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

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

Squeezing in driven bimodal Bose-Einstein Condensates: Erratic driving versus noise

We study the interplay of squeezing and phase randomization near the hyperbolic instability of a two-site Bose-Hubbard model in the Josephson interaction regime. We obtain results for the quantum Zeno suppression of squeezing, far beyond the previously found short time behavior. More importantly, we contrast the expected outcome with the case where randomization is induced by erratic driving with the same fluctuations as the quantum noise source, finding significant differences. These are related to the distribution of the squeezing factor, which has log-normal characteristics: hence its average is significantly different from its median due to the occurrence of rare events.Comment: 5 pages, 4 figure

Rigorous Dynamics and Radiation Theory for a Pauli-Fierz Model in the Ultraviolet Limit

The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behaviour of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behaviour is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibites in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator.Comment: Shortened version. To appear in J. Math. Phy

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

Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $\rho(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from $t = 0$ to $T$, where $E$ is a projector obeying $E\rho(0) E = \rho(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness conditions in $t$. Then the probability of always finding $E(t) = 1$ from $t = 0$ to $T$ is unity. Generically $E(T) \neq E$ and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.Comment: 16 pages, latex; new material and references adde

Exact results on the Kondo-lattice magnetic polaron

In this work we revise the theory of one electron in a ferromagnetically saturated local moment system interacting via a Kondo-like exchange interaction. The complete eigenstates for the finite lattice are derived. It is then shown, that parts of these states lose their norm in the limit of an infinite lattice. The correct (scattering) eigenstates are calculated in this limit. The time-dependent Schr\"odinger equation is solved for arbitrary initial conditions and the connection to the down-electron Green's function and the scattering states is worked out. A detailed analysis of the down-electron decay dynamics is given.Comment: 13 pages, 9 figures, accepted for publication in PR

No classical limit of quantum decay for broad states

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances

A perturbative approach for the dynamics of the quantum Zeno subspaces

In this paper we investigate the dynamics of the quantum Zeno subspaces which are the eigenspaces of the interaction Hamiltonian, belonging to different eigenvalues. Using the perturbation theory and the adiabatic approximation, we get a general expression of the jump probability between different Zeno subspaces. We applied this result in some examples. In these examples, as the coupling constant of the interactions increases, the measurement keeps the system remaining in its initial subspace and the quantum Zeno effect takes place.Comment: 14 pages, 3 figure