63 research outputs found
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
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
Description of isolated macroscopic systems inside quantum mechanics
For an isolated macrosystem classical state parameters are
introduced inside a quantum mechanical treatment. By a suitable mathematical
representation of the actual preparation procedure in the time interval
a statistical operator is constructed as a solution of the Liouville
von Neumann equation, exhibiting at time the state parameters ,
, and {\it preparation parameters} related to times . 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
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
The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions
We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation
Time Asymmetric Quantum Physics
Mathematical and phenomenological arguments in favor of asymmetric time
evolution of micro-physical states are presented.Comment: Tex file with 2 figure
A multi-instrument comparison of integrated water vapour measurements at a high latitude site
We compare measurements of integrated water vapour (IWV) over a subarctic site (Kiruna, Northern Sweden) from five different sensors and retrieval methods: Radiosondes, Global Positioning System (GPS), ground-based Fourier-transform infrared (FTIR) spectrometer, groundbased microwave radiometer, and satellite-based microwave radiometer (AMSU-B). Additionally, we compare also to ERA-Interim model reanalysis data. GPS-based IWV data have the highest temporal coverage and resolution and are chosen as reference data set. All datasets agree reasonably well, but the ground-based microwave instrument only if the data are cloud-filtered. We also address two issues that are general for such intercomparison studies, the impact of different lower altitude limits for the IWV integration, and the impact of representativeness error. We develop methods for correcting for the former, and estimating the random error contribution of the latter. A literature survey reveals that reported systematic differences between different techniques are study-dependent and show no overall consistent pattern. Further improving the absolute accuracy of IWV measurements and providing climate-quality time series therefore remain challenging problems
Rigged Hilbert Space Approach to the Schrodinger Equation
It is shown that the natural framework for the solutions of any Schrodinger
equation whose spectrum has a continuous part is the Rigged Hilbert Space
rather than just the Hilbert space. The difficulties of using only the Hilbert
space to handle unbounded Schrodinger Hamiltonians whose spectrum has a
continuous part are disclosed. Those difficulties are overcome by using an
appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an
eigenket to each energy in the spectrum of the Hamiltonian, regardless of
whether the energy belongs to the discrete or to the continuous part of the
spectrum. The collection of eigenkets corresponding to both discrete and
continuous spectra forms a basis system that can be used to expand any physical
wave function. Thus the RHS treats discrete energies (discrete spectrum) and
scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page
Irreversible Quantum Mechanics in the Neutral K-System
The neutral Kaon system is used to test the quantum theory of resonance
scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with
complex Hamiltonian is obtained by truncating the complex basis vector
expansion of the exact theory in Rigged Hilbert space. This can be done for K_1
and K_2 as well as for K_S and K_L, depending upon whether one chooses the
(self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP.
As an unexpected curiosity one can show that the exact theory (without
truncation) predicts long-time 2 pion decays of the neutral Kaon system even if
the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include
- …