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Copy file name to clipboardExpand all lines: paper.md
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affiliations:
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- name: Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan.
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index: 1
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date: 21 September 2018
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date: 10 December 2018
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bibliography: paper.bib
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---
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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 phenomena, such as superfluid turbulence [@Roche2008; @White2014; @Navon2016], chaotic dynamics [@Gardiner2002; @Kyriakopoulos2014; @Zhang2017], and other analogous quantum systems [@DalibardRMP2011].
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Numerical simulations of BECs that directly mimic what can be seen in experiments are valuable for fundamental research in these areas.
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These systems can be created in an experimental laboratory and allow for the the exploration of physical phenomenon such as superfluid turbulence [@Roche2008; @White2014; @Navon2016], chaotic dynamics [@Gardiner2002; @Kyriakopoulos2014; @Zhang2017], and analogues of other quantum systems [@DalibardRMP2011].
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Numerical simulations of BECs that directly mimic experiments are valuable to fundamental research in these areas and allow for theoretical advances before experimental validation.
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The dynamics of BEC systems can be found by solving the non-linear Schrödinger equation known as the Gross--Pitaevskii Equation (GPE),
where $\Psi(\mathbf{r},t)$ is the three-dimensional many-body wavefunction of the quantum system, $\mathbf{r} = (x,y,z)$, $m$ is the atomic mass, $V(\mathbf{r})$ is an external potential, $g = \frac{4\pi\hbar^2a_s}{m}$ 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 three dimensions, but it can easily be modified for one or two dimensions [@PethickSmith2008].
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The split-operator method is one straightforward technique to solve the GPE and has previously been accelerated with GPU devices [@Ruf2009; @Bauke2011]
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No generalized software packages are available using this method on GPU devices; however, software packages have been designed to simulate BECs with other methods, including GPELab [@Antoine2014] the Massively Parallel Trotter-Suzuki Solver [@Wittek2013], and XMDS [@xmds].
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Here, the GPE is shown in three dimensions, but it can easily be modified to one or two dimensions [@PethickSmith2008].
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One of the most straightforward methods for solving the GPE is the split-operator method, which has previously been accelerated with GPU devices [@Ruf2009; @Bauke2011].
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No generalized software packages are vailable using this method on GPU devices that allow for user-configurable simulations and a variety of different system types; however,
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several software packages exist to simulate BECs with other methods and on different architectures, including GPELab [@Antoine2014] the Massively Parallel Trotter-Suzuki Solver [@Wittek2013], and XMDS [@xmds].
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GPUE is a GPU-based GPE solver via the split-operator method for superfluid simulations of both linear and non-linear Schrödinger equations, emphasizing 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 quantum vortex dynamics in two and 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, emphasizing superfluid vortex dynamics in two and three dimensions. GPUE is a fast, robust, and accessible software suite to simulate physics for fundamental research in the area of quantum systems and has been used to manipulate large vortex lattices in two dimensions [@ORiordan2016; @ORiordan2016b] along with ongoing studies of vortex dynamics.
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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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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 configurable physical system parameters and GPUE’s high-performance numerical solver improves over other 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 dynamics of quantum systems. GPUE additionally features a numerical solver with improvements over other suites [@WittekGPE2016; @ORiordan2017]. All of GPUE's features and functionality 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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We would also like to thank Thomas Busch, Rashi Sachdeva, Tiantian Zhang, Albert Benseney, and Angela White for discussions on useful physical systems to simulate with the GPUE codebase, along with Peter Wittek and Tadhg Morgan for contributions to the code, itself.
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These acknowledgements can be found in `acknowledgements.md`.
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These acknowledgements can be found in `GPUE/acknowledgements.md`.
Copy file name to clipboardExpand all lines: py/vort.py
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@@ -245,13 +245,13 @@ def run(start,fin,incr): #Performs the tracking
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v0c=vorts_c.element(index_r[0]).sign#Get the sign of the smallest distance vortex
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v0p=vorts_p.element(i3).sign# Get the sign of the current vortex at index i3
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v1c=vorts_c.element(index_r[0]).uid#Get uid of current vortex
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#Check if distance is less than 7 grid points, and that the sign is matched between previous and current vortices, and that the current vortex has a negative uid, indicating that a pair has not yet been found. If true, then update the current vortex index to that of the previous vortex index, and turn vortex on --- may be dangerous
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if (index_r[1] <30) and (vorts_c.element(index_r[0]).sign==vorts_p.element(i3).sign) and (vorts_c.element(index_r[0]).uid<0) and (vorts_p.element(i3).isOn==True):
print"Failed to find any matching vortex. Entering interactive mode. Exit with Ctrl+D"
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fromIPythonimportembed; embed()
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#Check if distance is less than 7 grid points, and that the sign is matched between previous and current vortices, and that the current vortex has a negative uid, indicating that a pair has not yet been found. If true, then update the current vortex index to that of the previous vortex index, and turn vortex on --- may be dangerous
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if (index_r[1] <30) and (vorts_c.element(index_r[0]).sign==vorts_p.element(i3).sign) and (vorts_c.element(index_r[0]).uid<0) and (vorts_p.element(i3).isOn==True):
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