Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of quantum dynamics and a time-energy uncertainty relation for
  mixed states   In this paper we establish important relations between Hamiltonian dynamics
and Riemannian structures on phase spaces for unitarily evolving finite level
quantum systems in mixed states. We show that the energy dispersion (i.e.
$1/\hbar$ times the path integral of the energy uncertainty) of a unitary
evolution is bounded from below by the length of the evolution curve. Also, we
show that for each curve of mixed states there is a Hamiltonian for which the
curve is a solution to the corresponding von Neumann equation, and the energy
dispersion equals the curve's length. This allows us to express the distance
between two mixed states in terms of a measurable quantity, and derive a
time-energy uncertainty relation for mixed states. In a final section we
compare our results with an energy dispersion estimate by Uhlmann.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci