bath_mapper.coupling_to_spectral_function

bath_mapper.coupling_to_spectral_function(mode_boson_system, frequencies, background=None, additional_damping=None, allow_empty_coupling=None)

Convert a physical coupling as described by a spin/fermion system coupled to a bosonic bath to a spectral function.

If the system part of the input MixedLindbladOpenSystem is a spin system, the MixedLindbladOpenSystem should adhere to the following assumptions: * The coherent system terms can be of any form as they are not taken into account here. * The coherent pure bosonic (bath) terms should be interaction-free, and should therefore only be of the form (omega * b^dagger b). * The coherent coupling terms between system and bath should be limited to one single Pauli operator coupling to a single bosonic creation operator

plus its hermitian conjugate: (sigma_{x, y, z} * (b + b^dagger)).

  • The noise terms should only act on the bosonic bath and should be limited to pure damping.

If the system part of the input MixedLindbladOpenSystem is a fermionic system, the MixedLindbladOpenSystem should adhere to the following assumptions: * The coherent system terms can be of any form as they are not taken into account here. * The coherent pure bosonic (bath) terms should be interaction-free, and should therefore only be of the form (omega * b^dagger b). * The coherent coupling terms between system and bath should be limited to c_i a_j operator coupling to a single bosonic creation operator

plus its hermitian conjugate: (c_i a_j * (b + b^dagger)).

  • The noise terms should only act on the bosonic bath and should be limited to pure damping.

Parameters:

  • mode_boson_system (MixedLindbladOpenSystem) -- A struqture_py coupled open spin-boson system or fermion-boson system in the form of a MixedLindbladOpenSystem. The coupling between fermion/spin and bosonic subsystem is limited to one single Pauli operator (in the case of a SpinBRNoiseOperator) or a c_i a_j operator (in the case of a FermionBRNoiseOperator) coupling to a single bosonic creation operator plus its Hermitian conjugate. The bosonic subsystem is limited to an interaction-free system, with the eigenfrequencies directly given by the coefficients of the occupation operators in the Hamiltonian (omega * b^dagger b). The Lindblad terms of the open system can only act on the bosonic subsystem and are limited to pure damping.

  • frequencies (List[float]) -- The frequencies for which every datapoint in the spectral function is defined.

  • background (Optional[float]) -- A constant background/offset that is included in the on-diagonal spectral functions. Defaults to 0.0

  • additional_damping (Optional[float]) -- An optional constant damping to be added to the one calculated from the open system.

  • allow_empty_coupling (Optional[bool]) -- Allow a mixed system input with no coupling between subsystems.Will produce a zero spectral function.

Returns:

The calculated spectral function.

Return type:

BRNoiseOperator

Raises:

  • ValueError -- Frequencies must increase monotonically.

  • ValueError -- The coupling type has been incorrectly specified.

  • ValueError -- Spectral function must define a value for each frequency.

  • ValueError -- Could not construct the products needed to index the mode_boson_system.