R. Correa da Silva | Searcharxiv

arXiv2019

Pure and mixed states

We present a review on the notion of pure states and mixtures as mathematical concepts that apply for both classical and quantum physical theories, as well as for any other theory depending on statistical description. Here, states will be presented as expectation values on suitable algebras of observables, in a manner intended for the non-specialist reader; accordingly, basic literature on the subject will be provided. Examples will be exposed together with a discussion on their meanings and implications. An example will be shown where a pure quantum state converges to a classical mixture of particles as Planck's constant tends to zero.

math-ph↗

arXiv2018

Noncommutative Lp-Spaces and Perturbations of KMS States

We extend the theory of perturbations of KMS states to some class of unbounded perturbations using noncommutative Lp-spaces. We also prove certain stability of the domain of the Modular Operator associated to a ||.||p-continuous state. This allows us to define an analytic multiple-time KMS condition and to obtain its analyticity together with some bounds to its norm. Apart from that, this work contains a detailed review, with minor contributions due to the author, starting with the description of C*-algebras and von Neumann algebras followed by weights and representations, a whole chapter is devoted to the study of KMS states and its physical interpretation as the states of thermal equilibrium, then the Tomita-Takesaki Modular Theory is presented, furthermore, we study analytical properties of the modular operator automorphism group, positive cones and bounded perturbations of states, and finally we start presenting multiple versions of noncommutative Lp-spaces.

math-ph↗