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