Differential geometry of density states

Geometry of quantum systems: density states and entanglement

Various problems concerning the geometry of the space u∗(H) of Hermitian operators on a Hilbert space H are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into Kähler submanifolds. It is also shown that the space D(H) of density states on an n-dimensional Hilbert space H is naturally a manifold stratified space with the strat...

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

Density Operators as an Arena for Differential Geometry+

What I am going to describe may be called an interplay between concepts of differential geometry and the superposition principle of quantum physics. In particular, it concerns a metrical distance introduced by Bures [14] as a non-commutative version of a construction of Kakutani [24] on the one hand, and on the other hand the purifications of mixed states in physically larger systems, including...

Geometry II - Discrete Differential Geometry

Differential Geometry

We discuss intrinsic aspects of Krupka's approach to nite{order variational sequences. We recover in an intrinsic way the second{order varia-tional calculus for aane Lagrangians by means of a natural generalisation of rst{ordertheories. Moreover, we nd an intrinsic expressionfor the Helmholtz morphism using a technique introduced by Koll a r that we have adapted to our context. Introduction The...