CONSTRUCTION AND ANALYSIS OF QUANTUM STOCHASTIC DYNAMICS USING NONCOMMUTATIVE 𝑳𝑷 − SPACES
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Date
2011-08-26
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Ahmadu Bello University Zaria
Abstract
A noncommutative algebra involving operators of the form 𝜌Λ
𝛼 (𝑡) ∙ 𝜌Λ
𝛼 (𝑡) is defined.
Using the noncommutative 𝐿𝑝 −spaces technique, we give a constructive approach to
quantum Markov evolution of infinite system, based on the notion of the
thermodynamic limit. The infinite Markov time evolution is constructed as the
thermodynamic limit of the corresponding finite volume (dynamics) evolution. The
extended Markov time evolution is then studied, with a view of addressing questions of
exponential stability and ergodicity . In quantum spin system the existence of non local
physical correlation at a phase transition is a manifestation of the entanglement among
the constituents parts. We studied asymptotic entanglement within the frame work of
open quantum systems for two independent quantum harmonic oscillators interacting
with an environment. The question of separability is addressed using the Peres-Simon equation