7,352 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
Solving the measurement problem: de Broglie-Bohm loses out to Everett
The quantum theory of de Broglie and Bohm solves the measurement problem, but
the hypothetical corpuscles play no role in the argument. The solution finds a
more natural home in the Everett interpretation.Comment: 20 pages; submitted to special issue of Foundations of Physics, in
honour of James T. Cushin
Misleading signposts along the de Broglie-Bohm road to quantum mechanics
Eighty years after de Broglie's, and a little more than half a century after
Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics),
which is presumably the simplest theory which explains the orthodox quantum
mechanics formalism, has reached an exemplary state of conceptual clarity and
mathematical integrity. No other theory of quantum mechanics comes even close.
Yet anyone curious enough to walk this road to quantum mechanics is soon being
confused by many misleading signposts that have been put up, and not just by
its detractors, but unfortunately enough also by some of its proponents.
This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted
for publication in Foundations of Physics. A "slip of pen" in the
bibliography has been corrected -- thanks go to Oliver Passon for catching
it
Classical mechanics without determinism
Classical statistical particle mechanics in the configuration space can be
represented by a nonlinear Schrodinger equation. Even without assuming the
existence of deterministic particle trajectories, the resulting quantum-like
statistical interpretation is sufficient to predict all measurable results of
classical mechanics. In the classical case, the wave function that satisfies a
linear equation is positive, which is the main source of the fundamental
difference between classical and quantum mechanics.Comment: 11 pages, revised, to appear in Found. Phys. Let
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
Beable trajectories for revealing quantum control mechanisms
The dynamics induced while controlling quantum systems by optimally shaped
laser pulses have often been difficult to understand in detail. A method is
presented for quantifying the importance of specific sequences of quantum
transitions involved in the control process. The method is based on a
``beable'' formulation of quantum mechanics due to John Bell that rigorously
maps the quantum evolution onto an ensemble of stochastic trajectories over a
classical state space. Detailed mechanism identification is illustrated with a
model 7-level system. A general procedure is presented to extract mechanism
information directly from closed-loop control experiments. Application to
simulated experimental data for the model system proves robust with up to 25%
noise.Comment: Latex, 20 pages, 13 figure
Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality
The Fourier transform is often used to connect the Lorentzian energy
distribution for resonance scattering to the exponential time dependence for
decaying states. However, to apply the Fourier transform, one has to bend the
rules of standard quantum mechanics; the Lorentzian energy distribution must be
extended to the full real axis instead of being bounded from
below (``Fermi's approximation''). Then the Fourier transform
of the extended Lorentzian becomes the exponential, but only for times , a time asymmetry which is in conflict with the unitary group time evolution
of standard quantum mechanics. Extending the Fourier transform from
distributions to generalized vectors, we are led to Gamow kets, which possess a
Lorentzian energy distribution with and have exponential
time evolution for only. This leads to probability predictions
that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.
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
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