Jader E. Brasil

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20182022

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math.DS2022

Thermodynamic formalism for general iterated function systems with measures

Jader E. Brasil, Elismar R. Oliveira, Rafael Rigão Souza

This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators…

math.DS2019

Lyapunov exponents for Quantum Channels: an entropy formula and generic properties

Jader E. Brasil, Josue Knorst, Artur O. Lopes

We denote by $M_{k}$ the set of $k$ by $k$ matrices with complex entries. We consider quantum channels $ϕ_{L}$ of the form: given a measurable function $L : M_{k} \to M_{k}$ and a measure $μ$ …

math.DS2019

Thermodynamic Formalism for Quantum Channels: Entropy, Pressure, Gibbs channels and generic properties

Jader E. Brasil, Josue Knorst, Artur O. Lopes

Denote $M_{k}$ the set of complex $k$ by $k$ matrices. We will analyze here quantum channels $ϕ_{L}$ of the following kind: given a measurable function $L : M_{k} \to M_{k}$ and the measure $…

math.DS2018

Quantum Spin probabilities at positive temperature are Hölder Gibbs probabilities

Jader E. Brasil, Artur O. Lopes, Jairo K. Mengue +1

We consider the KMS state associated to the Hamiltonian $H = σ^{x} \otimes σ^{x}$ over the quantum spin lattice $C^{2} \otimes C^{2} \otimes C^{2} \otimes ...$ . For…