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Physica Scripta

Unstable States in Quantum Many-Body Theory

J. Bang, G.M. Vagradov

Published Apr 1, 1985• 2 citations
Publisher

Abstract

Unstable states of a general type of many-body system characterized by a combination of outgoing waves and bound states in all channels are investigated. It is seen, that the time-development in general will contain both oscillating and exponentially decaying terms.
DOI
10.1088/0031-8949/31/4/001

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After reviewing the description of an unstable state in the framework of Lee Hamiltonians (valid both for Quantum Mechanics (QM) and Quantum Field Theory (QFT)), we consider some theoretical aspects of non-exponential decays: the case of two decay channels, the broadening of the energy spectrum at short times, the effect of an imperfect measurement, the link to QFT, and the decay of an unstable moving particle with definite momentum. All the presented effects were not confirmed in experiments, hence are at the present stage predictions.
Abstract A quantum model of the scattering of a particle via absorption and re-emission at the origin is described. The model is capable of exhibiting an arbitrary number of resonances, and the associated unstable states are discussed. The emphasis is on obtaining exact results. It is found that the exponential decay law is of limited application, and that in all cases of non-zero coupling the decay goes ultimately as t−3. Finally, it is pointed out that the treatment of unstable states in this type of model depends only on a knowledge of the phase shift as a function of radial momentum, and a possible phenomenological method is suggested.
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In this paper, the non-exponential decay is analyzed with the help of simple computer experiments performed by T. Petrosky, simulating classical radiation damping. The non-exponential decay is studied and shown to depend on the preparation of the system. However, whatever the initial preparation, the system reaches the decay predicted by classical radiation theory after a short time we call the Zeno's time. The similitude of Petrosky's results with computer experiments for the approach to equilibrium in many-body systems is emphasized. However, while there one deals with times which are multiple of the relaxation time, the irreversibility manifest in radiation theory occurs always over a much shorter time scale, the Zeno's time. In atomic systems, this would be a time order of 10/sup /minus/18/ seconds. These results are of great interest for the understanding of the microscopic mechanism of radiation. Let us consider a charged oscillator. In a first stage, this oscillator has to produce the field oscillators to which it may transfer energy through the usual resonance mechanism. Radiation appears therefore as a kind of non linear autocatalytic process, involving a self-organization mechanism. The behavior during the Zeno period can be explained easily in terms of subdynamics as introduced by the Brussel's group. We see that there is no transition from reversibility to irreversibility. Irreversible processes start at the very moment at which the system is prepared. It is important to stress that an unstable particle is itself the result of irreversible processes. As a result, an unstable particle (or an excited atomic state) can no more be described in terms of wave functions, as irreversible processes are not included in Schroedinger's equation. 14 refs. 3 figs.