1d High Temperature Quarkonium Lindblad Dynamics CN & RN-SBP Solver

//*********************************************************************************
//
// THIS PROGRAM IMPLEMENTS A 1D VERSION OF THE MASTER EQUATION FOR HEAVY
// QUARKONIUM DERIVED BY Y. AKAMATSU IN
//
// ``Heavy quark master equations in the Lindblad form at high temperatures,''
// Phys. Rev. D 91, no. 5, 056002 (2015)
// doi:10.1103/PhysRevD.91.056002
// [arXiv:1403.5783 [hep-ph]].
//
// ON THE LEVEL OF THE DENSITY MATRIX AND INCLUDES FULL DISSIPATIVE EFFECTS.
// THE SAME EQUATION OF MOTION HAS BEEN APPROXIMATELY UNRAVELLED VIA QUANTUM
// STATE DIFFUSION IN
//
// T. Miura, Y. Akamatsu, M. Asakawa and A. Rothkopf,
// ``Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma,''
// Phys. Rev. D 101, no.3, 034011 (2020)
// doi:10.1103/PhysRevD.101.034011
// [arXiv:1908.06293 [nucl-th]].
//
// This code deploys a novel discrete finite difference operator, specifically
// designed to guarantee the trace conservation of the Lindblad dynamics
// called a reparametrization neutral summation-by-parts operator. Its derivation
// is outlined in an upcoming joint publication
//
// O.Ålund, Y. Akamatsu, F. Laurén, T. Miura, J. Nordström and A. Rothkopf
// ``Trace preserving quantum dynamics using a novel reparametrization-neutral
// summation-by-parts difference operator.''
//
// CODE AUTHOR: Dr. Alexander Karl Rothkopf DATE: April 4th 2020
//
//*********************************************************************************

# ==================================================================
# In order to compile the different source code files you need to
# install the PETSC and SLEPC library
# from https://www.mcs.anl.gov/petsc/ (tested on v.3.12)
# and from https://slepc.upv.es (tested on v.3.12)
# respectively. The Makefile requires that the environment variables
# PETSC_DIR, PETSC_ARCH and SLEPC_DIR are set accordingly. The values
# currently used in the Makefile thus need to be adjusted.
#
# The Lindblad dynamics code allows the user to compute the eigen-
# functions of the Hamiltonian directly without resorting to a
# distributed solver, which furthermore requires the EIGEN library to
# be present, which can be found at
# http://eigen.tuxfamily.org/ (tested on v.3.3.7)
# Please adjust the EIGENPATH environmental variable accordingly.
#
# MasterPETSC1DxyNewD: Lindblad dynamics with RN-SBP operator
#
#      run the program via example script file # FLB_1D_PETSC_XY_DEBYE_TM_T01_IC0.scr
#
# MasterPETSC1DxyNaiveD: Lindblad dynamics with naive operator
#
#     run the program via example script file
#     FLB_1D_PETSC_XY_DEBYE_TM_T01_IC0_NAIVED.scr
#
# EigenStates1DNewD: Distributed computation of Eigenstates of
#     the Hamiltonian to be used in the Lindblad
#     dynamics as initial conditions and/or in
#     order to compute density matrix in the
#     state basis.
#     run the program as mpirun -n #nodes EigenStates1DNewD.run
# ==================================================================