https://github.com/lukeroantree4815162342/mastersproject

Code for "Computational Methods For Ultrafast Quantum Physics"
https://github.com/lukeroantree4815162342/mastersproject

high-performance high-performance-computing mathematics numpy physics physics-simulation python python3 quantum-mechanics scipy sparse-matrix

Last synced: 26 days ago
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Code for "Computational Methods For Ultrafast Quantum Physics"

• Host: GitHub
• URL: https://github.com/lukeroantree4815162342/mastersproject
• Owner: LukeRoantree4815162342
• Created: 2018-11-02T17:27:16.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2019-05-22T19:24:10.000Z (over 5 years ago)
• Last Synced: 2024-11-13T00:31:58.170Z (3 months ago)
• Topics: high-performance, high-performance-computing, mathematics, numpy, physics, physics-simulation, python, python3, quantum-mechanics, scipy, sparse-matrix
• Language: Jupyter Notebook
• Size: 680 KB
• Stars: 1
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Masters Project: Computational Methods For Ultrafast Quantum Physics

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## My project focuses on efficiently modelling laser pulse interactions with atoms

To do this;

> I solve (find eigenstates of) the Time-Independent Schrodinger Equation for a given potential distribution (so far using a soft-core potential to numerically simulate a Coulomb potential while avoiding the problem at the centre)

> I pick a state, and propagate it through time (as described by the TDSE) to see how it evolves under a chosen time-dependent potential. I model the Coulomb interaction with a soft-core potential.

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## Optimisations So Far:

### Sparse Storage for Hamiltonian; I use sparse diagonal storage, allowing much larger numbers of spatial points to be used

### Sparse Eigensolver; I use a Krylov subspace based eigensolver that allows sparse inputs, speeding up finding states

### ML For Shift-Inverse Method; The eigensolver has a parameter to allow it to look for eigenstates with eigenvalues near a value provided; I trained a Neural Network to predict the eigenvalue of the Ground State based on the potential distribution, and pass this result into the eigensolver - this speeds it up dramatically

### Finite Difference Propagator; Implemented an arbitrary-order finite difference method time propagator

### Krylov-Subspace Propagator; Implemented an arbitrary-order Arnoldi-based time propagator

### Parallelised The FD Propagator; I used multiprocessing to more efficiently propagate the state through time (speed-ups depending on number of cores available in the computer / server cluster used)

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## TODO:

### Re-Write In Fortran; In progress, switching over to MPI & OpenMP for parallelisation

### Apply some results found to existing RMT code to investigate if it can similarly be improved, and if it can maintain stability under these