Aron Beekman ベークマン アーロン
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PhD thesis –
other pages: CV
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 Entity-Relationship diagrams of the extensive data structures.
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–vortex-type duality transformations to describe two-dimensional quantum liquid crystals in terms of dual gauge fields.
My publications on:
Google Scholar •
- 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),
- 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),
- 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),
- Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
Ann. Phys. 361, 461–489 (2015),
- 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 magnon-skyrmion scattering in chiral magnets
J. Iwasaki, A.J. Beekman and N. Nagaosa,
Phys. Rev. B 89, 064412 (2014),
- 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),
- Type-II Bose-Mott insulators
A.J. Beekman and J. Zaanen,
Phys. Rev. B 86, 125129 (2012) (Editors' suggestion),
- The emergence of gauge invariance: the stay-at-home 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 Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions
A.J. Beekman, D. Sadri and J. Zaanen,
New. J. Phys. 13:033004 (2011), arXiv:1006.2267
- (Dutch) Vortexdualiteit
Nederlands Tijdschrift voor Natuurkunde, Dec 2012
- (Dutch) 100 jaar supergeleiding
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 symmetry-broken state, the dynamics are obtained by a duality transformation, where each world sheet component has
a precise physical meaning. Furthermore, the order-to-disorder (quantum) phase transition is now viewed as the
proliferation of topological defects, and this well-known vortex–boson duality is generalized to 3+1
dimensions. The highlight result is the prediction of vortex lines of quantized electric current in charged Bose-Mott
insulators, with possible relevance to underdoped cuprate superconductors
» Vortex duality in higher dimensions (pdf, 4.4 MB)
— also available at Leiden University Library
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 so-called quantum doubles in 2+1-dimensional 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 n-gon, 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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