| Autor: |
Brasil, Jader E., Lopes, Artur O., Mengue, Jairo K., Moreira, Carlos G. |
| Předmět: |
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| Zdroj: |
Communications in Contemporary Mathematics; Feb2021, Vol. 23 Issue 1, pN.PAG-N.PAG, 32p |
| Abstrakt: |
We consider the KMS state associated to the Hamiltonian H = σ x ⊗ σ x over the quantum spin lattice ℂ 2 ⊗ ℂ 2 ⊗ ℂ 2 ⊗ ⋯. For a fixed observable of the form L ⊗ L ⊗ L ⊗ ⋯ , where L : ℂ 2 → ℂ 2 is self-adjoint, and for positive temperature T one can get a naturally defined stationary probability μ T on the Bernoulli space { 1 , 2 } ℕ . The Jacobian of μ T can be expressed via a certain continued fraction expansion. We will show that this probability is a Gibbs probability for a Hölder potential. Therefore, this probability is mixing for the shift map. For such probability μ 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 μ 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). [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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