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bibliography.bib
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@inproceedings{sandvik2010computational,
title={Computational studies of quantum spin systems},
author={Sandvik, Anders W},
booktitle={AIP Conference Proceedings},
volume={1297},
number={1},
pages={135--338},
year={2010},
organization={AIP}
}
@book{fradkin2013field,
title={Field theories of condensed matter physics},
author={Fradkin, Eduardo},
year={2013},
publisher={Cambridge University Press}
}
@article{onsager1944crystal,
title={Crystal statistics. I. A two-dimensional model with an order-disorder transition},
author={Onsager, Lars},
journal={Physical Review},
volume={65},
number={3-4},
pages={117},
year={1944},
publisher={APS}
}
@article{chiu2016classification,
title={Classification of topological quantum matter with symmetries},
author={Chiu, Ching-Kai and Teo, Jeffrey CY and Schnyder, Andreas P and Ryu, Shinsei},
journal={Reviews of Modern Physics},
volume={88},
number={3},
pages={035005},
year={2016},
publisher={APS}
}
@article{thouless1982quantized,
title={Quantized Hall conductance in a two-dimensional periodic potential},
author={Thouless, David J and Kohmoto, Mahito and Nightingale, M Peter and den Nijs, Md},
journal={Physical Review Letters},
volume={49},
number={6},
pages={405},
year={1982},
publisher={APS}
}
@article{Kohmoto1985a,
abstract = {The topological aspects of wavefunctions for electrons in a two dimensional periodic potential with a magnetic field are discussed. Special attention is paid to the linear response formula for the Hall conductance $\sigma$xy. It is shown that the quantized value of $\sigma$xyis related to the number of zeros of wavefunctions in the magnetic Brillouin zone. A phase of wavefunctions cannot be determined in a unique and smooth way over the entire magnetic Brillouin zone unless the magnetic subband carries no Hall current. {\textcopyright} 1985.},
author = {Kohmoto, Mahito},
doi = {10.1016/0003-4916(85)90148-4},
file = {:Users/mira/Dropbox (OIST)/Papers/Imported/Kohmoto.pdf:pdf},
isbn = {0003-4916},
issn = {1096035X},
journal = {Annals of Physics},
keywords = {QHE,Topological Phases,historical,mathy},
mendeley-tags = {QHE,Topological Phases,historical,mathy},
number = {2},
pages = {343--354},
title = {{Topological invariant and the quantization of the Hall conductance}},
volume = {160},
year = {1985}
}
@article{Simon1983,
abstract = {It is shown that the "geometrical phase factor" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. This not only takes the mystery out of Berry's phase factor and provides calculational simple formulas, but makes a connection between Berry's work and that of Thouless et al. This connection allows the author to use Berry's ideas to interpret the integers of Thouless et al. in terms of eigenvalue degeneracies.},
author = {Simon, Barry},
doi = {10.1103/PhysRevLett.51.2167},
file = {:Users/mira/Dropbox (OIST)/Papers/Imported/PhysRevLett.51.2167.pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
keywords = {Historical,Topological Phases},
mendeley-tags = {Historical,Topological Phases},
number = {24},
pages = {2167--2170},
title = {{Holonomy, the quantum adiabatic theorem, and Berry's phase}},
volume = {51},
year = {1983}
}
@article{Berry1984,
abstract = {M. V. BerryAbstract A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters {\$}\backslashmathbf{\{}R{\}}{\$} in its Hamiltonian {\$}\backslashhat{\{}H{\}}(\backslashmathrm{\{}R{\}}){\$}, will acquire a geometrical phase factor {\$}\backslashexp {\{}i\backslashgamma(\backslashmathrm{\{}C{\}}){\}}{\$} in addition to the familiar dynamical phase factor. An explicit general formula for {\$}\backslashgamma{\$}(C) is derived in terms of the spectrum and eigenstates of {\$}\backslashhat{\{}H{\}}(\backslashmathbf{\{}R{\}}){\$} over a surface spanning C. If C lies near a degeneracy of {\$}\backslashhat{\{}H{\}}, \backslashgamma{\$}(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration {\$}\backslashgamma{\$}(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.},
