Description:

Abstract: The unfavorable scaling of wavefunction storage severely impacts the feasibility of
quantum dynamical calculations in finite-temperature condensed phase systems. Feynman’s path integral formulation offers a powerful alternative. However, the path sum involves astronomical numbers of terms, and stochastic sampling methods are unable to deal with the oscillatory quantum phase.

A series of developments have led to efficient real-time path integral methods suitable for
simulating a variety of processes. The quasi-adiabatic propagator path integral (QuAPI) for systembath dynamics achieves linear scaling with the number of time steps by propagating a tensor that spans the bath-induced memory. Recent work showed that the path integral variables can be further disentangled within the memory interval, leading to a small-matrix decomposition of the path integral (SMatPI) that enables simulation of multistate systems and long-memory processes. A different decomposition leads to the modular path integral (MPI) for extended systems with a quasione-dimensional topology, which allows the inclusion of any number of finite-temperature vibrational modes and scales linearly with system length. In addition to these fully quantum mechanical methods, the quantum-classical path integral (QCPI) offers a rigorous formulation of nonadiabatic dynamics in nonlinear environments.

These methods are used to investigate quantum coherence and its destruction in exciton transfer processes, as well as the dynamics of coupled qubits interacting with phonon baths. Besides allowing accurate numerical simulation, the structure of the path integral leads to insightful perspectives of decoherence, which is seen to have classical as well as strictly quantum mechanical origins. 

Speaker: Professor Nancy Makri, Edward William and Jane Marr Gutgsell Chair, University of Illinois, Urbana-Champaign

Host: Anupam Garg