Physical Sciences and Mathematics Commons^™

On The Generators Of Quantum Dynamical Semigroups, Alexander Wiedemann

Theses and Dissertations

In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. We define the class of pair block diagonal generators, which allows for additional interaction coefficients but preserves the main structural properties. Namely, when the basis of the underlying Hilbert space is given by the eigenbasis of the Hamiltonian (for example the generic semigroups), then the action of the semigroup leaves invariant the diagonal and off-diagonal matrix spaces. In this case, we explicitly compute all invariant states of the semigroup.

In order to define this class we …

Classical And Quantum Kac’S Chaos, Rade Musulin

Theses and Dissertations

In 1956 Kac studied the Boltzmann equation, an integro-differential equation which describes the density function of the distribution of the velocities of the molecules of dilute monoatomic gases under the assumption that the energy is only transferred via collisions between the molecules. In an attempt at a solution to the Boltzmann equation, Kac introduced a property of the density function that he called the “Boltzmann property" which describes the behavior of the density function at a given fixed time as the number of particles tends to infinity. The Boltzmann property has been studied extensively since then, and has been abstracted …