• Effective action to level p=6 (PDF file);
• Link to the Monte Carlo parallel (MPI) code used in this investigation: speedup-mpi.tgz;
• Serial version of the above code: speedup-serial.tgz.

/* Path Integral Monte Carlo code developed by A. Balaz
(antun [at] ipb [dot] ac [dot] rs) for the paper:

"Systematically accelerated convergence of path integrals"
by A. Bogojevic, A. Balaz, and A. Belic
Phys. Rev. Lett. 94, 180403 (2005)

Address: Institute of Physics, Belgrade, Serbia
Scientific Computing Laboratory, http://www.scl.rs/speedup/

Public use and modification of this code is allowed providing the above paper is properly acknowledged. The author would be grateful for all information and/or comments regarding the use of the code.
*/

This MPI code gives a Monte Carlo simulation that calculates imaginary time amplitudes for the transition from a to b in time T for generic thery. The Planck constant hbar=1. Trajectories are generated using the bisection method. The variable s determines the level of bisection, i.e. time discretization N takes the values 2^0, 2^1, ..., 2^s.

The user configurable section is in file p.c. In it users need to define the level parameter p (1 <= p <= 18) and to supply the potential V and its derivatives.

COMPILING:

1) Supply the appropriate level p (by adjusting #define statement) and function V0() in file p.c.
2) A typical serial compiling line (e.g. for level p=2) looks like:

mpicc -O5 -o speedup-p2 main.c p.c nr.c -lm -lsprng -I.

Note that you need to have installed SPRNG libraries, http://sprng.cs.fsu.edu/
(The above example [-lsprng] is for the case of system wide installation of SPRNG.
In the case of a custom installation this needs to be changed appropriatel.)

USAGE:

mpirun [-nolocal] -np NP speedup-p2 T a b s Nmc seed par[0] ...

NP is the number of processes.
speedup-p2 is the compile name of the simulation working at level p=2.

T is the time of propagation.
a is the position at time t=0.
b is the position at time t=T.
s is the bisection level.
Nmc is the number of Monte Carlo samples used.
seed is seed value used by the SPRNG (random number generator).
par[0], ... are additional parameters defining the potential
(initialize as many as needed and use them in the same order
in the user supplied function V0 in file p.c).

Codes used in:

A. Balaz, I. Vidanovic, A. Bogojevic, A. Belic, and A. Pelster
"Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator"
J. Stat. Mech. (2011) P03004
arXiv e-print: 0912.2743

A. Balaz, I. Vidanovic, A. Bogojevic, A. Belic, and A. Pelster
"Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism"
J. Stat. Mech. (2011) P03005
arXiv e-print: 1011.5185