Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Representations of Coherent and Squeezed States in a ff-deformed Fock Space

We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_{\lambda}$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the standard Fock space) and the fact that they can be regarded as $f$-deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.Comment: 13 pages, 4 Figure

The anomaly line bundle of the self-dual field theory

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication in CM

Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy

Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium. We find, for specific choices of initial parameters, that as much as 90% of the kinetic energy can be localized (at least conceptually) in the `front half' of such Gaussian wave packets, and we visualize these effects.Comment: 22 pages, RevTeX, four .eps figures, to appear in Found. Phys. Lett. Vol. 17, Dec. 200

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Spin Glass and Antiferromagnetic Behaviour in a Diluted fcc Antiferromagnet

We report on a Monte Carlo study of a diluted Ising antiferromagnet on a fcc lattice. This is a typical model example of a highly frustrated antiferromagnet, and we ask, whether sufficient random dilution of spins does produce a spin glass phase. Our data strongly indicate the existence of a spin glass transition for spin--concentration $p<0.75$: We find a divergent spin glass susceptibility and a divergent spin glass correlation length, whereas the antiferromagnetic correlation length saturates in this regime. Furthermore, we find a first order phase transition to an antiferromagnet for $1\ge p>0.85$, which becomes continuous in the range $0.85>p>0.75$. Finite size scaling is employed to obtain critical exponents. We compare our results with experimental systems as diluted frustrated antiferromagnets as ${\rm Zn_{1-p}Mn_{p}Te}$.Comment: 29 pages (revtex) and 10 figures uuencoded and Z-compresse

Parental breeding age effects on descendants' longevity interact over 2 generations in matrilines and patrilines

Individuals within populations vary enormously in mortality risk and longevity, but the causes of this variation remain poorly understood. A potentially important and phylogenetically widespread source of such variation is maternal age at breeding, which typically has negative effects on offspring longevity. Here, we show that paternal age can affect offspring longevity as strongly as maternal age does and that breeding age effects can interact over 2 generations in both matrilines and patrilines. We manipulated maternal and paternal ages at breeding over 2 generations in the neriid fly Telostylinus angusticollis. To determine whether breeding age effects can be modulated by the environment, we also manipulated larval diet and male competitive environment in the first generation. We found separate and interactive effects of parental and grand-parental ages at breeding on descendants' mortality rate and life span in both matrilines and patrilines. These breeding age effects were not modulated by grand-parental larval diet quality or competitive environment. Our findings suggest that variation in maternal and paternal ages at breeding could contribute substantially to intrapopulation variation in mortality and longevity