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HEOMLS Matrix for Fermionic Baths

The HEOM Liouvillian superoperator matrix struct M_Fermion <: AbstractHEOMLSMatrix which describes the interactions between the system and multiple Fermionic baths.

Construct Matrix

To construct the HEOM matrix in this case, one can call

M_Fermion(Hsys, tier, Bath, parity) with the following parameters:

args (Arguments)

  • Hsys : The time-independent system Hamiltonian
  • tier::Int : the tier (cutoff level) for the fermionic bath
  • Bath::Vector{FermionBath} : objects for different fermionic baths
  • parity::AbstractParity : the parity label of the operator which HEOMLS is acting on. Defaults to EVEN.

kwargs (Keyword Arguments)

  • threshold::Real : The threshold of the importance value. Defaults to 0.0.
  • verbose::Bool : To display verbose output and progress bar during the process or not. Defaults to true.

For example:

Hs::QuantumObject # system Hamiltonian
tier = 3
Bath::FermionBath

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

Fields

The fields of the structure M_Fermion are as follows:

  • data : the sparse matrix of HEOM Liouvillian superoperator
  • tier : the tier (cutoff level) for the fermionic hierarchy
  • dimensions : the dimension list of the coupling operator (should be equal to the system dimensions).
  • N : the number of total ADOs
  • sup_dim : the dimension of system superoperator
  • parity : the parity label of the operator which HEOMLS is acting on.
  • bath::Vector{FermionBath} : the vector which stores all FermionBath objects
  • hierarchy::HierarchyDict: the object which contains all dictionaries for fermion-bath-ADOs hierarchy.

One can obtain the value of each fields as follows:

M::M_Fermion

M.data
M.tier
M.dimensions
M.dims
M.N
M.sup_dim
M.parity
M.bath
M.hierarchy