Quantum Graphity
Nov. 23rd, 2009 05:02 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
109кстати, уже все в курсе, что вселенная - это граф?
At high temperature, the graph representing the state of the system is highly connected and has diameter close to 1. There is no notion of locality, as most of the Universe is one-edge adjacent to any vertex. Said differently, there is no notion of a subsystem, in the sense of a local neighborhood, since the neighborhood of any vertex is the entire KN. The microscopic degrees of freedom are the j and m labels.
At low temperature, the graph has far fewer edges than KN. Permutation invariance of the state breaks to translation invariance. Subsystems can be defined as subgraphs of the ground state or, better, as the emergent matter excitations, and the dynamics of the emergent matter is local by correspondence with lattice field theory.
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.0861v2.pdf
At high temperature, the graph representing the state of the system is highly connected and has diameter close to 1. There is no notion of locality, as most of the Universe is one-edge adjacent to any vertex. Said differently, there is no notion of a subsystem, in the sense of a local neighborhood, since the neighborhood of any vertex is the entire KN. The microscopic degrees of freedom are the j and m labels.
At low temperature, the graph has far fewer edges than KN. Permutation invariance of the state breaks to translation invariance. Subsystems can be defined as subgraphs of the ground state or, better, as the emergent matter excitations, and the dynamics of the emergent matter is local by correspondence with lattice field theory.
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.0861v2.pdf