AG Mathematische Physik, Christiaan van de Ven: Large deviations in mean-field quantum spin systems

Christiaan van de Ven

Large deviations in mean-field quantum spin systems

Abstract:

Continuous
fields of C*-algebras form an important ingredient for describing
emergent phenomena, such as phase transitions and spontaneous symmetry
breaking. In this talk, I consider the continuous C*-bundle generated by
increasing symmetric tensor powers of the complex (\ell\times\ell)
matrices, which can be interpreted as abstract description of mean-field
theories defining the macroscopic limit of infinite quantum systems.
Within this framework I discuss the principle of large deviations for
the local Gibbs state in the high temperature regime and characterize
the limit of the ensuing logarithmic generating function. To this end,
it has proved necessary to demonstrate the existence of a semiclassical
analog of the Baker-Campbel-Hausdorff formula, defined in terms of a
series of nested Poisson brackets.