BosonStrings

Normal ordered strings of bosonic operators in Julia.

Installation

] add https://github.com/nicolasloizeau/BosonStrings.jl

Getting started

Algebra

Compute $a_{1}^{\dagger 1} a_{1}^1 \cdot a_{1}^{\dagger 2} a_{1}^2$

using BosonStrings
o1 = Operator(1) #single boson operator
o1 += 1, (1, 1, 1) #add a† a
o2 = Operator(1)
o2 += 1, (1, 2, 2) #add a†^2 a^2
o = o1 * o2
println(o)

julia> o
(1.0 + 0.0im) (†3)(3)
(2.0 + 0.0im) (†2)(2)

we get $a_{1}^{\dagger 1} a_{1}^1 \cdot a_{1}^{\dagger 2} a_{1}^2 = a_{1}^{\dagger 3} a_{1}^3 + 2a_{1}^{\dagger 2} a_{1}^2$

Expectation values with Fock States

Compute $\langle 2 |o| 2 \rangle$:

julia> inner(2, o, 2)
4.0 + 0.0im