Aron Beekman ベークマン アーロン
on this page:
Highlights –
Publications –
Popular –
PhD thesis –
MSc thesis
other pages: CV
Highlights
Recent software projects

Database design and Django implementation for the SciPost Foundation's extended metadata facilities initiative.
Scientific metadata is to be collected, processed and published openly in a transparent and interlinked way. The project involves keeping track of the source of each individual piece of data, and tracking its history. I also created visually clear and appealing EntityRelationship diagrams of the extensive data structures.
Academic reviews

Just as the equation x^2 = 1 is invariant under x → x, but its solutions x = 1 and x = 1 are not, spontaneous symmetry breaking is the phenomenon that physical systems may not possess all symmetries of the laws of nature that dictate their behaviour. In 2019 we published a tutorial/review aimed at graduate students in physics that conveys the deep importance of broken symmetry in many areas of physics.
 Quantum liquid crystals are collective quantum states of matter that feature the same partial breaking of spatial symmetries as liquid crystals. In 2017 we published a comprehensive review on using particle–vortextype duality transformations to describe twodimensional quantum liquid crystals in terms of dual gauge fields.
Publications
My publications on:
arXiv •
Inspire •
Google Scholar •
ResearcherID •
ORCID
 Theory of generalized Josephson effects
A.J. Beekman, PTEP 2020, 073B09 (2020), arXiv:1907.13284
 Stability and absence of a Tower of States in ferrimagnets
L. Rademaker, A.J. Beekman, J. van Wezel, Phys. Rev. Research 2, 013304 (2020), arXiv:1909.11381
 Introduction to spontaneous symmetry breaking
A.J. Beekman, L. Rademaker, J. van Wezel, SciPost Phys. Lect. Notes 11 (2019), arXiv:1909.01820
 Charged and neutral fixed points in the O(N)+O(N)model with Abelian gauge fields
A.J. Beekman, G. Fejos, Phys. Rev. D, 100, 016005 (2019),
arXiv:1903.05331
 Dual gauge field theory of quantum liquid crystals in three dimensions
A.J. Beekman, J. Nissinen, K. Wu, J. Zaanen, Phys. Rev. B 96, 165115 (2017) (Editors' suggestion),
arXiv:1703.03157
 Dual gauge field theory of quantum liquid crystals in two dimensions
A.J. Beekman, J. Nissinen, K. Wu, K. Liu, R.J. Slager, Z. Nussinov, V. Cvetkovic, J. Zaanen,
Phys. Rep. 683, 1–110 (2017),
arXiv:1603.04254
 Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
A.J. Beekman,
Ann. Phys. 361, 461–489 (2015),
arXiv:1408.1691
 Photodrive of magnetic bubbles via magnetoelastic waves
N. Ogawa, W. Koshibae, A.J. Beekman, N. Nagaosa, M. Kubota, M. Kawasaki and Y. Tokura,
PNAS 112(29), 8977–8981 (2015)
 Theory of magnonskyrmion scattering in chiral magnets
J. Iwasaki, A.J. Beekman and N. Nagaosa,
Phys. Rev. B 89, 064412 (2014),
arXiv:1309.2361
 Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D
A.J. Beekman, K. Wu, V. Cvetkovic and J. Zaanen,
Phys. Rev. B 88, 024121 (2013),
arXiv:1301.7329
 TypeII BoseMott insulators
A.J. Beekman and J. Zaanen,
Phys. Rev. B 86, 125129 (2012) (Editors' suggestion),
arXiv:1207.0286
 The emergence of gauge invariance: the stayathome gauge versus local–global duality
J. Zaanen and A.J. Beekman,
Ann Phys 327(4):1146–1161 (2012), arXiv:1108.2791
 Electrodynamics of Abrikosov vortices: the field theoretical formulation
A.J. Beekman and J. Zaanen,
Front. Phys. 6(4):357–369 (2011), arXiv:1106.3946
 Condensing NielsenOlesen strings and the vortexboson duality in 3+1 and higher dimensions
A.J. Beekman, D. Sadri and J. Zaanen,
New. J. Phys. 13:033004 (2011), arXiv:1006.2267
Popular
 (Dutch) Vortexdualiteit
Nederlands Tijdschrift voor Natuurkunde, Dec 2012
PDF (1.0MB)
 (Dutch) 100 jaar supergeleiding
at sargasso.nl
and sciencepalooza.nl
part 1,
part 2
PhD Thesis
In my dissertation at Leiden University under supervision of Jan Zaanen, I explore the implications of regarding a topological defect line in 3+1 dimesions as a world sheet.
From the Goldstone mode in a symmetrybroken state, the dynamics are obtained by a duality transformation, where each world sheet component has
a precise physical meaning. Furthermore, the ordertodisorder (quantum) phase transition is now viewed as the
proliferation of topological defects, and this wellknown vortex–boson duality is generalized to 3+1
dimensions. The highlight result is the prediction of vortex lines of quantized electric current in charged BoseMott
insulators, with possible relevance to underdoped cuprate superconductors
» Vortex duality in higher dimensions (pdf, 4.4 MB)
— also available at Leiden University Library
MSc Thesis
To obtain my Master's degree (Universiteit van Amsterdam, Institute for Theoretical Physics), I looked into the earlier work of my supervisor Sander Bais and some of his PhD students, in which they explored the extension of group symmetry to socalled quantum doubles in 2+1dimensional systems. In this way, the quantum numbers of topological excitations are taken into account as well as those of the regular (gauge) particles. Furthermore, this formalism provides directly for a description of the braid properties of the particles. Such structure can for example arise in gauge theories where the original symmetry is broken down to a finite group.
A next step was to look at the possible condensate phases in such systems; that is, we imagine the new ground state of the system to be one filled with background particles, all represented by a certain state vector of one of the irreducible representations of the symmetry algebra. Because of the braiding with the condensate particles, not every excitation in the new phase can exist freely, and some of them will be ‘confined’.
In my thesis work, I have calculated through almost all possible condensate states in models where the original symmetry is that of an even dihedral group, the symmetry group of a regular ngon, with n even. This leads to a redefinition of the braiding properties of the particles that exist freely in the condensate state. Furthermore, in some condensates the remaining symmetry algebra turns out to be much larger than one would naively expect from just looking at the breaking of the topological and regular parts of the quantum double.
» Quantum double symmetries of the even dihedral groups and their breaking (pdf, 1.0 MB)
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