Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper Bounds in Quantum Dynamics   We develop a general method to bound the spreading of an entire wavepacket
under Schr\"odinger dynamics from above. This method derives upper bounds on
time-averaged moments of the position operator from lower bounds on norms of
transfer matrices at complex energies.
  This general result is applied to the Fibonacci operator. We find that at
sufficiently large coupling, all transport exponents take values strictly
between zero and one. This is the first rigorous result on anomalous transport.
  For quasi-periodic potentials associated with trigonometric polynomials, we
prove that all lower transport exponents and, under a weak assumption on the
frequency, all upper transport exponents vanish for all phases if the Lyapunov
exponent is uniformly bounded away from zero. By a well-known result of Herman,
this assumption always holds at sufficiently large coupling. For the particular
case of the almost Mathieu operator, our result applies for coupling greater
than two.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th