# Error using an exponential function in a Hamiltonian

**URL:** <https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540>\
**Category:** New to Julia\
**Tags:** question\
**Created:** [May 29, 2023, 7:25am UTC](https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540 "2023-05-29T07:25:13Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Anil\_Kumar](https://avatars.discourse-cdn.com/v4/letter/a/f05b48/32.png) [@Anil\_Kumar](https://discourse.julialang.org/u/Anil_Kumar)\
**Post date:** [May 29, 2023, 7:25am UTC](https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540/1 "2023-05-29T07:25:14Z")

</div>

I am trying to modify a model with some extra terms, but getting an error.

```julia
using QuantumCumulants
using OrdinaryDiffEq, ModelingToolkit
hc = FockSpace(:cavity)
hm = FockSpace(:motion)
h = hc ⊗ hm
t = (0.0,10000.0)
@qnumbers a::Destroy(h,1) b::Destroy(h,2) 
@cnumbers Δ ωm t0 gm E gm κ 
function F(t,t0,E,Δ)
    if t.<=t0
        E0=E*t0
        F=1im*E0/Δ *(1-exp(1im*Δ*t))
    else
        F=zero(1im)
    end
    return F
end

# H= -Δ*a'*a + ωm*b'*b+gm*(a'+a)*(b +b') + E*(a + a') # works fine without exp() and F

H= -Δ*a'*a + ωm*b'*b+gm*(a'+a)*(exp.(-1im*ωm.*t).*b + exp.(1im*ωm.*t).*b') + (F.*a + conj(F).*a')#test Hamiltonian
eqs = meanfield([b'*b,a'*a],H,[a];rates=[κ],order=2)
eqs_completed = complete(eqs)
@named sys = ODESystem(eqs_completed)
u0 = zeros(ComplexF64, length(eqs_completed)) 
u0[1] = 4*1e3 # Initial condition
p0 = (Δ=>-1, ωm=>10, E=>1e5, gm=>1e-4,t0=>2,κ=>1) 
prob = ODEProblem(sys,u0,t,p0)
sol = solve(prob,RK4())
#plot
using Plots
n = abs.(sol[a'*a])
plot(sol.t, n, xlabel="t", label="n_m")

```

I found an errors:

1. no method matching length, I think some issue in vectors multiplication using exp(). In addition, I guess my F has different time length than operators a and b in H etc. Please let me know any hints/comments.

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 29, 2023, 7:28am UTC](https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540/2 "2023-05-29T07:28:40Z")

</div>

What’s the stacktrace? What line is it pointing to?

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<div class="post-metadata">

**Author:** ![Anil\_Kumar](https://avatars.discourse-cdn.com/v4/letter/a/f05b48/32.png) [@Anil\_Kumar](https://discourse.julialang.org/u/Anil_Kumar)\
**Post date:** [May 29, 2023, 10:01am UTC](https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540/3 "2023-05-29T10:01:40Z")

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It points to the line where Hamiltonian H is written. And Stacktrace is below.

Stacktrace:  
[1] \_similar\_shape(itr::Destroy{ProductSpace{Vector{FockSpace{Symbol}}}, Symbol, Int64, Base.ImmutableDict{DataType, Any}}, #unused#::Base.HasLength)  
@ Base ./array.jl:663  
[2] \_collect(cont::UnitRange{Int64}, itr::Destroy{ProductSpace{Vector{FockSpace{Symbol}}}, Symbol, Int64, Base.ImmutableDict{DataType, Any}}, #unused#::Base.HasEltype, isz::Base.HasLength)  
@ Base ./array.jl:718  
[3] collect(itr::Destroy{ProductSpace{Vector{FockSpace{Symbol}}}, Symbol, Int64, Base.ImmutableDict{DataType, Any}})  
@ Base ./array.jl:712  
[4] broadcastable(x::Destroy{ProductSpace{Vector{FockSpace{Symbol}}}, Symbol, Int64, Base.ImmutableDict{DataType, Any}})  
@ Base.Broadcast ./broadcast.jl:704  
[5] broadcasted(::Function, ::Base.Broadcast.Broadcasted{Base.Broadcast.Style{Tuple}, Nothing, typeof(exp), Tuple{Base.Broadcast.Broadcasted{Base.Broadcast.Style{Tuple}, Nothing, typeof(\*), Tuple{Base.RefValue{SymbolicUtils.BasicSymbolic{CNumber}}, Tuple{Float64, Float64}}}}}, ::Destroy{ProductSpace{Vector{FockSpace{Symbol}}}, Symbol, Int64, Base.ImmutableDict{DataType, Any}})  
@ Base.Broadcast ./broadcast.jl:1302  
[6] top-level scope  
@ In[80]:21

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [June 9, 2023, 10:12pm UTC](https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540/4 "2023-06-09T22:12:26Z")

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This looks like it may not be Symbolics but instead QuantumCumulants-specific. Have you opened an issue on the QuantumCumulants.jl github repo?

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<div class="post-metadata">

**Author:** ![Anil\_Kumar](https://avatars.discourse-cdn.com/v4/letter/a/f05b48/32.png) [@Anil\_Kumar](https://discourse.julialang.org/u/Anil_Kumar)\
**Post date:** [June 11, 2023, 1:18am UTC](https://discourse.julialang.org/t/error-using-an-exponential-function-in-a-hamiltonian/99540/5 "2023-06-11T01:18:03Z")

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No. I don’t know how to do that. but I will try.