Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons

Unitarity as preservation of entropy and entanglement in quantum systems

The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite quantum systems.Comment: To be submitted to the special issue of Foundations of Physics on the occassion of the seventieth birthday of Emilio Santos. v2: 10 pages, no figures, RevTeX4; Corrected and extended version, containing new results on consequences of entanglement preservatio

A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

Does a Computer have an Arrow of Time?

In [Sch05a], it is argued that Boltzmann's intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. [Haw94] presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explana- tions for the alignment of the two arrows will be briefly discussed.Comment: 31 pages, no figures, publication versio

Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions

Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and classical time-evolving distribution functions are exposed by both analytical and numerical means. The quantum-classical correspondence of low-order statistical moments is also studied. The results shed considerable light on quantum-classical correspondence.Comment: 16 pages, 5 figures, to appear in Physical Review

An Inhomogeneous Model Universe Behaving Homogeneously

We present a new model universe based on the junction of FRW to flat Lemaitre-Tolman-Bondi (LTB) solutions of Einstein equations along our past light cone, bringing structures within the FRW models. The model is assumed globally to be homogeneous, i.e. the cosmological principle is valid. Local inhomogeneities within the past light cone are modeled as a flat LTB, whereas those outside the light cone are assumed to be smoothed out and represented by a FRW model. The model is singularity free, always FRW far from the observer along the past light cone, gives way to a different luminosity distance relation as for the CDM/FRW models, a negative deceleration parameter near the observer, and correct linear and non-linear density contrast. As a whole, the model behaves like a FRW model on the past light cone with a special behavior of the scale factor, Hubble and deceleration parameter, mimicking dark energy.Comment: 23 pages, 19 figures, published version in GR

CHIRAL BACKGROUND FOR THE TWO PION EXCHANGE NUCLEAR POTENTIAL: A PARAMETRIZED VERSION

We argue that the minimal chiral background for the two-pion exchange nucleon-nucleon interaction has nowadays a rather firm conceptual basis, which entitles it to become a standard ingredient of any modern potential. In order to facilitate applications, we present a parametrized version of a configuration space potential derived previously. We then use it to assess the phenomenological contents of some existing NN potentials.Comment: REVTEX style, 16 pages, 5 PostScript figures compressed, tarred and uuencode

The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur

Energy and decay width of the pi-K atom

The energy and decay width of the pi-K atom are evaluated in the framework of the quasipotential-constraint theory approach. The main electromagnetic and isospin symmetry breaking corrections to the lowest-order formulas for the energy shift from the Coulomb binding energy and for the decay width are calculated. They are estimated to be of the order of a few per cent. We display formulas to extract the strong interaction S-wave pi-K scattering lengths from future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra