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arXiv · 2008.02578

W*-Dynamics of Infinite Dissipative Quantum Systems

Geoffrey L. Sewell
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Abstract

We formulate the dynamics of an infinitely extended open dissipative quantum system, ${\Sigma]$,in the Schroedinger picture.The generic model on which this is based comprises a C*-algebra,$[\cal A}$,of observables, a folium, ${\cal F}$, of states on this algebra and a one parameter semigroup,${\tau}$, of linear transformations of ${\cal F}$ that represents its dynamics and is given by a natural infinite volume limit of the corresponding semigroup for a finite system. On this basis, we establish that the dynamic of ${\Sigma}$ is given by a one parameter semigroup of completely positive transformations of the W*-star algebra dual to ${\cal F}$. This result serves to extend our earlier formulation [1[ of infinitely extended conservative systems to open dissipative ones.

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Geoffrey L. Sewell. 2020-08-06. W*-Dynamics of Infinite Dissipative Quantum Systems. https://arxiv.org/abs/2008.02578

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