wigner, On the Quantum Correction For Thermodynamic Equilibrium, Physical Review 40, 749 (1932).
 A. Bose and N. Makri, Wigner phase space distribution via classical adiabatic switching, The Journal of Chemical Physics 143, 114114 (2015).
 A. Bose and N. Makri, Wigner Distribution by Adiabatic Switching in Normal Mode or Cartesian Coordinates and Molecular Applications, Journal of Chemical Theory and Computation 14, 5446 (2018).
 A. Bose and N. Makri, Coherent State-Based Path Integral Methodology for Computing the Wigner Phase Space Distribution, The Journal of Physical Chemistry A 123, 4284 (2019).
 A. Bose and N. Makri, Quasiclassical Correlation Functions from the Wigner Density Using the Stability Matrix, Journal of Chemical Information and Modeling 59, 2165 (2019).
 N. Makri and D. E. Makarov, Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory, The Journal of Chemical Physics 102, 4600 (1995).
 N. Makri and D. E. Makarov, Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology, The Journal of Chemical Physics 102, 4611 (1995).
 R. Lambert and N. Makri, Quantum-classical path integral. II. Numerical methodology, The Journal of Chemical Physics 137, 22A553 (2012).
 R. Lambert and N. Makri, Quantum-classical path integral. I. Classical memory and weak quantum nonlocality, The Journal of Chemical Physics 137, 22A552 (2012). 2
 A. Bose and N. Makri, Non-equilibrium reactive flux: A unified framework for slow and fast reaction kinetics, The Journal of Chemical Physics 147, 152723 (2017).
 A. Bose and N. Makri, Quantum-classical path integral evaluation of reaction rates with a near-equilibrium flux formulation, International Journal of Quantum Chemistry 121, 10.1002/qua.26618 (2021).
 A. Bose and N. Makri, All-Mode Quantum–Classical Path Integral Simulation of Bacteriochlorophyll Dimer Exciton-Vibration Dynamics, The Journal of Physical Chemistry B 124, 5028 (2020).
 A. Bose, A Pairwise Connected Tensor Network Representation of Path Integrals, arXiv pre-print server (2021).
 A. Bose and P. L. Walters, A tensor network representation of path integrals: Implementation and analysis, arXiv pre-print server (2021).