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

Rothkopf, Alexander

//*********************************************************************************
//
// 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)
#
# 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
# ==================================================================

The author of the code gladly acknowledges support by the Research Council of Norway under the FRIPRO Young Research Talent grant 286883. Developing and testing this code has utilized computing resources provided by UNINETT Sigma2 - the National Infrastructure for High Performance Computing and Data Storage in Norway under project NN9578K-QCDrtX "Real-time dynamics of nuclear matter under extreme conditions"
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