archivePrefix = {arXiv},
arxivId = {1108.0910},
author = {Berry, M. V.},
doi = {10.1098/rspa.1984.0023},
eprint = {1108.0910},
file = {:Users/mira/Library/Application Support/Mendeley Desktop/Downloaded/Berry - 1984 - Quantal Phase Factors Accompanying Adiabatic Changes.pdf:pdf},
isbn = {00804630},
issn = {1364-5021},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
keywords = {Topological Phases,historical},
mendeley-tags = {Topological Phases,historical},
number = {1802},
pages = {45--57},
title = {{Quantal Phase Factors Accompanying Adiabatic Changes}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1984.0023},
volume = {392},
year = {1984}
}
@article{takayama1980continuum,
title={Continuum model for solitons in polyacetylene},
author={Takayama, Hajime and Lin-Liu, Yo R and Maki, Kazumi},
journal={Physical Review B},
volume={21},
number={6},
pages={2388},
year={1980},
publisher={APS}
}
@article{su1980soliton,
title={Soliton excitations in polyacetylene},
author={Su, W-P\_ and Schrieffer, JR and Heeger, AJ},
journal={Physical Review B},
volume={22},
number={4},
pages={2099},
year={1980},
publisher={APS}
}
@article{bader2013solving,
title={Solving the Schr{\"o}dinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients},
author={Bader, Philipp and Blanes, Sergio and Casas, Fernando},
journal={The Journal of chemical physics},
volume={139},
number={12},
pages={124117},
year={2013},
publisher={AIP}
}
@phdthesis{o2017non,
title={Non-equilibrium vortex dynamics in rapidly rotating Bose-Einstein condensates},
author={O'Riordan, Lee James},
year={2017},
school={Okinawa Institute of Science and Technology Graduate University}
}
@book{murray1999solar,
title={Solar system dynamics},
author={Murray, Carl D and Dermott, Stanley F},
year={1999},
publisher={Cambridge university press}
}
@book{glowinski2017splitting,
title={Splitting methods in communication, imaging, science, and engineering},
author={Glowinski, Roland and Osher, Stanley J and Yin, Wotao},
year={2017},
publisher={Springer}
}
@article{bauke2011accelerating,
title={Accelerating the Fourier split operator method via graphics processing units},
author={Bauke, Heiko and Keitel, Christoph H},
journal={Computer Physics Communications},
volume={182},
number={12},
pages={2454--2463},
year={2011},
publisher={Elsevier}
}
@ARTICLE{1970Bimka..57...97H,
title = "{Monte Carlo Sampling Methods using Markov Chains and their Applications}",
journal = {Biometrika, Vol.~57, No.~1, p.~97-109, 1970},
year = 1970,
month = apr,
volume = 57,
pages = {97-109},
doi = {10.1093/biomet/57.1.97},
adsurl = {http://adsabs.harvard.edu/abs/1970Bimka..57...97H},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{1953JChPh..21.1087M,
author = {{Metropolis}, N. and {Rosenbluth}, A.~W. and {Rosenbluth}, M.~N. and
{Teller}, A.~H. and {Teller}, E.},
title = "{Equation of State Calculations by Fast Computing Machines}",
journal = {\jcp},
year = 1953,
month = jun,
volume = 21,
pages = {1087-1092},
doi = {10.1063/1.1699114},
adsurl = {http://adsabs.harvard.edu/abs/1953JChPh..21.1087M},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{Markov,
author = {A. Markov , A},
year = {2006},
month = {12},
pages = {591 - 600},
title = {An Example of Statistical Investigation of the Text Eugene Onegin Concerning the Connection of Samples in Chains},
volume = {19},
journal = {Science in Context},
doi = {10.1017/S0269889706001074}
}