Aaron Fenyes's scientific contributions
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Publications (6)
The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular singularities can become a Volterra equation with regular singularities. It can also reveal hidden structure, espe...
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...
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...
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...
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...
Physics http://deepblue.lib.umich.edu/bitstream/2027.42/63930/1/fenyes_aaron_2009.pdf
Citations
... Remark 4.25. Definition 4.24 is adequate for our purposes but does not capture the most general rank one spectral networks which can occur in nature, e.g. from trajectory structures of meromorphic or holomorphic quadratic differentials on Riemann surfaces; see [GMN2,HN,Fe], for example. ...
... Cloning in the context of classical mechanics was raised in John Baez's 2008 classical mechanics class lectures (See [4,5]). Further study by Fenyes [2] gave a more general formulation of cloning in classical physics allowing for the presence of a cloning machine, in which they show, using their formulation of cloning, that systems with phase space (R 2N , dx i ∧ dy i ) can always be cloned. ...
... 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. ...
Reference: A Physical Perspective on Classical Cloning
