HEOMLS Matrix for Schrödinger Equation

The HEOM Liouvillian superoperator matrix with cutoff level of the hierarchy equals to 0: struct M_S <: AbstractHEOMLSMatrix

This corresponds to the standard Schrodinger (Liouville-von Neumann) equation, namely

\[\hat{\mathcal{M}}[\cdot]=-i \left[H_{s}, \cdot \right]_-,\]

where $[\cdot, \cdot]_-$ stands for commutator.

Construct Matrix

To construct the HEOM matrix for Schrödinger Equation, one can call

M_S(Hsys, parity) with the following parameters:

args (Arguments)

Hsys : The time-independent system Hamiltonian
parity::AbstractParity : the parity label of the operator which HEOMLS is acting on. Defaults to EVEN.

kwargs (Keyword Arguments)

verbose::Bool : To display verbose output during the process or not. Defaults to true.

For example:

Hs::QuantumObject # system Hamiltonian

# create HEOMLS matrix in both EVEN and ODD parity
M_even = M_S(Hs) 
M_odd  = M_S(Hs, ODD)

The fields of the structure M_S are as follows:

data : the sparse matrix of HEOM Liouvillian superoperator
tier : the tier (cutoff level) for the hierarchy, which equals to 0 in this case
dims : the dimension list of the coupling operator (should be equal to the system dims).
N : the number of total ADOs, which equals to 1 (only the reduced density operator) in this case
sup_dim : the dimension of system superoperator
parity::AbstractParity : the parity label of the operator which HEOMLS is acting on.

One can obtain the value of each fields as follows:

M::M_S

M.data
M.tier
M.dims
M.N
M.sup_dim
M.parity