Title: Real-time path integral methods for electron-vibration dynamics
Abstract: The unfavorable scaling of wavefunction storage severely impacts the feasibility of quantum
dynamical calculations on large molecular and condensed-phase systems. Feynman’s path integral
formulation offers an attractive alternative, replacing wavefunctions by a sum of quantum
mechanical amplitudes along all possible paths. However, the path sum involves astronomical
numbers of terms, and stochastic methods are unable to deal with the oscillatory quantum phase.
Since the early 1990s, the iterative quasi-adiabatic propagator path integral (QuAPI)
methodology has enabled numerically exact, fully quantum mechanical simulation of dynamical
properties for a small system coupled to a bath of harmonic oscillators, at zero or finite temperature.
The QuAPI algorithm achieves linear scaling with the number of time steps by propagating a tensor
that spans the memory interval, but the storage of QuAPI tensors effectively restricts application of
the method to small systems and short or intermediate memory. Much recent effort has focused on
the development of algorithms that reduce the storage requirements of QuAPI. In particular, recent
work showed that one can further disentangle the path integral variables through the rigorous small
matrix decomposition (SMatPI), which leads to expressions that involve matrices of size equal to
that of the system’s reduced density matrix (RDM). The SMatPI algorithm eliminates tensor storage,
enabling the simulation of long-memory processes and multistate systems.
These methods are used to investigate the complex effects arising from the interplay
between electronic coherence and nuclear motion in a variety of processes. This seminar will focus
on the intricate mechanistic details of excitation energy transfer (EET) in large molecular aggregates
and photosynthetic light harvesting complexes.
Last, it has been shown that the time evolution of the full RDM encodes powerful
information related to the amount of delocalization and instantaneous population derivatives.
Coherence maps offer a powerful visualization tool for understanding the creation and destruction of
quantum superpositions and enable a state-to-state pathway analysis of dynamical processes.
Keywords: Density matrix, decoherence, system-bath, energy transfer
Host: Prof. Yang Yang