TY - JOUR
T1 - Convergence characteristics of a domain decomposition scheme for approximation of quantum forces
AU - Park, Sojung
AU - Yoon, Jungim
AU - Wee, Daehyun
PY - 2013
Y1 - 2013
N2 - We investigate the convergence characteristics of a domain decomposition scheme to approximately compute quantum forces in the context of semiclassical Bohmian mechanics. The study is empirical in nature. Errors in the approximate quantum forces are compiled while relevant parameters in the numerical scheme are systematically changed. The compiled errors are analyzed to extract underlying trends. Our analysis shows that the number of Bohmian particles used in discretization has relatively weak influence on the error, while the length scale of interaction among subdomains controls the error in most cases. More precisely, the overall numerical error decreases as the length scale of interaction among subdomains decreases, if the error due to the truncation of the tail of the probability density distribution is adequately controlled. Our results suggest that it may be necessary to develop an efficient method to effectively control the error due to the truncation of the tail. Further studies, especially rigorous mathematical ones, should follow to understand and improve the behavior of the scheme.
AB - We investigate the convergence characteristics of a domain decomposition scheme to approximately compute quantum forces in the context of semiclassical Bohmian mechanics. The study is empirical in nature. Errors in the approximate quantum forces are compiled while relevant parameters in the numerical scheme are systematically changed. The compiled errors are analyzed to extract underlying trends. Our analysis shows that the number of Bohmian particles used in discretization has relatively weak influence on the error, while the length scale of interaction among subdomains controls the error in most cases. More precisely, the overall numerical error decreases as the length scale of interaction among subdomains decreases, if the error due to the truncation of the tail of the probability density distribution is adequately controlled. Our results suggest that it may be necessary to develop an efficient method to effectively control the error due to the truncation of the tail. Further studies, especially rigorous mathematical ones, should follow to understand and improve the behavior of the scheme.
KW - Bohmian mechanics
KW - Convergence
KW - Domain decomposition
KW - Quantum trajectories
UR - http://www.scopus.com/inward/record.url?scp=84885856819&partnerID=8YFLogxK
U2 - 10.1016/j.cap.2013.03.026
DO - 10.1016/j.cap.2013.03.026
M3 - Article
AN - SCOPUS:84885856819
SN - 1567-1739
VL - 13
SP - 1296
EP - 1300
JO - Current Applied Physics
JF - Current Applied Physics
IS - 7
ER -