TY - JOUR
T1 - Tree-Based Implementation of the Small Matrix Path Integral for System-Bath Dynamics
AU - Wang , Geshuo
AU - Cai , Zhenning
JO - Communications in Computational Physics
VL - 2
SP - 389
EP - 418
PY - 2024
DA - 2024/09
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0329
UR - https://global-sci.org/intro/article_detail/cicp/23387.html
KW - t-SMatPI, Open quantum system, Catalan number.
AB - <p style="text-align: justify;">The small matrix path integral (SMatPI) method is an efficient numerical approach to simulating the evolution of a quantum system coupled to a harmonic bath.
The method relies on a sequence of kernel matrices that defines the non-Markovian
dynamics of the quantum system. In the original SMatPI method, these kernels are
computed indirectly through the QuAPI method. Instead, we focus on the definition
of the kernel matrices and reveal a recurrence relation in these matrices. Using such
a relationship, a tree based algorithm (t-SMatPI) is developed, which is shown to be
much faster than straightforward computation of the kernel matrices based on their
definitions. This algorithm bypasses the step to compute the SMatPI matrices by other
path integral methods and provides more understanding of the SMatPI matrices themselves. Meanwhile, it keeps the memory cost and computational cost low. Numerical
experiments show that the t-SMatPI algorithm gives exactly the same result as i-QuAPI
and SMatPI. In spite of this, our method may indicate some new properties of open
quantum systems, and has the potential to be generalized to higher-order numerical
schemes.</p>