104 research outputs found
Path integral in a magnetic field using the Trotter product formula
The derivation of the Feynman path integral based on the Trotter product
formula is extended to the case where the system is in a magnetic field.Comment: To appear in the American Journal of Physics, 200
Slow relaxation, confinement, and solitons
Millisecond crystal relaxation has been used to explain anomalous decay in
doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons.
Our model exhibits confinement of mechanical energy released by excitation.
Extending the model to long times is justified by its relation to solitons,
excitations previously proposed to occur in alkali halides. Soliton damping and
observation are also discussed
HINDERED DECAY : QUANTUM ZENO EFFECT THROUGH ELECTROMAGNETIC FIELD DOMINATION
The lifetime of an unstable atom can be extended by watching it closely, i.e., illuminating it with an intense electromagnetic field of appropriate frequency. This is an example of ``dominated evolution'' and is closely related to the so-called ``quantum Zeno effect.'' For a metastable atom bathed in a laser beam at the frequency of another of its transitions, we obtain an expression for the modified lifetime as a function of beam intensity. This provides an example of the quantum Zeno effect on a truly decaying system, and also should be useful for probing short distance features of atomic wave functions
General equation for Zeno-like effects in spontaneous exponential decay
It was shown that different mechanisms of perturbation of spontaneous decay
constant: inelastic interaction of emitted particles with particle detector,
decay onto an unstable level, Rabi transition from the final state of decay
(electromagnetic field domination) and some others are really the special kinds
of one general effect - perturbation of decay constant by dissipation of the
final state of decay. Such phenomena are considered to be Zeno-like effects and
general formula for perturbed decay constant is deduced.Comment: LaTeX 2.09 file, 11 pages, no figures. Accepted in Physics Letters
Stability of quantum breathers
Using two methods we show that a quantized discrete breather in a 1-D lattice
is stable. One method uses path integrals and compares correlations for a
(linear) local mode with those of the quantum breather. The other takes a local
mode as the zeroth order system relative to which numerical, cutoff-insensitive
diagonalization of the Hamiltonian is performed.Comment: 4 pages, 3 figure
Quantum Zeno-like effect and spectra of particles in cascade transition
Shr\"odinger equation for two-step spontaneous cascade transition in a
three-level quantum system is solved by means of Markovian approximation for
non-Markovian integro-differential evolution equations for amplitudes of
states. It is shown that both decay constant and radiation shift of initial
level are affected by instability of intermediate level of the cascade. These
phenomena are interpreted as the different manifestations of quantum Zeno-like
effect. The spectra of particles emitted during the cascade transition are
calculated in the general case and, in particular, for an unusual situation
when the initial state is lower than the intermediate one. It is shown that the
spectra of particles do not have a peak-like shape in the latter case.Comment: 13 pages, no figures, to be published in Physica
Stability and instability in parametric resonance and quantum Zeno effect
A quantum mechanical version of a classical inverted pendulum is analyzed.
The stabilization of the classical motion is reflected in the bounded evolution
of the quantum mechanical operators in the Heisenberg picture. Interesting
links with the quantum Zeno effect are discussed.Comment: 6 pages, 3 figure
Quantum Zeno and anti-Zeno effects by indirect measurement with finite errors
We study the quantum Zeno effect and the anti-Zeno effect in the case of
`indirect' measurements, where a measuring apparatus does not act directly on
an unstable system, for a realistic model with finite errors in the
measurement. A general and simple formula for the decay rate of the unstable
system under measurement is derived. In the case of a Lorentzian form factor,
we calculate the full time evolutions of the decay rate, the response of the
measuring apparatus, and the probability of errors in the measurement. It is
shown that not only the response time but also the detection efficiency plays a
crucial role. We present the prescription for observing the quantum Zeno and
anti-Zeno effects, as well as the prescriptions for avoiding or calibrating
these effects in general experiments.Comment: 4 pages, 3 figure
Quantum Zeno effect in a probed downconversion process
The distorsion of a spontaneous downconvertion process caused by an auxiliary
mode coupled to the idler wave is analyzed. In general, a strong coupling with
the auxiliary mode tends to hinder the downconversion in the nonlinear medium.
On the other hand, provided that the evolution is disturbed by the presence of
a phase mismatch, the coupling may increase the speed of downconversion. These
effects are interpreted as being manifestations of quantum Zeno or anti-Zeno
effects, respectively, and they are understood by using the dressed modes
picture of the device. The possibility of using the coupling as a nontrivial
phase--matching technique is pointed out.Comment: 11 pages, 4 figure
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