Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jump time and passage time: the duration of a quantum transition   Under unitary evolution, systems move gradually from state to state. An
unstable atom has amplitude in its original state after many lifetimes
($\tau_L$). But in the laboratory, transitions seem to go instantaneously, as
suggested by the term "quantum jump."
  The problem studied here is whether the "jump" can be assigned a duration, in
theory and in experiment. Two characteristic times are defined, jump time
($\tau_J$) and passage time ($\tau_P$). Both use Zeno time, $\tau_Z$, defined
in terms of $H$ and its initial state as $\tau_Z \equiv \hbar/\sqrt{<\psi|
(H-E_\psi)^2 |\psi>}$, with $E_\psi \equiv <\psi|H|\psi>$.
  $\tau_J$ is defined in terms of the time needed to slow (\`a la the quantum
Zeno effect) the decay: $\tau_J \equiv \tau_Z^2/\tau_L$. It appears in several
contexts. It is related to tunneling time in barrier penetration. Its inverse
is the bandwidth of the Hamiltonian, in a time-energy uncertainty principle.
$\tau_J$ is also an indicator of the duration of the quadratic decay regime in
both experiment and in numerical calculations (cf. Fig.~2 of PRA 57,1509
(1998).)
  The passage time, $\tau_P$, arises from unitary evolution sans
interpretation. It is based on a bound of Fleming (Nuov. Cim. 16 A, 232
(1973)): for any $H$ and $\psi$ a system cannot evolve to a state orthogonal to
$\psi$ for $t< \tau_P \equiv \pi \tau_Z/2$. By including apparatus in $H$,
$\tau_P$ limits the observation of decay according to the quantum measurement
ideas proposed in "Time's Arrows and Quantum Measurement," Cambridge U. Press,
1997, thereby allowing an experimental test of these ideas.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cs