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 -