Using Density Operators
Features
The MCTDH programs can be used to describe a system using a density operator rather than a wavefunction. The program is used in exactly the same way as for wavefunctions, including the appropriate keyword (e.g. density2)in the RUN-SECTION of the input file. There are, however, some features which are not yet implemented for density operators. If an input file requests any of these features the programs stop and give appropriate error messages.
Furthermore, there are some features which affect only the density operator programs. They are described in the MCTDH input documentation, in the MCTDH output documentation, and in the MCTDH Hamiltonian/Liouvillian documentation together with the other features. A short list is given below.
Special input key words
- the key word ctrace in the Run-Section, which yields the ctrace file in a density operator propagation
- the key words projection, no_projection, closed, and open in the Operator-Section
- the SPDO-Basis-Section
- the temperature, left_state, and right_state key words in the Init_wf-Section
- the key words lmf and df in the Integrator-Section
- example inputs for propagations using density operators of type I and II
Special operators
- Dissipative Liouvillians are defined in the Dissipative-Section of the operator file.
- Raising operators, lowering operators, and number operators are introduced (see Built-in Symbols ). These can also be used in wave function calculations.
Analysis
For the analysis of a density operator calculation some of the standard MCTDH analysis programs can be used, e.g. the autospec program or the overlap program. It is even possible to compute the overlap between type I and type II density-operators. New analysis programs are listed together with the standard programs in the documentation of the analyse programs (see main menu).