| Autor: |
Brasil, Jader E., Lopes, Artur O., Mengue, Jairo K., Moreira, Carlos G. |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We consider the KMS state associated to the Hamiltonian $H= \sigma^x \otimes \sigma^x$ over the quantum spin lattice $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes ...$. For a fixed observable of the form $L \otimes L \otimes L \otimes ...$, where $L:\mathbb{C}^2 \to \mathbb{C}^2 $ is self adjoint, and for positive temperature $T$ one can get a naturally defined stationary probability $\mu_T$ on the Bernoulli space $\{1,2\}^\mathbb{N}$. The Jacobian of $\mu_T$ can be expressed via a certain continued fraction expansion. We will show that this probability is a Gibbs probability for a H\"older potential. Therefore, this probability is mixing for the shift map. For such probability $\mu_T$ we will show the explicit deviation function for a certain class of functions. When decreasing temperature we will be able to exhibit the explicit transition value $T_c$ where the set of values of the Jacobian of the Gibbs probability $\mu_T$ changes from being a Cantor set to being an interval. We also present some properties for quantum spin probabilities at zero temperature (for instance, the explicit value of the entropy). |
| Databáze: |
arXiv |
| Externí odkaz: |
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