Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bound of minimal time evolution in quantum mechanics   We show that the total time of evolution from the initial quantum state to
final quantum state and then back to the initial state, i.e., making a round
trip along the great circle over S^2, must have a lower bound in quantum
mechanics, if the difference between two eigenstates of the 2\times 2
Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not
reduce it to arbitrarily small value. In fact, we show that whether one uses a
hermitian Hamiltonian or a non-hermitian, the required minimal total time of
evolution is same. It is argued that in hermitian quantum mechanics the
condition for minimal time evolution can be understood as a constraint coming
from the orthogonality of the polarization vector \bf P of the evolving quantum
state \rho={1/2}(\bf 1+ \bf{P}\cdot\boldsymbol{\sigma}) with the vector
\boldsymbol{\mathcal O}(\Theta) of the 2\times 2 hermitian Hamiltonians H
={1/2}({\mathcal O}_0\boldsymbol{1}+ \boldsymbol{\mathcal
O}(\Theta)\cdot\boldsymbol{\sigma}) and it is shown that the Hamiltonian H can
be parameterized by two independent parameters {\mathcal O}_0 and \Theta.

3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: math
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph