We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1Dmodels.The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented ...We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1Dmodels.The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to themaximal order p=18 in the time of propagation(Monte Carlo time step),which substantially improves the convergence of discretized amplitudes to their exact continuum values.Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes,using the recursive Schrodinger equation approach.In addition to the general 1D quantum theory,developed Mathematica codes are capable of calculating effective actions for specific models,for general 2D and 3D potentials,as well as for a general many-body theory in arbitrary number of spatial dimensions.展开更多
基金The authors gratefully acknowledge useful discussions with Axel Pelster and Vladimir Slavni´c.This work was supported in part by the Ministry of Education and Science of the Republic of Serbia,under project No.ON171017,and bilateral project NAD-BEC funded jointly with the German Academic Exchange Service(DAAD),and by the European Commission under EU FP7 projects PRACE-1IP,HP-SEE and EGI-InSPIRE.
文摘We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1Dmodels.The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to themaximal order p=18 in the time of propagation(Monte Carlo time step),which substantially improves the convergence of discretized amplitudes to their exact continuum values.Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes,using the recursive Schrodinger equation approach.In addition to the general 1D quantum theory,developed Mathematica codes are capable of calculating effective actions for specific models,for general 2D and 3D potentials,as well as for a general many-body theory in arbitrary number of spatial dimensions.
