function diffeqsolver(s0, tspan, J::LorentzianSD, Jshared::LorentzianSD, bfields, bfieldshared, matrix::Coupling; JH=zero(I), S0=1/2, Bext=[0, 0, 1], saveat=[], save_fields=false, projection=true, alg=Tsit5(), atol=1e-3, rtol=1e-3)

Solves the dynamics of a system of ineracting spins under the influence of both local (unique to each spin) and global (shared by all spins) stochastic noise from the environment.

Arguments

• s0: Array of length 3N specifying the initial conditions of the N spins. The order the initial consitions is first the Sx,Sy,Sz for the first spin, then for the second, and so on.
• tspan: The time span to solve the equations over, specified as a tuple (tstart, tend).
• Jlist::Vector{LorentzianSD}: The list of spectral densities of the environment(s).
• bfield: An array of tuples of functions Array{Tuple{Function, Function, Function}} representing the time series of the noise for each environment.
• bcoupling::Vector{Vector{T}} T <: Real: A vector (of length the number of baths) of vectors (of length the number of spins), specifying if each bath couples to each spin.
• matrix::Vector{TT} TT <: Coupling: A vector of Coupling structs specifying the spin-environment coupling matrix for each environment.
• JH=zero(I): (Optional) The spin-spin coupling matrix. Default is zero matrix (i.e. non-interacting spins).
• S0=1/2: (Optional) The spin quantum number. Default is 1/2.
• Bext=[0, 0, 1]: (Optional) The external magnetic field vector. Default is [0, 0, 1] (normalised length pointing in the z direction).
• saveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.
• save_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.
• projection=false: (Optional) Specifies whether to project the spin vectors onto the unit sphere at each time step, hence forcing the numerical conservation of the spin length. Default is false.
• alg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.
• atol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.
• rtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.

Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

Note: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)

Returns

An ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.

function diffeqsolver(s0, tspan, J::LorentzianSD, Jshared::LorentzianSD, bfields, bfieldshared, matrix::Coupling; JH=zero(I), S0=1/2, Bext=[0, 0, 1], saveat=[], save_fields=false, projection=true, alg=Tsit5(), atol=1e-3, rtol=1e-3)

Solves the dynamics of a system of ineracting spins under the influence of either local (unique to each spin) or global (shared by all spins) stochastic noise from the environment.

Arguments

• s0: Array of length 3N specifying the initial conditions of the N spins. The order the initial consitions is first the Sx,Sy,Sz for the first spin, then for the second, and so on.
• tspan: The time span to solve the equations over, specified as a tuple (tstart, tend).
• J::LorentzianSD: The spectral density of the noise acting on the spins (either local or shared depending on the value of bfields).
• bfields: For local baths, an array of tuples of functions Array{Tuple{Function, Function, Function}} representing the time series of the local stochastic field for each spin. For a global bath, a tuple of functions Tuple{Function, Function, Function} representing the time series of the global stochastic field shared by all the spins.
• matrix::Coupling: The spin-environment coupling matrix.
• JH=zero(I): (Optional) The spin-spin coupling matrix. Default is zero matrix (i.e. non-interacting spins).
• S0=1/2: (Optional) The spin quantum number. Default is 1/2.
• Bext=[0, 0, 1]: (Optional) The external magnetic field vector. Default is [0, 0, 1] (normalised length pointing in the z direction).
• saveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.
• save_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.
• projection=false: (Optional) Specifies whether to project the spin vectors onto the unit sphere at each time step, hence forcing the numerical conservation of the spin length. Default is false.
• alg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.
• atol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.
• rtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.

Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

Note: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)

Returns

An ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.

function diffeqsolver(x0, p0, tspan, J::LorentzianSD, bfield, matrix::Coupling; JH=zero(I), Ω=1.0, counter_term=true, saveat=[], save_fields=false, alg=Tsit5(), atol=1e-3, rtol=1e-3)

Solves the dynamics of a system of ineracting oscillators under the influence of either local (unique to each oscillator) or global (shared by all oscillators) stochastic noise from the environment.

Arguments

• x0: Array of length N specifying the initial position of the N oscillators.
• p0: Array of length N specifying the initial momentum of the N oscillators.
• tspan: The time span to solve the equations over, specified as a tuple (tstart, tend).
• J::LorentzianSD: The spectral density of the noise acting globally on the harmonic oscillators.
• bfield: A tuple of functions Tuple{Function, Function, Function} representing the time series of the global stochastic field shared by all the harmonic oscillators.
• matrix::Coupling: The harmonic oscillators-environment coupling matrix.
• JH=zero(I): (Optional) The oscillator-oscillator coupling matrix. Default is zero matrix (i.e. non-interacting oscillators).
• Ω=1.0: (Optional) The natural angular frequency of the harmonic oscillators (currently the same for all). Default is 1.
• counter_term=true: (Optional) Whether to include the counter-term or not. Default is true.
• saveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.
• save_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.
• alg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.
• atol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.
• rtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.

Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

Note: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)

Returns

An ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.