8,385 research outputs found
Resonances, Unstable Systems and Irreversibility: Matter Meets Mind
The fundamental time-reversal invariance of dynamical systems can be broken
in various ways. One way is based on the presence of resonances and their
interactions giving rise to unstable dynamical systems, leading to well-defined
time arrows. Associated with these time arrows are semigroups bearing time
orientations. Usually, when time symmetry is broken, two time-oriented
semigroups result, one directed toward the future and one directed toward the
past. If time-reversed states and evolutions are excluded due to resonances,
then the status of these states and their associated backwards-in-time oriented
semigroups is open to question. One possible role for these latter states and
semigroups is as an abstract representation of mental systems as opposed to
material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum
Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior
Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting,
7-22 July 2004, University of Denver. Accepted for publication in the
Internation Journal of Theoretical Physic
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
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
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained
and characterized. It is shown that the natural mathematical setting for the
analytic continuation of the solutions of the Lippmann-Schwinger equation is
the rigged Hilbert space rather than just the Hilbert space. It is also argued
that this analytic continuation entails the imposition of a time asymmetric
boundary condition upon the group time evolution, resulting into a semigroup
time evolution. Physically, the semigroup time evolution is simply a (retarded
or advanced) propagator.Comment: 32 pages, 3 figure
Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems
The notion that elementary systems correspond to irreducible representations
of the Poincare group is the starting point for this paper, which then goes on
to discuss how a semigroup for the time evolution of unstable states and
resonances could emerge from the underlying Poincare symmetry. Important tools
in this analysis are the Clebsch-Gordan coefficients for the Poincare group.Comment: 17 pages, 1 figur
A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes
We design a novel provably stable discontinuous Galerkin spectral element
(DGSEM) approximation to solve systems of conservation laws on moving domains.
To incorporate the motion of the domain, we use an arbitrary
Lagrangian-Eulerian formulation to map the governing equations to a fixed
reference domain. The approximation is made stable by a discretization of a
skew-symmetric formulation of the problem. We prove that the discrete
approximation is stable, conservative and, for constant coefficient problems,
maintains the free-stream preservation property. We also provide details on how
to add the new skew-symmetric ALE approximation to an existing discontinuous
Galerkin spectral element code. Lastly, we provide numerical support of the
theoretical results
Empirical evidence on the geographic and industrial distribution of aerospace expenditures
Gemini project subcontract expenditure effects on specific industries and region
Quantum Einstein's Equations and Constraints Algebra
In this paper we shall address this problem: Is quantum gravity constraints
algebra closed and what are the quantum Einstein equations. We shall
investigate this problem in the de-Broglie--Bohm quantum theory framework. It
is shown that the constraint algebra is weakly closed and the quantum
Einstein's equations are derived.Comment: 13 pages, No figure, RevTeX. To appear in Pramana J. Phys., 200
Reply to Comments of Bassi, Ghirardi, and Tumulka on the Free Will Theorem
We show that the authors in the title have erred in claiming that our axiom
FIN is false by conflating it with Bell locality. We also argue that the
predictions of quantum mechanics, and in particular EPR, are fully Lorentz
invariant, whereas the Free Will Theorem shows that theories with a mechanism
of reduction, such as GRW, cannot be made fully invariant.Comment: We sharpen our theorem by replacing axiom FIN by a weaker axiom MIN
to answer the above authors' objection
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