bath_mapper.calculate_excitation_spectral_function

bath_mapper.calculate_excitation_spectral_function(mode_fermion_system, temperature, number_frequencies=None)

Determine the bath excitation spectral function from a given Hamiltonian.

If the system of the mixed Hamiltonian is a spin system: Core has arbitrary many spins and bath has free electrons, and spin-bath operator is of the form: t_sij * sigma_s * c_dag_i c_j, with summation over s, i, j and where sigma_s is a spin operator built from the X, Y, Z Pauli operators. We do not (need to) keep track of electron-spin transitions. Also the actual spin-operator can be sigma_s^-, sigma_s^+, or sigma_sz, but is not specified.

If the system of the mixed Hamiltonian is a fermionic system: Core has arbitrary many fermions and bath has free electrons, and system-bath operator is of the form: t_ijkl * c_dag_i c_j * c_dag_k c_l, with summation over i, j, k, l and where c_dag_i c_j is a system term and c_dag_k c_l is a bath term. We do not (need to) keep track of electron-system transitions.

Parameters:

  • mode_fermion_system (MixedHamiltonianSystem) -- A MixedHamiltonianSystem composed of a spin/fermion system coupled to a noninteracting fermionic bath.

  • temperature (float) -- Bath temperature. Enters later via fermi distributions of bath.

  • number_frequencies (int) -- The number of frequency points on which the excitation spectral function is calculated. Defaults to 100.

Returns:

(BRNoiseOperator, List[float]) - The SpinBRNoiseOperator/FermionBRNoiseOperator and corresponding frequencies from the input.

Raises:

  • ValueError -- Could not convert mode_fermion_system to MixedHamiltonianSystem.

  • ValueError -- The incorrect number of spin/fermion subsystems have been specified.

  • ValueError -- The temperature input is not valid, as it is negative.

  • ValueError -- No interaction between system and bath. Cannot construct spectral function.

  • ValueError -- calculate_excitation_spectral_function only supports uniform coupling types.

  • ValueError -- This function cannot be run with symbolic values in the Hamiltonian.