Time scales in quantum mechanics by a scattering map

Inside quantum mechanics the problem of decoherence for an isolated, finite system is linked to a coarse-grained description of its dynamics.Comment: 10 pages, latex, no figure

Physics of a microsystem starting from non-equilibrium quantum statistical mechanics

In this paper we address the problem to give a concrete support to the idea, originally stemming from Niels Bohr, that quantum mechanics must be rooted inside the physics of macroscopic systems. It is shown that, starting from the formalism of the non-equilibrium statistical operator, which is now a consolidated part of quantum statistical mechanics, particular correlations between two isolated systems can be singled out and interpreted as microsystems. In this way also a new framework is established in which questions of decoherence can be naturally addressed.Comment: 14 pages, latex, no figures, contribution to the Proceedings of the XXXIII Symposium on Mathematical Physics (Torun, Poland

Description of isolated macroscopic systems inside quantum mechanics

For an isolated macrosystem classical state parameters $\zeta(t)$ are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval $[T,t_0]$ a statistical operator is constructed as a solution of the Liouville von Neumann equation, exhibiting at time $t$ the state parameters $\zeta(t')$, $t_0\leq t' \leq t$, and {\it preparation parameters} related to times $T \leq t'\leq t_0$. Relation with Zubarev's non-equilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution by a semigroup is obtained for a restricted set of relevant observables, slowly varying on a suitable time scale.Comment: 13 pages, latex, romp31 style, no figures, to appear in the Proceedings of the XXXI Symposium on Mathematical Physics (Torun, Poland), to be published in Rep. Math. Phy

Maybe Definitely – Definitely Maybe? EC Competition Law – Is the Time Ripe for Reform?

[Summary]. The aim of this article is to discuss whether the timing for the Commission’s Proposal for reforming the implementation of Articles 81 and 82 of the EC Treaty is appropriate based on legal certainty considerations. The Proposal suggests to decentralise the day-to-day application of the EC antitrust rules further than is the case today and to abolish the present notification system whereby undertakings can apply for exemptions pursuant to Article 81(3) and negative clearances. The article provides examples showing that presently, the answers to certain legal questions of EC competition rules are vague or contradictory, and that if the proposed reform were to be implemented in its present form, the undertakings would have to carry the full risk for compliance with the competition rules but without a simple or straightforward way of obtaining guidance or legally binding exemptions or negative clearances. While recognising the need for a reform of the implementation system of the EC competition rules, the article argues that consistency and coherence in the understanding and application of the competition rules are a prerequisite to ensure legal certainty which, in turn, is a prerequisite for the implementation of the Commission’s plans to decentralise EC competition law application. It is therefore suggested that the time is not yet ripe for the type of reform proposed by the Commission and that efforts should instead focus on creating the basis for such a reform by adopting clear guidelines and/or binding legislation that secure the legal certainty of the undertakings that have to operate under the EC competition law framework

Subdynamics through Time Scales and Scattering Maps in Quantum Field Theory

It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics, e.g., hydrodynamics, kinetic theory, master equation for a particle interacting with matter, we look for the structure of this more general dynamics.Comment: 16 pages, latex, no figures, to appear in the Proceedings of the Third International Conference on Quantum Communication & Measurement 1996 (Hakone, Japan

Translation-covariant Markovian master equation for a test particle in a quantum fluid

A recently proposed master equation in the Lindblad form is studied with respect to covariance properties and existence of a stationary solution. The master equation describes the interaction of a test particle with a quantum fluid, the so-called Rayleigh gas, and is characterized by the appearance of a two-point correlation function known as dynamic structure factor, which reflects symmetry and statistical mechanics properties of the fluid. In the case of a free gas all relevant physical parameters, such as fugacity, ratio between the masses, momentum transfer and energy transfer are put into evidence, giving an exact expansion of the dynamic structure factor. The limit in which these quantities are small is then considered. In particular in the Brownian limit a Fokker-Planck equation is obtained in which the corrections due to quantum statistics can be explicitly evaluated and are given in terms of the Bose function $g_0 (z)$ and the Fermi function $f_0 (z)$.Comment: 18 pages, revtex, no figures, to appear in J. Math. Phy

Subdynamics of relevant observables: a field theoretical approach

An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation of the subdynamics of a microsystem interacting through collisions with a macrosystem is given, leading to a master-equation expressed in terms of the operator-valued dynamic structure factor, a two-point correlation function which compactly takes the statistical mechanics properties of the macrosystem into account. For the case of a free quantum gas the dynamic structure factor can be exactly calculated and in the long wavelength limit a Fokker-Planck equation for the description of quantum dissipation and in particular quantum Brownian motion is obtained, where peculiar corrections due to quantum statistics can be put into evidence.Comment: 28 pages, latex, no figure

Time scale, objectivity and irreversibility in quantum mechanics

It is argued that setting isolated systems as primary scope of field theory and looking at particles as derived entities, the problem of an objective anchorage of quantum mechanics can be solved and irreversibility acquires a fundamental role. These general ideas are checked in the case of the Boltzmann description of a dilute gas.Comment: 13 pages, latex, no figures, to appear in the Proceedings of the XXI International Colloquium on Group Theoretical Methods in Physics, 1996 (Goslar, Germany

Subdynamics as a mechanism for objective description

The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics that is briefly presented.Comment: latex, 15 pages. Paper submitted to Proc. Conference "Mysteries, Puzzles And Paradoxes In Quantum Mechanics, Workshop on Entanglement And Decoherence, Palazzo Feltrinelli, Gargnano, Garda Lake, Italy, 20-25 September, 199

The Origin of Hot Subluminous Horizontal-Branch Stars in Omega Centauri and NGC 2808

Hot subluminous stars lying up to 0.7 mag below the extreme horizontal branch (EHB) are found in the UV color-magnitude diagrams of omega Cen and NGC 2808. Such stars are unexplained by canonical HB theory. In order to explore the origin of these subluminous stars, we evolved a set of low-mass stars from the main sequence through the helium-core flash to the HB for a wide range in the mass loss along the red-giant branch (RGB). Stars with the largest mass loss evolve off the RGB to high effective temperatures before igniting helium in their cores. Our results indicate that the subluminous EHB stars, as well as the gap within the EHB of NGC 2808, can be explained if these stars undergo a late helium-core flash on the white-dwarf cooling curve. Under these conditions the flash convection will penetrate into the stellar envelope, thereby mixing most, if not all, of the envelope hydrogen into the hot helium- burning interior. This phenomenon is analogous to the "born-again" scenario for producing hydrogen-deficient stars during a very late helium-shell flash. "Flash mixing" greatly enhances the envelope helium and carbon abundances and, as a result, leads to an abrupt increase in the HB effective temperature. We argue that the EHB gap in NGC 2808 is caused by this theoretically predicted dichotomy in the HB morphology. Using new helium- and carbon-rich stellar atmospheres, we show that the flash-mixed stars have the same reduced UV flux as the subluminous EHB stars. Moreover, we demonstrate that models without flash mixing lie, at most, ~0.1 mag below the EHB and hence fail to explain the observations. Flash mixing may also provide a new evolutionary channel for producing the high gravity, He-rich sdO and sdB stars.Comment: 8 pages, 5 figures, to appear in "Omega Centauri: a Unique Window into Astrophysics" (Cambridge, August, 2001), ASP Conf. Ser., edited by F. van Leeuwen, G. Piotto, and J. Hughe