220 research outputs found
Zero energy resonance and the logarithmically slow decay of unstable multilevel systems
The long time behavior of the reduced time evolution operator for unstable
multilevel systems is studied based on the N-level Friedrichs model in the
presence of a zero energy resonance.The latter means the divergence of the
resolvent at zero energy. Resorting to the technique developed by Jensen and
Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is
characterized by the zero energy eigenstate that does not belong to the Hilbert
space. It is then shown that for some kinds of the rational form factors the
logarithmically slow decay of the reduced time evolution operator can be
realized.Comment: 31 pages, no figure
Macroscopic Zeno effect and stationary flows in nonlinear waveguides with localized dissipation
We theoretically demonstrate the possibility to observe the macroscopic Zeno
effect for nonlinear waveguides with a localized dissipation. We show the
existence of stable stationary flows, which are balanced by the losses in the
dissipative domain. The macroscopic Zeno effect manifests itself in the
non-monotonic dependence of the stationary flow on the strength of the
dissipation. In particular, we highlight the importance of the parameters of
the dissipation to observe the phenomenon. Our results are applicable to a
large variety of systems, including condensates of atoms or quasi-particles and
optical waveguides.Comment: 5 pages, 3 figures, accepted to Phys. Rev. Let
Quantum Zeno control of coherent dissociation
We study the effect of dephasing on the coherent dissociation dynamics of an
atom-molecule Bose-Einstein condensate. We show that when phase-noise intensity
is strong with respect to the inverse correlation time of the stimulated
process, dissociation is suppressed via a Bose enhanced Quantum Zeno effect.
This is complementary to the quantum zeno control of phase-diffusion in a
bimodal condensate by symmetric noise (Phys. Rev. Lett. {\bf 100}, 220403
(2008)) in that the controlled process here is phase-{\it formation} and the
required decoherence mechanism for its suppression is purely phase noise.Comment: 5 pages, 4 figure
Exact positivity of the Wigner and P-functions of a Markovian open system
We discuss the case of a Markovian master equation for an open system, as it
is frequently found from environmental decoherence. We prove two theorems for
the evolution of the quantum state. The first one states that for a generic
initial state the corresponding Wigner function becomes strictly positive after
a finite time has elapsed. The second one states that also the P-function
becomes exactly positive after a decoherence time of the same order. Therefore
the density matrix becomes exactly decomposable into a mixture of Gaussian
pointer states.Comment: 11 pages, references added, typo corrected, to appear in J. Phys.
Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
The long-time behavior of the survival probability for unstable multilevel
systems that follows the power-decay law is studied based on the N-level
Friedrichs model, and is shown to depend on the initial population in unstable
states. A special initial state maximizing the asymptote of the survival
probability at long times is found and examined by considering the spontaneous
emission process for the hydrogen atom interacting with the electromagnetic
field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.
Suppression of Zeno effect for distant detectors
We describe the influence of continuous measurement in a decaying system and
the role of the distance from the detector to the initial location of the
system. The detector is modeled first by a step absorbing potential. For a
close and strong detector, the decay rate of the system is reduced; weaker
detectors do not modify the exponential decay rate but suppress the long-time
deviations above a coupling threshold. Nevertheless, these perturbing effects
of measurement disappear by increasing the distance between the initial state
and the detector, as well as by improving the efficiency of the detector.Comment: 4 pages, 4 figure
Initial wave packets and the various power-law decreases of scattered wave packets at long times
The long time behavior of scattered wave packets from a
finite-range potential is investigated, by assuming to be
initially located outside the potential. It is then shown that can
asymptotically decrease in the various power laws at long time, according to
its initial characteristics at small momentum. As an application, we consider
the square-barrier potential system and demonstrate that exhibits
the asymptotic behavior , while another behavior like can
also appear for another .Comment: 5 pages, 1 figur
The role of initial state reconstruction in short and long time deviations from exponential decay
We consider the role of the reconstruction of the initial state in the
deviation from exponential decay at short and long times. The long time decay
can be attributed to a wave that was, in a classical-like, probabilistic sense,
fully outside the initial state or the inner region at intermediate times,
i.e., to a completely reconstructed state, whereas the decay during the
exponential regime is due instead to a non-reconstructed wave. At short times
quantum interference between regenerated and non-regenerated paths is
responsible for the deviation from the exponential decay. We may thus conclude
that state reconstruction is a ``consistent history'' for long time deviations
but not for short ones.Comment: 4 pages, 6 figure
Time-reversal symmetric resolution of unity without background integrals in open quantum systems
We present a new complete set of states for a class of open quantum systems,
to be used in expansion of the Green's function and the time-evolution
operator. A remarkable feature of the complete set is that it observes
time-reversal symmetry in the sense that it contains decaying states (resonant
states) and growing states (anti-resonant states) parallelly. We can thereby
pinpoint the occurrence of the breaking of time-reversal symmetry at the choice
of whether we solve Schroedinger equation as an initial-condition problem or a
terminal-condition problem. Another feature of the complete set is that in the
subspace of the central scattering area of the system, it consists of
contributions of all states with point spectra but does not contain any
background integrals. In computing the time evolution, we can clearly see
contribution of which point spectrum produces which time dependence. In the
whole infinite state space, the complete set does contain an integral but it is
over unperturbed eigenstates of the environmental area of the system and hence
can be calculated analytically. We demonstrate the usefulness of the complete
set by computing explicitly the survival probability and the escaping
probability as well as the dynamics of wave packets. The origin of each term of
matrix elements is clear in our formulation, particularly the exponential
decays due to the resonance poles.Comment: 62 pages, 13 figure
A quantum decay model with exact explicit analytical solution
A simple decay model is introduced. The model comprises of a point potential
well, which experiences an abrupt change. Due to the temporal variation the
initial quantum state can either escape from the well or stay localized as a
new bound state. The model allows for an exact analytical solution while having
the necessary features of a decay process. The results show that the decay is
never exponential, as classical dynamics predicts. Moreover, at short times the
decay has a \textit{fractional} power law, which differs from perturbation
quantum methods predictions.Comment: 4 pages, 3 figure
- …