notas

**This is an old revision of the document!**

No momento estou colocando links que me interessam. Assim que tiver tempo pretendo organizar isso…

http://www.jornaldaciencia.org.br/Detalhe.jsp?id=70812

Explicação simples sobre partículas virtuais: http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/

- Relação entre massa e energia. Um dos principais mecanismos do aumento da massa de um elétron acelerado pode ser a força de “back-reaction” devido ao seu próprio campo eletromagnético (que o freia a assim aumenta sua massa). O mecanismo é similar a auto indução : http://dx.doi.org/10.1119/1.4807754

The idea here is to find a observable which can tell when a state is entangled. Most of the works are based on the fact that for separable states

<latex>$

\langle S_i . S_j \rangle | _{sep} = | \langle S_i \rangle . \langle S_j \rangle | \leq | \langle S_i \rangle | \langle S_j \rangle | \le s |

$</latex>

The first inequality comes from the fact that \langle S_i \rangle behaves like a vector and the Cauchy-Schwarz inequality. The second inequality comes from the fact that the eigenvalues of

http://www.newscientist.com/special/seven-wonders-of-the-quantum-world

**For Quantum Information, Two Wrongs Can Make a Right**
http://www.sciencemag.org/cgi/content/full/321/5897/1783

**Quantum information: To compute or not to compute?**
http://www.nature.com/nature/journal/v439/n7079/full/439919a.html

**Quantum physics: Total surveillance**
http://www.nature.com/nature/journal/v446/n7133/full/446275a.html

http://www.nature.com/nature/journal/v448/n7156/full/448872a.html

http://www.nature.com/nature/journal/v456/n7224/full/456880a.html

Fundamentos da matemática

http://www.cs.umaine.edu/~chaitin

**Psicologia Evolutiva**
http://www.jornaldaciencia.org.br/Detalhe.jsp?id=70392

- Appeared first in an attempt to explain High Tc superconductors with spins liquids, which can not be described by the Landau symmetry breaking theory.
- Chiral spin state: breaks time reversal and parity symmetry, but not spins rotation
- But different states have the same symmetry! New kind of order which is beyond symmetry description → Topologial order

- New Kind of order that can not be described by the usual LGW symmetry-breaking model

- Quasi-particles are anyons (wave function is multiplied by e^i\theta when particles are swapped anticlockwise or e^-i\theta if clockwise. In 3-D theta can only be 0 (bosons) or Pi(fermions).)

- But High Tc do not break time reversal and parity symmetries. Not described by the chiral states. (symmetric spins liquids were introduced to explain High Tc, some are gapless and not described by topological order, which by construction only describes gapped quantum states)
- Others Examples: Quantum Hall Systems, Kitaev Toric Code

- If there is no local order parameter. How to sign the transition? New universal properties beyond local parameters and long range order
- Ground state degeneracy. It depends on the topology and therefore have information about global properties (the topology), even tough the local operators are short-ranged. There is a hidden long range correlation!
- non-Abelian Berry's phase of degenerated ground states and edge excitation
- Topolocial Entanglement Entropy
- Fidelity can sign the transition: D. F. Abasto, A. Hamma, and P. Zanardi, Phys. Rev. A 78, 010301(R) (2008).
- Local fidelity? E. Eriksson and H. Johannesson, Phys. Rev. A 79, 060301(R) (2009).
- How about the Discord (and the mutual informationa)?: Yi-Xin Chen and Sheng-Wen Li, Phys. Rev. A 81, 032120 (2010)

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