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3
votes
0answers
39 views

Does the Lyapunov exponent and Entropy change? [closed]

If $\lambda$ is the largest positive Lyapunov exponent of a piecewise linear dynamical chaotic discrete in time map, then is there a relationship between the entropy and its $\lambda$. In the paper ...
1
vote
0answers
118 views

Basic questions about fusion of two anyons

Suppose we have two anyons $a$ and $b$ on a manifold, and we use $|a\otimes b\rangle$ to label the corresponding wavefunction. Based on the fusion rule: $a\otimes b=\oplus_c N_{ab}^c c$, we may ...
4
votes
1answer
463 views

A naive question about topologically ordered wavefunction?

Topological entanglement entropy (TEE, proposed by Levin, Wen, Kitaev, and Preskill) is a direct characterization of the topological order encoded in a wavefunction. Here I have some confusions, and ...
0
votes
2answers
412 views

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link http://books.google.ca/books?id=lEu7CTGjdDkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#...
4
votes
2answers
626 views

topological entanglement entropy for a punctured torus and sphere

Topological entanglement entropy (http://arxiv.org/pdf/cond-mat/0510613.pdf, http://arxiv.org/abs/hep-th/0510092) is usually calculated for surfaces with boundary. How would it look like for compact ...
12
votes
1answer
366 views

How to understand topological order at finite temperature?

I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features ...
11
votes
1answer
2k views

Quantum dimension in topological entanglement entropy

In 2D the entanglement entropy of a simply connected region goes like \begin{align} S_L \to \alpha L - \gamma + \cdots, \end{align} where $\gamma$ is the topological entanglement entropy. $\gamma$ is ...
8
votes
0answers
233 views

Topological entanglement entropy only defined for a system in the ground state?

What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
2
votes
1answer
929 views

Topological phase

Can anybody tell me, if generically any system, which is solely described by a topological field theory, resides in a topological phase? I cant find any clear notion of topological phase. Only ...
4
votes
2answers
161 views

Knotted token-ring network

Suppose we have a rigid token-ring network. An observer at any node can seemingly determine the angular momentum of the network by measuring the time it takes for a packet to travel around the ring ...
4
votes
1answer
303 views

Entropy of a polymer contained in a sphere with infinitely thin chords

Imagine that I have a polymer (approximated as a freely diffusing, freely jointed chain with some number of subunits 'N'), and I place this polymer into a sphere of some volume 'V'. Next, I proceed to ...