Open Quantum System Theory for Molecular Systems
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QUANTArhei: Open Quantum System Theory for Molecular Systems

Quantarhei is a Molecular Open Quantum Systems Simulator written predominantly in Python. Its name is derived from the famous aphorism "Panta rhei" of the Greek philosopher Heraclitus of Ephesus. "Panta rhei" means "Everything flows" or "Everything is in flux" which is quite fitting when you change Panta into Quanta.

In "Quantarhei" the last four letter ("rhei") should be written in Greek, i.e. (using LateX convention) "\rho \epsilon \iota".

Quantarhei is in flux, but it already provides helper classes to define molecules, their aggregates and their interaction with external environment. It can calculate absorption spectra of individual molecules and their aggregates and excitation energy transfer dynamics using various types of Redfield and Foerster theories.

Quantarhei provides Python code (optimized with Numpy) for all its implemented methods and theories, and allows extensions and replacements of the reference Python code with optimised routines written in C, Fortran or other lower level languages.

In the first development stage, we concentrate on bringing to you tools to quickly build essential components of a quantum mechanical simulation, such as Hamiltonian, relaxation tensors, various initial conditions for density matrix etc.

Quantarhei is at its experimental stage. Current version is Version

Quantarhei is available in source form on GitHub and from PyPI for installation with the pip command.


The work on Quantarhei is supported by

Neuron Fund for Support of Science

through the Impuls grant in physics 2014 (2015-2017)


Czech Science Foundation (GACR)

through grants: 14-25752S (2014-2016) and 17-22160S (2017- )

New in 0.0.43

For users:
  • PureDephasing super-operator to allow additional pure dephasing for realistic lineshapes in effective lineshape description of time-resolved experiments
  • Empty relaxation superopetator (as an empty Lindblad form) introduced (as a temporary fix to allow pure dephasing dynamics only)
  • Consistent calculation of pure dephasing of non-optical coherence elements of the density matrix from effective lineshape theory (including electronic only dephasing in vibrational-electronic systems)
  • Some bug fixes

New in 0.0.42

For users:
  • Improved effective lineshapes for 2D spectrum calculations
  • Calculation of absorption spectrum using first order Liouville pathways
  • Some bug fixes including an frequency factor in absorption spectrum

New in 0.0.41

For users:
  • Some bug fixes
  • Better Louville pathway manipulation features

New in 0.0.40

For users:
  • Some bug fixes
  • Minor new features

New in 0.0.39

For users:
  • Some bug fixes

New in 0.0.38

For users:
  • Some bug fixes

New in 0.0.37

For users:
  • Some bug fixes
For developers
  • Some unused files removed
  • More precise dependencies on other packages specified in setup

New in 0.0.36

For users:
  • Quantarhei now available also as a conda package
  • Recommended installation procedure documented
  • TwoDSpectrum class revised - new method names, better storage model (keeps track of rephasing and non-rephasing part, groups of pathways associated with different processes when required, stores different pathways separately when required)
  • Improved TwoDSpectrumContainer (can hold a group of spectra identified by an arbitrary ValueAxis (most notably TimeAxis and FrequencyAxis), integer index or list of strings). Copies the new storage improvement on TwoDSpectrum.
  • labsetup class changed to LabSetup and extended by information about pulse profiles and spectra. labsetup is left as deprecated for compatibility
  • Fourier transform of 2D spectra in t2, via TwoDSpectrumContainer; also enables FFT with window function
  • Functions of ValueAxis introduced in a special module; Tukey window function for FFT in waiting time is one of them
  • SuperOperator is BasisManaged; basis management is solved for both time-dependent and time-independent super operators
  • RelaxationTensor now inherits from SuperOperator and it is BasisManaged through that inheritance
  • EvolutionSuperOperator tested, documented and it is BasisManaged
  • EvolutionSuperOperator’s method apply() can be applied with time argument which is of type TimeAxis type, float or array of floats; returns DensityMatrix or DensityMatrixEvolution
  • Quantarhei driver qrhei changes format: use ‘qrhei run scriptname’ to run scripts and consult the -h option of ‘qrhei run’; parallel runs untested in this version
  • Documentation contains a description of the concept of “user”, “advanced”, and “expert” levels of classes in Quantarhei.
  • List of classes completely covered by documentation and doctests included in on-line documentation
  • Classes Mode, SubMode, Molecule, TwoDSpectrumContainer completely documented
  • Documentation enhanced
  • Countless small improvements and bug fixes
For developers:
  • Code of conduct file now in the root directory of the package
  • Absorption spectroscopy related classes now organized in one file per class fashion so that automatic documentation is easier to read
  • New subpackage quantarhei.testing united all custom functions that support testing. It includes module previously found in subpacked (now removed) and a module which supports tests with behave package
  • Behave package is now used for some tests (in particular for tests of the “qrhei” driver). Future acceptance tests should preferentially be written with this package
  • New helper script “ghenerate” autogenerates Python step files for tests with ‘behave’ package from the Gherkin feature files

