Heat fluctuations using TEDOPA

This is a package¹ for calculating FLUCTUATIONS of heat transfer in the Spin-Boson model² using the Time Evolving Density matrices using Orthogonal Polynomial Algorithm (TEDOPA)³⁴.

We employ the Thermofield-based chain-mapping approach for open quantum systems⁵ that enables us to use a vacuum initial matrix product state (pure) for the environment instead of a thermal state (mixed), thereby speeding up the computation greatly.

In this package, we use the ITensor library⁶ in Julia for tensor network manipulations.  

This package uses julia = "1.8.2" version.

 

PLEASE NOTE THE FOLLOWING POINTS before running these codes on Julia:

The scripts files define all the parameters of the model: scripts\mean_Q.jl (computes mean heat exchange), scripts\var_Q.jl (computes variance of heat exchange), scripts\obs_exp.jl (computes expected value of any observable).

Hamiltonians and Gates are defined in the file src\ham_gates.jl.

Initial state of the (system+environment) is defined in the file src\init_state.jl.

The heat characteristic function⁷ is calculated in the file src\charfn.jl.

 

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To (locally) reproduce this project, do the following:

0. Download this code base. Notice that raw data are typically not included in the git-history and may need to be downloaded independently.
1. Open a Julia console and do:

   julia> using Pkg
   julia> Pkg.add("DrWatson") # install globally, for using `quickactivate`
   julia> Pkg.activate("path/to/this/project")
   julia> Pkg.instantiate()
   

This will install all necessary packages for you to be able to run the scripts and everything should work out of the box, including correctly finding local paths.

You may notice that some scripts start with the commands:

using DrWatson
@quickactivate :flucn_tedopa

which auto-activate the project "flucn_tedopa" and enable local path handling from DrWatson.

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Footnotes

1. This code base is using the Julia Language and DrWatson to make a reproducible scientific project named flucn_tedopa ↩

2. Popovic, Maria, Mark T. Mitchison, Aidan Strathearn, Brendon W. Lovett, John Goold, and Paul R. Eastham. "Quantum heat statistics with time-evolving matrix product operators." PRX Quantum 2, no. 2 (2021): 020338. ↩

3. Prior, Javier, Alex W. Chin, Susana F. Huelga, and Martin B. Plenio. "Efficient simulation of strong system-environment interactions." Physical review letters 105, no. 5 (2010): 050404. ↩

4. Chin, Alex W., Ángel Rivas, Susana F. Huelga, and Martin B. Plenio. "Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials." Journal of Mathematical Physics 51, no. 9 (2010): 092109. ↩

5. de Vega, Inés, and Mari-Carmen Banuls. "Thermofield-based chain-mapping approach for open quantum systems." Physical Review A 92, no. 5 (2015): 052116. ↩

6. https://itensor.github.io/ITensors.jl/dev/index.html ↩

7. Esposito, Massimiliano, Upendra Harbola, and Shaul Mukamel. "Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems." Reviews of modern physics 81, no. 4 (2009): 1665. ↩