Aaron Fenyes's scientific contributions

Publications (5)

Preprint
The Hamiltonian operator describing a quantum particle on a path often extends holomorphically to a complex neighborhood of the path. When it does, it can be seen as the local expression of a complex projective structure, and its perturbations become deformations of that geometric structure. We'll describe the Hamiltonian of a free particle as a co...
Article
The "abelianization" process introduced by Gaiotto, Hollands, Moore, and Neitzke turns $\operatorname{SL}_K \mathbb{C}$ local systems on a punctured surface into $\mathbb{C}^\times$ local systems, giving coordinates on the decorated $\operatorname{SL}_K \mathbb{C}$ character variety that are known to match Fock and Goncharov's cluster coordinates i...
Article
In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give exam...
Article
Physics http://deepblue.lib.umich.edu/bitstream/2027.42/63930/1/fenyes_aaron_2009.pdf
Article
1 Background 1.1 Motivation The fact that you can't clone a quantum system is closely related to the fact that the tensor product in the category of Hilbert spaces is non-Cartesian. At the end of his 2008 classical mechanics course, John Baez pointed out that the ten-sor product in the category of Poisson manifolds is also non-Cartesian, which shou...

Citations

... This case is more difficult, since problems of dynamics mix with the combinatorial problems. Some of the necessary tools in case K = 2 have been developed in [14]. ...
... Wootters and Zurek's [1] work on the no-cloning theorem has led to extensive research on the quantum cloning process and its physical implications. While the studies in the quantum regime are both abstract [2][3][4][5][6] and application-based [7][8][9][10][11], work on the classical cloning process has been extremely limited and restricted to a purely mathematical approach [12][13][14][15]. There appears to be a belief that the classical cloning process is trivial, perhaps because it is so familiar. ...