New in 0.0.35

For users:
  • Method get_DensityMatrix() of the Aggregate class improved. It accepts some new options which makes specification of desired density matrix more flexible
  • Experimental implementation of circular and linear dichroisms and fluorescence spectra
  • Documentation is now available on A badge Documentation Status which informations about the status of automatic documentation builds was added to README
  • Many small improvements and bug fixes
For developers:
  • The code is now hosted on and the builds are tested after every commit. Corresponding badge Build Status has been added to README
  • The code is now hosted on and its coverage by tests is measured. Corresponding badge showing the coverage Coverage has beed added to README

New in 0.0.34

For users
  • Some issues with addition of bath correlation functions was fixed
  • First entry in a database of literature bath correlation functions was created: the vibrational part of the FMO spectral density from Wendling et al., (2004)
  • Aggregate can return a matrix of Franck-Condon factors (get_FC_factor_matrix())
  • Aggregate can transform excited state site-basis shifted vibrational representation of an arbitrary operator to the unshifted (ground state) one (transform_2_unshifted(A, inverse=True/False) )
  • Several new tested examples
  • RelaxationTensors (Redfield, Foerster, Lindblad, etc.) can now be multiplied by a constant or added (addition only if they are in tensor, i. e. not in operator, form)
  • Tested examples can be fetched into IPython notebook or Python/IPython console by %example magic command or fetch_example function from quantarhei.wizard.magic module
  • Small improvements and bug fixes

New in 0.0.33

For users:

  • Evolution superoperators for relaxation tensors with constant coefficients (EvolutionSuperOperator class)
  • Liouville pathway analysis including relaxation pathways (in Aggregate class)
  • Small improvements and bug fixes

For developers:

  • Aggregate class is broken into smaller pieces which snowball the functionality. Basic class is AggregateBase; new functions of this powerful class are defined in separate child classes. Aggregate class inherits from the whole chain of classes
  • quantarhei.REAL and quantarhei.COMPLEX types should be now used for numpy arrays throughout the package. These types can be controlled and with it the used numerical precision and memory needs

New in 0.0.32

For users:

  • Electronic Lindblad form for vibronic Frenkel exciton model
  • Propagation with relaxation tensor (in particular Redfield and Time-dependent Redfield) in operator representation (where applicable it is much faster than with the tensorial representation)
  • Redfield tensor and Time-dependent Redfield tensor can be calculated for a model with arbitrary number of vibrational states
  • Aggregate can vibrationally trace arbitrary operator defined on its Hilbert space
  • Small improvements and bug fixes

New in version 0.0.31

For users:

  • Arbitrary time independent Lindblad form
  • quantarhei.wizard module which contains IPython magic commands and some helpful Python console commands
  • Simulation templates which can be fetched into IPython notebooks or console by %template magic command (IPython) or fetch_template (console and IPython)
  • Part of the test suit available for installed Quantarhei package
  • Some small improvements and bug fixes

For developers:

  • Makefile is back in the package root directory
  • examples directory depleted in favor of quantarhei/wizard/examples directory
  • New tests under quantarhei/tests directory (mostly unit tests which contain plots)
  • pytest required to run newtests with matplotlib plots