We have studied the distribution of resonance widths P(Gamma) in one-, two-, and three-dimensional multiple light scattering systems. P(Gamma) should follow a universal power law P(Gamma) approximately Gamma(-1) in the localized regime as confirmed by extensive numerical calculations. This behavior can be interpreted as an unambiguous signature of exponential Anderson localization of light in open systems.

Exact solutions to many-body interacting systems of both bosonic and fermionic particles confined to harmonic potential in an arbitrary number of dimensions are given. Energy levels and their degeneracies for trapped identical particles interacting via harmonic forces are calculated. This specific form of the interaction allows for analytical solutions. The mutual interaction, attractive or repulsive, modifies significantly the properties of the considered system. For a large number of particles the interaction essentially results in a frequency shift. Statistical properties ͑e.g., microcanonical and grand canonical partition functions͒ as well as some illustrative, physically relevant examples are discussed. Our results give an unusual opportunity for further studies of interacting systems in the framework of the exactly soluble model.

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The concept of the classical-like Wehrl entropy is shown to be a very sensitive and informative measure describing the time evolution of a quantum system. Its applications to the 3aynes-Cummings model reveal relevant aspects of the field dynamics. The Wehrl entropy provides a compact one-parameter description giving, among other things, a clear signature for the splitting of the q function. It gives also a clear indication of the phase randomization of the coherent electromagnetic field states during the interaction with a two-level atom. PACS number(s): 42.50.Md, 42.50.Dv, 42.50.Ct I. INTRODUCTION~n ) = D(n)~0) = exp(nuta*a)~0 ) .(2) Solvable models in quantum theory are so rare that they are worth studying in their own right. Even simplified they provide a clear understanding of the physical phenomena involved and can be useful in controlling various approximations indispensable for the treatment

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Quantum-mechanical entropies of position and momentum operators in a given state are shown to be reasonable and sensitive measures for squeezing of quantum fluctuations. It is shown to be true not only for states having Gaussian wave functions but also for more general, both pure and mixed, quantum states. A simple proof that the squeezing exhibited by the variance is always accompanied by a corresponding entropy reduction below the entropy vacuum level is given. These results show that the information entropy is not only a theoretically satisfactory concept but can also be useful as a tool for more practical quantum-optics applications. ͓S1050-2947͑97͒02609-7͔ PACS number͑s͒: 03.65. Bz, 42.50.Dv, 42.50.Lc, 03.65.Ca In quantum mechanics two noncommuting observables cannot be simultaneously measured with arbitrary precision. This fact, often called the Heisenberg uncertainty principle, is a fundamental restriction that is related neither to imperfections of the existing real-life measuring devices nor to the experimental errors of observation ͓1͔. It is rather the intrinsic property of the quantum state itself. Paradoxically enough, the uncertainty principle provides the only way to avoid many interpretational problems. It can also be used to make qualitative predictions in atomic physics, e.g., the size of the ground-state energy of an atom and the spread of the ground-state wave function ͓2͔. The uncertainty principle specified for given pairs of observables finds its mathematical manifestation as the uncertainty relations. The first rigorous derivation of the uncertainty relation from the quantum-mechanical formalism applied for the basic noncommuting observables, i.e., for the position and momentum (͓x ,p ͔ϭi;បϭ1), is due to Kennard ͓3͔ ͑see also the work of Robertson ͓4͔͒. This derivation, repeated in most textbooks on quantum mechanics ever since, leads to the celebrated inequalityIn fact, it can be considered as a simple consequence of the properties of the Fourier transform that connects the wave functions of the system in the position and momentum representation.In the above expression the fundamental quantum uncertainty inherently tied to the pair of noncommuting observables is measured by the variance of the corresponding Hermitian operators. For example, for x ϭx † ,where ͗ ͘ denotes the averaging with respect to a given state.It should be noted, however, that the variance is not the only measure of quantum uncertainty that can be used to express the uncertainty principle. Being just the second central moment of the probability distribution, it gives only a rough characterization of the probability distribution that is not of the Gaussian shape. It is, of course, possible to introduce higher moments ͓5͔, but all of them considered separately still contain only a restricted amount of information about the spreading of the values around the mean value. It is now commonly recognized that in many cases the variances ͑or standard deviations͒ are not appropriate measures of the quantum uncertainty. There ...

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