. Pontificia Universidad Católica de Chile
The Generalised Quantum Harmonic Oscillator and its Decoherence-Free Sub-Algebra
We consider the definition of the generalised Quantum Harmonic Oscillator (QHO) introduced by Bath and Parthasarathy in . It is well-known (see ) that all QMS suffers decoherence in its evolution. Loosely speaking, one says that "the quantum evolution becomes classical", this means that after some time, the dynamics concentrates on a commutative sub-algebra of observables. In  we characterized decoherence-free subalgebras where the evolution preserves its quantum structure. In general, these sub-algebras are trivial, nevertheless some physical systems do contain non trivial decoherence sub-algebras. More precisely, the decoherence-free subalgebra is the biggest (non commutative) where the semigroup act as a group of endomorphisms. The conference will show that the generalised QHO has a non trivial decoherence-free subalgebra.
 Ph. Blanchard and R. Olkiewicz, Decoherence induced transition from quantum to classical dynamics. Rev. Math. Phys. 15 (2003), no. 3, 217-243.
 B.V.R. Bhat and K.R. Parthasarathy, Generalized harmonic oscillators in quantum probability, Sem. Probab. XXV (1991) 39-51.
 A. Dhahri, F. Fagnola and R. Rebolledo, The Decoherence-free Subalgebra of a Quantum Markov Semigroup with Unbounded Generator. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 3, 413-433.
 F. Fagnola and R. Rebolledo, Entropy Production for Quantum Markov Semigroups, Commun. Math. Phys. 335 (2015), 547-570.