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[HEOMLS Matrix for Fermionic Baths](@id doc-M_Fermion)

The HEOM Liouvillian superoperator matrix [struct M_Fermion <: AbstractHEOMLSMatrix](@ref M_Fermion) which describes the interactions between the system and multiple [Fermionic baths](@ref doc-Fermionic-Bath).

Construct Matrix

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

[M_Fermion(Hsys, tier, Bath, parity)](@ref M_Fermion) 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](@ref doc-Fermionic-Bath)
  • parity::AbstractParity : the [parity](@ref doc-Parity) label of the operator which HEOMLS is acting on. Defaults to EVEN.

kwargs (Keyword Arguments)

  • threshold::Real : The threshold of the [importance value](@ref doc-Importance-Value-and-Threshold). 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
  • dims : the dimension list of the coupling operator (should be equal to the system dims).
  • N : the number of total [ADOs](@ref doc-ADOs)
  • sup_dim : the dimension of system superoperator
  • parity : the [parity](@ref doc-Parity) label of the operator which HEOMLS is acting on.
  • bath::Vector{FermionBath} : the vector which stores all [FermionBath](@ref doc-Fermionic-Bath) objects
  • hierarchy::HierarchyDict: the object which contains all [dictionaries](@ref doc-Hierarchy-Dictionary) for fermion-bath-ADOs hierarchy.

One can obtain the value of each fields as follows:

M::M_Fermion

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