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paper.bib

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%% BEC
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@book{PethickSmith2008,
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Author = {{Pethick}, C.~J. and {Smith}, H.},
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Booktitle = {Pethick, C., and Smith, H. (2008). Bose–Einstein Condensation in Dilute Gases. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511802850},
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Publisher = {Cambridge University Press},
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Title = {{Bose–Einstein Condensation in Dilute Gases}},
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Year = 2008
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author = {Pethick, C.~J. and Smith, H.},
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booktitle = {Pethick, C., and Smith, H. (2008). Bose–Einstein Condensation in Dilute Gases},
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publisher = {Cambridge University Press},
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title = {Bose–Einstein Condensation in Dilute Gases},
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doi = {10.1017/CBO9780511802850},
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year = {2008}
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}
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@article{FetterRMP2009,
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%% GPUE
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@article{Oriordan2016,
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@article{ORiordan2016,
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title = {Moir\'e superlattice structures in kicked Bose-Einstein condensates},
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author = {O'Riordan, L.~J. and White, A.~C. and Busch, Th.},
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journal = {Phys. Rev. A},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.93.023609}
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}
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@article{Oriordan2016b,
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@article{ORiordan2016b,
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title = {Topological defect dynamics of vortex lattices in Bose-Einstein condensates},
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author = {O'Riordan, L.~J. and Busch, Th.},
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journal = {Phys. Rev. A},
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@article{DalibardRMP2011,
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title = {Colloquium: Artificial gauge potentials for neutral atoms},
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author = {Dalibard, J. and Gerbier, F. and Juzeli\bar{u}nas, G. and \{Ohberg, P.},
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author = {Dalibard, Jean and Gerbier, Fabrice and Juzeli\ifmmode \bar{u}\else \={u}\fi{}nas, Gediminas and \"Ohberg, Patrik},
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journal = {Rev. Mod. Phys.},
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volume = {83},
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issue = {4},

paper.md

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---
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title: 'GPUE: Graphics Processing Unit Gross-Pitaevskii Equation solver'
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title: 'GPUE: Graphics Processing Unit Gross--Pitaevskii Equation solver'
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tags:
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- CUDA
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- physics
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# Summary
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Bose--Einstein Condensates (BECs) are superfluid systems consisting of bosonic atoms that have been cooled and condensed into a single, macroscopic ground state [@PethickSmith2008, @FetterRMP2009].
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These systems can be created in an experimental laboratory, and allow for the the exploration of many interesting physical phenomenon, such as superfluid turbulence [@Roche2008,@White2014,@Navon2016], chaotic dynamics [@Gardiner2002,@Kyriakopoulos2014, @Zhang2017], and as analogues of other quantum systems [@DalibardRMP2011].
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Bose--Einstein Condensates (BECs) are superfluid systems consisting of bosonic atoms that have been cooled and condensed into a single, macroscopic ground state [@PethickSmith2008; @FetterRMP2009].
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These systems can be created in an experimental laboratory, and allow for the the exploration of many interesting physical phenomenon, such as superfluid turbulence [@Roche2008; @White2014; @Navon2016], chaotic dynamics [@Gardiner2002; @Kyriakopoulos2014; @Zhang2017], and as analogues of other quantum systems [@DalibardRMP2011].
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Numerical simulations of BECs allow for new discoveries that directly mimic what can be seen in experiments and are thus highly valuable for fundamental research.
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In practice, the dynamics of BEC systems can often be found by solving the non-linear Schrödinger equation known as the Gross--Pitaevskii Equation (GPE),
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where $\Psi(x,t)$ is the one-dimensional many-body wavefunction of the quantum system, $m$ is the atomic mass, $V(x)$ is a potential to trap the atomic system, $g = \frac{4\pi\hbar^2a_s}{m}$ is a coupling factor, and $a_s$ is the scattering length of the atomic species.
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Here, the GPE is shown in one dimension, but it can easily be extended to two or three dimensions.
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Though there are many methods to solve the GPE, one of the most straightforward is the split-operator method, which has previously been accelerated with GPU devices [@Ruf2009,@Bauke2011]; however, there are no generalized software packages available using this method on GPU devices that allow for user-configurable simulations and a variety of different system types.
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Though there are many methods to solve the GPE, one of the most straightforward is the split-operator method, which has previously been accelerated with GPU devices [@Ruf2009; @Bauke2011]; however, there are no generalized software packages available using this method on GPU devices that allow for user-configurable simulations and a variety of different system types.
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Even so, there are several software packages designed to simulate BECs with other methods, including GPELab [@Antoine2014] the Massively Parallel Trotter-Suzuki Solver [@Wittek2013], and XMDS [@xmds].
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GPUE is a GPU-based Gross-Pitaevskii Equation solver via the split-operator method for superfluid simulations of both linear and non-linear Schrödinger equations, with an emphasis on Bose--Einstein Condensates with vortex dynamics in 2 and 3 dimensions. GPUE provides a fast, robust, and accessible method to simulate superfluid physics for fundamental research in the area and has been used to simulate and manipulate large vortex lattices in two dimensions [@Oriordan2016, @Oriordan2016b], along with ongoing studies on vortex turbulence in two dimensions and vortex structures in three dimensions.
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GPUE is a GPU-based Gross--Pitaevskii Equation solver via the split-operator method for superfluid simulations of both linear and non-linear Schrödinger equations, with an emphasis on Bose--Einstein Condensates with vortex dynamics in 2 and 3 dimensions. GPUE provides a fast, robust, and accessible method to simulate superfluid physics for fundamental research in the area and has been used to simulate and manipulate large vortex lattices in two dimensions [@ORiordan2016; @ORiordan2016b], along with ongoing studies on vortex turbulence in two dimensions and vortex structures in three dimensions.
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For these purposes, GPUE provides a number of unique features:
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1. Dynamic field generation for trapping potentials and other variables on the GPU device.
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2. Vortex tracking in 2D and vortex highlighting in 3D.
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3. Configurable gauge fields for the generation of artificial magnetic fields and corresponding vortex distributions [@DalibardRMP2011,@Ghosh2014].
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3. Configurable gauge fields for the generation of artificial magnetic fields and corresponding vortex distributions [@DalibardRMP2011; @Ghosh2014].
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4. Vortex manipulation via direct control of the wavefunction phase [@Dobrek1999].
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All of these features enable GPUE to simulate a wide variety of linear and non-linear (BEC) dynamics of quantum systems. The above features enable highly configurable physical system parameters, and allow for the simulation of state-of-the-art system dynamics. GPUE additionally features a highly performant numerical solver implementation, with performance greater than other available suites [@WittekGPE2016, @ORiordan2017]. All GPUE features and functionalities have been described in further detail in the documentation [@documentation].
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All of these features enable GPUE to simulate a wide variety of linear and non-linear (BEC) dynamics of quantum systems. The above features enable highly configurable physical system parameters, and allow for the simulation of state-of-the-art system dynamics. GPUE additionally features a highly performant numerical solver implementation, with performance greater than other available suites [@WittekGPE2016; @ORiordan2017]. All GPUE features and functionalities have been described in further detail in the documentation [@documentation].
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# Acknowledgements
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This work has been supported by the Okinawa Institute of Science and Technology Graduate University and by JSPS KAKENHI Grant Number JP17J01488.

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