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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

12 votes

Examples of non-rigorous but efficient mathematical methods in physics

The replica method and the cavity method have been used by physicists to calculate thermodynamic quantities in various statistical mechanics settings (including quite a few classes of random combinato …
1 vote

abelian higgs vortices

I expect that this terminology came from an analogy of an analogy. Quoting from Quantum Field Theory of Anyons, by Fröhlich and Marchetti (1988), "Particles with real spin and intermediate statistic …
Peter Shor's user avatar
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5 votes

The Quantum Operations On The Bipartite Systems

If I understand the question right, essentially what is being asked is: for a general quantum operation on a system with two subsystems, can you learn what happens to subsystem 1 just by looking at th …
Peter Shor's user avatar
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15 votes
Accepted

Are there any known quantum algorithms that clearly fall outside a few narrow classes?

Does the Farhi-Goldstone-Gutman game tree evaluation algorithm and the extensions of it fall into one of these classes? You might put it in quantum simulation/annealing because of the technique used, …
Peter Shor's user avatar
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18 votes
Accepted

Quantum PCP Theorem

The quantum PCP conjecture (nobody has proved it, so you can't call it a theorem) is possibly (there are a few different ways of generalizing the classical PCP theorem to the quantum regime, and I don …
Peter Shor's user avatar
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11 votes

Relativistic Cellular Automata

What Willie's answer shows is that, for some non-trivial Lorentz-translatable cellular automaton, every cell would need an infinite number of neighbors. This cellular automaton couldn't work if any ce …
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